Rename Stanford (Rylie)

Big news! It turns out I have a long-lost twin.

Her name is Rylie and we’ve recently reconnected. As fate has it, she grew up in Portland, Maine, and is currently attending Universidad Centroccidental Lisandro Alvarado (UCLA).

She writes in her spare time as well, though doesn’t have anywhere to publish. As a result, we decided she would be a guest blogger here. All her posts will be tagged “Rylie” and there should be some mention of her authorship in the title.

She’ll make the blog better because, as you will see, her interests differ from mine. Going forward, expect this blog to cover more topics from diverse perspectives.

Enjoy her first post.

A proposal to rename Stanford University.

In January 1862, Leland Stanford, then governor of California, stood in front of the state legislature and said the following:

To my mind it is clear, that the settlement among us of an inferior race is to be discouraged by every legitimate means. Asia, with her numberless millions, sends to our shores the dregs of her population. Large numbers of this class are already here; and, unless we do something early to check their immigration, the question, which of the two tides of immigration, meeting upon the shores of the Pacific, shall be turned back, will be forced upon our consideration, when far more difficult than now of disposal. There can be no doubt but that the presence among us of numbers of degraded and distinct people must exercise a deleterious influence upon the superior race, and to a certain extent, repel desirable immigration

Stanford was a bigot, and his words should be condemned in the strongest possible terms. There is no room for hateful speech in a society that prides itself on tolerance, diversity, and justice. Stanford’s remarks reveal deep flaws within his character and thought that would be inexcusable today, and as we’re coming to believe, were inexcusable then. Unfortunately, this revelation taints the entirety of Stanford’s legacy. Every scientific advancement he commissioned, every crusty institution he created, was built on a foundation of oppressive prejudice and should be discarded. It is up to us to cancel him posthumously and wipe his existence from the history books. That will show him.

The first step towards this absolute and morally irreproachable goal is to rename the institution that bears his name: Stanford University. It is ignorant and hypocritical to attach power and prestige to a name that once belonged to a bona-fide racist and outright capitalist. Complicity in calling Stanford University “Stanford” is complicity in the face of systems and structural factors that have marginalized communities of color. It’s impossible —utterly inconceivable— to use the same sound to refer to Leland Stanford and a university without espousing the entirety of the former’s political ideology. This is why Stanford University must be renamed.

Knowing Stanford was a racist who believed a marginalized group was inferior to whites makes people feel unsafe and attacked. It’s true Stanford is dead and all of the racists of his time died with him, but that’s not enough. As long as his name is uttered in any nonnegative context, it constitutes an assault on minorities and people of color. In the same way we must condone Aristotle’s view that women are inferior if we want to consider his unrelated views on logic, we must hold racist beliefs and attitudes if we are to seriously consider any single aspect of the Stanford legacy. This sound commitment is an infallible guard against racist thought. As we all know, ideas and institutions are only as good as the political ideology of their sources.

“But Rylie,” one might unreasonably ask, “Stanford isn’t even named for Leland the capitalist bigot. It was named for his son, Leland Stanford Jr. who died of typhoid at 15. Leland Sr. established the university as a grieving father wishing to honor his son.” Anyone can see this objection relies on two untenable concepts that have been used to justify marginalization and oppression for centuries. First, naming your son after yourself is the ultimate expression of narcissistic, patriarchal, insecure, toxic masculinity. In this act, Leland Sr. has symbolically transferred male power and privilege between generations, reinforcing existing oppressive structures and setting norms for his son’s behavior. For this reason, Leland Jr. has full culpability for his father’s crimes, and no university should be named after him, either. Absolving children of their father’s transgressions ignores the perverse effects of patriarchy, and allows historical crimes to go unpunished.

Second, there are no honorable deeds under capitalism. Leland Sr.’s decision to create a university in memory of his son was only possible under an exploitive system where people of color suffered for the enrichment of white males. His fortune was stained by the blood of the oppressed, meaning any act making use of it —besides full-blown redistribution— is incapable of withstanding moral scrutiny. Dissociating actions from the circumstances that enabled them is a crime in itself. We must consider Stanford’s wealth within the broader global-historical context of oppression, injustice, and exploitive capitalism. Praising one deed within the system is equivalent to approving every aspect of it.

Until the University is renamed, I call on all clear-thinking individuals to boycott interactions with it. Students should not apply to Stanford, enroll, log into their zoom classes. What’s more, we should refrain from interacting with Stanford affiliates until they have signed a pledge dedicating themselves to our cause. We are on the cusp of a social revolution, and this is an unambiguous step in the right direction.

The worse you feel about us, the better you should feel about the world

Epistemic status: attitudinal and naïve

Occasionally I meet someone with a really awful view of human nature. They look at the world, see all the ways we fail to cooperate, and conclude humanity has been doomed from the start. To them, there’s something like an inherent deficit of altruism or foresight that prevents us from solving our most pressing problems. Specifically, they tend to be disappointed with progress on climate change or nuclear weapons, and are pretty dour as a result.

I’m confused by the dour-ness. I’ll grant cooperation is difficult, but if you really hold humans in such low esteem, shouldn’t you be constantly amazed by everything around you?  How can the misanthrope react to the cooperative feat that is you purchasing a pencil with anything but astonishment? Thousands of people had to coordinate their actions to collect the timber, shape the pencil, insert the graphite, and ship it to your locale. This is impressive to almost everybody. To the misanthrope, it should look like a miracle.

And miracles like this happen every day. Food from every corner of the globe is readily available at my grocery store. I can get nearly any book shipped to my door within two days. Humanity’s knowledge is at my fingertips. All of this is due to the coordination of thousands of actors.

There are other, arguably more important miracles. In much (though not all) of the world, I can openly practice any religion and not feel threatened for it. In many of the same places, I can critique those in power without fear of retribution. Throughout much of human history, almost nobody had these privileges.

All of these miracles have some kind of cooperation at their core. Cooperative actors create goods and services and distribute them to those in need. The political freedoms we enjoy are based on tolerance, which is a special kind of cooperative attitude [1].

I stand with the misanthropes. I believe there are dark, myopic parts of humanity that will never go away. But, I believe the natural consequence of this view is amazement, not depression. Things — more or less — work, and such an uncharitable view of human nature by itself could not predict much of the current world. Our faults persist, but in some significant capacity, we’re still able to cooperate. That’s amazing.

[1] “I disagree with their views on X, but these people are still worth cooperating with.”

A Dialogue on Income Inequality

Andrew and Parker are driving on Mulholland. To the south, they peer into the LA basin and glimpse downtown. To the north, the entire San Fernando Valley lies beneath them before it yields to the base of the Santa Susana mountains. Multimillion dollar houses flank them on both sides of the street. Most are gaudy, but a few have good taste. All cost more than the average American will earn over several lifetimes. 

Andrew: Nobody needs that much house! Why should a human on earth have 10,000 square feet, a movie room, wine cellar, infinity pool, vineyard, and 8-car garage?

Parker: The views are nice, though. I wouldn’t mind paying a lot to make sure I see sweeping vistas every day.

Andrew: Yeah, I wouldn’t mind the view either. Still, if you can afford a house like that, it’s a sign you’re making too much money.

Parker: What do you mean?

Andrew: Why is it alright for these people to have so much when others have so little? They live in the lap of luxury while others don’t even have a home. You’ve seen Skid Row; nobody should have to survive in those conditions. People sleeping on the streets and not having enough to eat is unacceptable. Take away 90% of a millionaire’s income and they can still live comfortably. Economic inequality is at an all-time high, and there’s something deeply wrong with that.

Parker: Yeah, I definitely agree. Skid Row should not exist, but I’m confused — what does inequality have to do with this?

Andrew: What’s there to be confused about? Some live in poverty while others spend millions on ugly houses they barely live in. That’s unjust. If we close the gap between the best and worst-off in our society, healthcare, education, housing, as well as other essential goods, will all be more accessible. People will live better lives.

Parker: I still don’t see the connection to inequality. You are —rightfully— upset some can’t afford basic services or have an acceptable standard of living, but what do other people being wealthy have to do with it? The problem, as far as I can tell, is some people don’t have enough resources to live fulfilling lives. I don’t see a clear connection between their deficit and others’ surplus.

There’s a difference between one person having enough of a resource and two people having the same amount. The concepts don’t necessarily follow from each other. Imagine it’s dinnertime and we each only have a bottle of ketchup to eat. This will not do. Ketchup is not nutritious, and eating it alone is pretty gross. We are equal, in the sense both of us have the same resources at our disposal, but it does not follow either of us has enough food. Likewise, it’s possible for both of us to have enough food and be unequal. Suppose we both got groceries and you are having a lobster feast at your house while I settle for a turkey sandwich at mine. There’s a dramatic inequality between us, but this doesn’t imply my turkey sandwich isn’t enough to sate me. I might want to be invited over, but I am still able to live and function on my sandwich. It’s enough.

My point is poverty and inequality are conceptually unrelated. If you care about one you don’t need to care about the other. That’s why I’m having trouble with your position. You talk about reducing poverty but then go on about inequality, which is different.

Andrew: Maybe the concepts of poverty and inequality are distinct, but reducing inequality is still important. Inequality is about making sure the world is fair and everyone gets a chance to lead a fulfilling life. Imagine a single mother who works two jobs supporting her kids and barely makes ends meet. She can’t afford a good education for her children, and she’s sacrificing her long-term health to keep them above the poverty line. Now remember how some of the wealthy earn their money. They just invest, sit back, and live off their returns without having to lift a finger. It’s deeply unfair the single mother has to toil and endanger herself while the millionaires can just park their assets somewhere and live lavishly. When one party works extremely hard and gets little, while the other does almost no work and gets a lot, it’s unfair. We need to remedy that.

Parker: I agree something is wrong there, but it doesn’t have to do with both the millionaire and the single mom. At base, we’re angry the single mom’s efforts go unrewarded. We believe everyone deserves a reasonable standard of living and opportunity for their children, so the fact she works so hard in unsuccessful pursuit of these offends us. Notice the issue fundamentally involves the relationship between her efforts and quality of life.

But the problem ends here. Knowing millionaires are lounging around getting ROI is irrelevant. Even if no millionaires existed, we should be just as angry about the single mom’s situation.

Andrew: But what you’re describing is still unfair. Suppose millionaires exist and the single mom gets a reasonable standard of living, like you say, for herself and her children. The millionaires might still be working half as hard and making twice as much! Think about Jeff Bezos. He might be working incredibly hard, but that cannot possibly justify $130 billion. Some earn a disproportionate amount for their effort, and this should hurt every egalitarian bone in your body.

Parker: Why? Isn’t it alright to be paid differently based on different contributions? LeBron James probably works harder than his fellow Lakers, but let’s imagine he decided to train the exact same number of hours as his teammates from tomorrow on. He shoots the same number of free-throws as them, runs the same distance as them, and lifts the exact same number of weights as they do. Most likely, he’s still going to be a better basketball player, so why shouldn’t he be paid more? He’s still the player putting points on the board, getting rebounds, etc. If anything, it would be unfair if he performed so much better than his colleagues but got paid the same.

Andrew: Your example doesn’t work. The reason why LeBron is a better basketball player is because he practiced much more in the past. Even before he starts training just as much as his teammates, he has still spent more hours on the court than just about anyone else. This is what makes him a better basketball player. If he is paid more like you describe, his income is still commensurate with his efforts.

Parker: But what if Milton Friedman (5’1, ~120 lbs.) and LeBron put in the same effort? Hour-for-hour, Milton spends his life on the court practicing with the same intensity as him. Should they be paid the same? Probably not. It’s safe to assume no matter how much Milton practices he will never be as good as LeBron. He’ll be decent, but don’t expect league MVP or even a triple-double anytime soon. If Milton can’t play at an NBA level, why give him an NBA salary?

LeBron is paid so much because he makes a large contribution. His work ethic, as well as his individual gifts and talents, give him the ability to do so. Milton shouldn’t feel aggrieved he is paid so much less as a basketball player, and we shouldn’t worry about it, either. His contributions are tiny.

Andrew: But you’re still missing something. Being a poor basketball player won’t upset Milton because he can fall back on economics and make his living that way, but not everyone has that option. If basketball is the only way people earn income, and Milton can’t earn enough to escape poverty, then there’s an injustice.

Parker: I agree. Everyone, no matter what kinds of contributions they can make, should be able to have a reasonable standard of living for their efforts. If we were an economy of basketball players and the Milton Freidmans of the world would starve because nobody wants them on their team, we should remedy that. Perhaps a livable basketball minimum wage is in order, or maybe we can change the rules and take Milton off the roster to have him work in the front office where his abilities and inclinations are better suited.

Notice we can solve the problem without talking about LeBron and how much he makes relative to other players. Inequality of income is not the root issue here.

Andrew: You’re not much of an egalitarian, are you.  

Parker: I think I’m an egalitarian in a specific way. Obviously, we need equal political liberties. I’m very enthusiastic about equal voting rights, an equal ability to express ourselves, and fair and equal treatment before the law more generally. I’m pretty sure nothing will shake my confidence in these concepts.

My views on the distribution of wealth and income stem from two principles that also take equality seriously. As mentioned, I believe everyone is entitled to a minimum standard of living in exchange for their efforts, regardless of the size of their contribution. Conscientious people, striving to care for themselves and their loved ones, should not live in poverty. Whether their inclinations or abilities match what the market demands is irrelevant. I should be clear this minimum standard of living is not glamorous, nor would most be comfortable staying there for the long-term. Yet, it is a dramatic improvement from poverty and would protect our ability to pursue meaningful lives. In a slogan, I’m for an equality of minimum condition.

The second principle is concerned with compensation. When individuals make contributions, they should be rewarded accordingly. If you invent a vaccine, write a novel, or create an organization, your accomplishment should be recognized in proportion to the good it brings. In the same way paying LeBron the same as his teammates when he’s league MVP is unfair, there’s something wrong with paying a great author the same as a mediocre one. Human achievement should be celebrated, and there is nothing wrong if that involves giving some dramatically more than others.

This idea appears more anti-egalitarian than not, but it embodies equality with respect to accomplishment. Part of rewarding achievement fairly is giving approximately the same level of recognition to contributions of the same import. I acknowledge we need to control for context to see how noteworthy an achievement is, but, in general, we should strive to reward contributions solely based on merit.

As a result, I think income inequality is conceptually unimportant. I’m concerned with an equality of minimum condition and rewarding those who push the needle on human progress and achievement. The bare knowledge two people earn vastly different sums of money does not bother me, and it shouldn’t upset you, either.

Andrew: I see a conflict here. You care about political liberties, but aren’t those inextricably tied to the resources at our disposal? The person with the funds to purchase billboards on Sunset has more political power than you or me. Freedom of speech is much more valuable to them, creating positions of advantage and disadvantage in the political landscape. This seems incompatible with support for equal political liberties.  

Parker: You’re right. I need to clarify my position. There’s a distinction between political liberties and the worth of those liberties to an individual. Liberties grant the ability to undertake certain actions. For instance, having liberty of movement allows us to travel unrestricted between different locales. Freedom of speech allows us to say what we believe (without inciting imminent lawless action, among other restrictions). Having these liberties means we are given the mostly unrestricted option to undertake the actions in question.

However, two individuals having identical liberties may not exercise them in the same way. Suppose we both have freedom of speech, but you’re a celebrity and I’m a recluse. Both of us generally have the ability to say what we believe, but this capacity is much more valuable to you. You have a legion of fans who will listen and react to your opinions, while I don’t have any audience. In fact, taking away my freedom of speech probably wouldn’t have any practical implications, as recluses don’t communicate with anyone in the first place.

This situation seems unobjectionable. If freedom of speech were of equal value to everybody, we would give equivalent coverage and consideration to eccentric hermits as well as established public figures. We care deeply about individuals’ abilities to exercise their liberties, but how much, or if, they benefit from such exercise is beyond our concern.

Andrew: This doesn’t protect against another form of political inequality, though. Even if we all have equal liberties, some might use their wealth and advantage to secure disproportionate political influence. Billionaires can donate to congressional campaigns, hire lobbyists, and purchase political ads to shape the ideological make-up of a government. Instead of having one vote, like the rest of us, the wealthy can in effect unilaterally determine the result of an election. This violates the basic political egalitarianism at the heart of democracy. As soon as some voices count more than others, we become an oligarchy masquerading as something else. It’s difficult to imagine how extreme wealth inequality and a functioning democracy can peacefully coexist.

Parker: This has bothered me, too. Initially, it seems unlikely we can allow radical inequality on one dimension and be committed egalitarians on another when the two seem closely related. Yet, I don’t think this is a knock-down argument against my position. First, notice the problem has to do with a relation between the two dimensions; economic inequality has a negative influence on political egalitarianism. We agree this relation is harmful, but there are at least two ways to address the issue. Acknowledging the relation as fixed and eliminating economic inequality is one method. If there is no inequality, the reasoning goes, then it can’t exercise a negative influence on politics. The other option is combatting the relation. Ensuring economic inequality and political power are independent of each other can also work. If money had no influence on politics, then political equality would be secure. Wealth could vary dramatically between individuals with no adverse consequences.

The objection you raise is valid and important, but we can resolve it without affirming egalitarianism on every dimension. If we were to argue from here, the conversation would then be about which of the two methods described is better. Your point is good, but it only kicks the can down the road.

Andrew: I have another concern about your reasoning. You mentioned if money had no influence on politics, then inequality could run rampant with no cause for concern, yes?

Parker: I would say “fluctuate wildly” rather than “run rampant,” but yes, that’s my view.

Andrew: When you say that, you’re ignoring the psychological effects of inequality. If everyone else is much wealthier than you, you’re bound to feel inferior. This can happen despite achieving a “reasonable standard of living.” You might be ostracized based on the clothes you can afford, the house you live in, or the car you drive if you’re the poorest in a community. The result is real emotional pain that can inhibit normal interaction among peers and your pursuit of a meaningful life.

Parker: But resolving income inequality is not the best solution. Here’s an unconventional example that illustrates my point.

Physically unattractive people are also mistreated. Research has shown unattractive people are presumed guilty more often in court, are less likely to receive help from strangers, friends, and family, and are punished more severely in school than their attractive counterparts. Indeed, men in the bottom third of attractiveness earn 22% less in lifetime earnings than those of average physical attractiveness. This is likely due to discriminatory practices (Minerva).

Presumably, being physically unattractive can also cause psychological distress, but our solution is not the make everyone equally beautiful. If I understand the zeitgeist correctly, we aspire to celebrate these differences and treat one another equally, regardless of physical characteristics. Attraction is unrelated to moral worth or human value, so it should be irrelevant to how we treat one another.

Income inequality is similar. Like the unattractive, low-income people are mistreated because of prejudice. We can either erase the differences to ensure everybody is treated with respect or realize income has no relation to an individual’s moral worth. The latter seems more consistent with the tolerant, accepting people we imagine ourselves to be.

Andrew: But there are two types of psychological harm income inequality can bring. You’ve addressed the damage that comes externally from poor treatment, but what about the internal effects on self-esteem? Even if they’re not mistreated, the least-wealthy in a community can begin to rationalize their relative economic position. Simply seeing others who are better-off can foster feelings of inferiority and lead individuals to conclude they have lesser moral worth.

Parker: But they’re wrong. All humans have equal moral worth, regardless of whether they feel it is true. It could be the case the market values their individual skills differently leading to different levels of income, but wealth does not track moral status. Humans might be treated differently —in a fair and reasonable manner— based on relevant characteristics, but it does not follow they are above or below others in the moral hierarchy. The blind are prohibited from driving, but they are not morally inferior to the rest of us. Celebrities might get preferential treatment at public venues, but their lives are no more valuable than ours.

I acknowledge there are areas where moral equality necessitates equal treatment. Politics is one of them. Our equal rights reflect our equivalent moral worth, regardless of other contingent properties. Wealth, power, sex, gender, or race (ideally) do not give someone more freedom of speech than others, or less of a right to vote than her peers.

The other is living standards. There’s debate about the exact qualities that yield moral status, but our ability to formulate a life plan and follow it is most likely relevant. To respect this, we must ensure each human has reasonable opportunities to pursue her plan. Providing a minimum standard of living in exchange for conscientious behavior does so.  

Large swaths of the economic sphere do not fall under either of these categories. It’s possible to affirm our equal moral worth while still having an unequal distribution of resources.

Andrew: Do you understand how callous this sounds? You’re discounting peoples’ legitimate feelings. You will never be able to comprehend what they’re going through, or how the state of the world makes affects them, yet you dismiss it all without reservation.

Parker: I would be more sympathetic if moral value was the sort of thing where feeling it to be a certain way makes it that way. Moral worth is “real” in the same way trees and rocks are real. It’s a quality imbued in each of us that is independent of what we think or want to believe. Nothing can change it, so it’s unclear why we should accommodate people who believe theirs’ has been diminished or destroyed.

We need a distinction, though. Individuals can believe their moral worth was disrespected without actual disrespect occurring, but it does not follow all instances of perceived offense are illegitimate. We should feel aggrieved when our humanity is ignored or violated, and acting on these feelings brings us closer to justice. I only want to emphasize our unrefined moral intuitions are imperfect guides to whether a transgression actually occurred.

If the theory I’ve described is correct, the internal psychological distress caused by income inequality is unjustified. An unequal distribution of resources is not an affront to anyone’s moral worth. Yes, certain feelings might arise, but they are subtly misguided. That some parties are dissatisfied is no reason to reject what I’ve been saying. Ideally, when people feel disrespected, our first responsibility is to see if disrespect has occurred. If so, we remedy the situation, giving redress when appropriate. Else, we demonstrate why their humanity was unoffended, and how they can come to recognize this. I believe your objection puts us in the latter situation.

Andrew: I’m not convinced, but suppose everything you’re saying is correct. This doesn’t change the fact your theory is politically unworkable. Nobody gets far calling other peoples’ feelings “unjustified” or “misguided.” If we allow income inequality to run rampant, as your theory permits, a new age of political instability will begin. People will feel mistreated, and no amount of philosophizing can change that. Perhaps a new revolution will occur where the wealthy minority is removed from power. Maybe it will be violent. Perhaps the state will dissolve into anarchy — who knows? My point is your theory fails the stability test. No matter how “right” it is, it will never be accepted, and no sane government valuing self-preservation will take it seriously.

Whether or not you think income inequality should be resolved for its own sake, you must recognize its practical implications. Inequality of all sorts foments unrest. Good governance requires a stable government, and constant agitation threatens that. Insofar as you care about good governance, you must also care about income inequality, as attenuating the latter preserves the former. You might not think income inequality is inherently bad, but related commitments can force you to acknowledge it’s a problem.

Parker: You’re right, but I think these distinctions are important. I admit if I was a policymaker, I would keep an eye on inequality and ensure it’s not too severe. Yet, my interest in economic inequality would be derivative in that it stems from an interest in social stability. There is, I maintain, nothing morally repugnant about dramatic differences in wealth. What’s dangerous about inequality are the riots and unrest that might ensue if it gets too dramatic. Social stability is important enough for me to sacrifice some of my ideals, but this doesn’t change my philosophical beliefs. There are good theoretical reasons why economic equality is not inherently valuable, but I don’t want my policymakers dying on that hill. Anarchy doesn’t listen to theoretical reasons.

Andrew: I’m glad we see eye-to-eye on that. I still think economic equality is independently important, but at least I understand why you believe otherwise. I also think it’s interesting how your relatively extreme philosophical belief is tempered when it confronts certain political facts.

Parker: Yeah, it’s interesting.

Here is the link to the Minverva article. The main ideas covered in the dialogue aren’t particularly original. For instance, Harry Frankfurt’s article on economic inequality has heavily influenced my thinking.

My personal views on economic inequality aren’t Andrew’s and aren’t Parker’s. I think Parker’s onto something deep and important, but I have reservations about some of what she says. If you want to hear my full thoughts, send me an email and we can chat.

Tennis and Probability


Imagine there’s a tennis match in Kyrgyzstan between two players you’ve never heard of. You don’t know their rankings, match histories, or even what they look like, but you’re tasked with predicting who will win. The only piece of information at your disposal is player1 has a p chance of winning any given point against player2. In other words, if player1 and player2 played 100 points, on average player1 would win p*100 of these points.

Given only the information above, who do you think will win? How confident should you be they will win?


I’m sure there’s a mathematical pen-and-paper way to solve this problem. I don’t know it, so we’re going to rely on computer simulations. We can understand how likely it is player1 will win by simulating some large number of matches between both players while factoring in player1’s chance of winning any given point. Our confidence in player1 is represented by the proportion of matches she wins out of the large number simulated.

Here’s an example. Suppose we know player1 has a .51 chance of winning any given point against player2. At 15-0, she has a .51 chance of winning the next point and going up 30-0. At 0-40, she has a .51 chance of getting to 15-40, but a .49 chance of losing the point and the game.

To determine our confidence player1 will win an entire match, we might simulate 1000 such matches between player1 and player2 and count how many player1 won. For instance, she might win 586 of the 1000 matches. As a result, if all we know is player1 has a .51 chance of winning any given point, we might say we are 586/1000 = 58.6% confident she will win the match.

The model we consider does this for a specific type of tennis match. All simulated matches are best-of-3 sets with a 7-point tiebreaker played at 6 games all. What’s more, the deuce is “played out,” meaning players must win by two points to win a game. I chose this format because it’s the most common type played on the ATP and WTA tours.  

We run the simulation and graph the results. 3000 matches were simulated for 50 probabilities on the interval [.4, .6]. The exact code used for all the simulations in this post is here.

Figure 1

Figure 1 plots the probability player1 has of winning any given point against the probability she wins the match. For instance, if she has a .4 chance of winning a point, it’s very unlikely (~0% chance) she will win the match. Likewise, if she has a .60 chance of winning a given point, her probability of victory is ~100%.

As expected, if player1 has a .5 chance of winning a point, she has a 50% chance of winning the match. Based on this, we might expect a .525 chance of winning a point to yield a 52.5% chance of victory. Yet, our intuition fails to grasp the benefits of a slight edge. Just increasing the probability of winning a point from .5 to .525 causes the probability of winning the match to increase from 50% to 75%! A .025 increase in win probability at the point level leads to a 25% increase at the match level. To put this in perspective, we might say the difference between a player that wins 50% of her matches and one that wins 75% of them is the latter wins 2.5 more points out of 100 than the former. To make it even more concrete, we can surmise the difference between Pete Sampras (64 career singles titles) and Carl-Uwe Steeb (3 career singles titles) is only 2.5 points per 100!

Fully explaining Pete Sampras’ dominance and Carl-Uwe Steeb’s adequacy is far beyond the scope of our model, though. At best, we can say a player with a .525 point win rate would have a match record like Sampras’. However, this does not imply Sampras actually won 52.5% of the points he played or a player who does win that proportion will be a 14-time grand-slam champion. We are only noting similarities between the statistics of idealized players considered in the model and actual ones. Resemblance only suggests both players could have other common properties.

Still, the results are striking. Player1 only needs a .55 probability of winning a given point to win ~95% of the matches she plays. Approaching .6 almost guarantees she’ll win every time. Even a .51 probability of winning a point increases the odds of winning to ~.6.

Any tennis player will tell you the margins are slim, but now you’ve seen it computationally demonstrated. Common tennis platitudes like “every point counts” and “make them work for each point” take on additional significance. The practical implication is to focus more on individual points as opposed to games or sets when playing a match. Any competitive tennis player should already do this, but now they have an additional, semi-scientific reason to do so.

Back to Kyrgyzstan. We understand player1 has a p chance of winning a given point. If p > .5, we should be confident she will win. If p > .525, we should be really confident she will win. The same holds on the other side of .5. If p < .475, we should root for an upset. If p < .45, there’s pretty much no hope.

There’s another match happening in Zanzibar. We still know player1 has p chance of winning any given point, but now we know something else: she chokes. Whenever she has game, set, or match point, her probability of winning said point drops from p to pc. As an example, imagine her p = .55 and pc = .35. Suppose she’s also up 40-15 in a game against player2. Although her probability of winning a given point is .55, because it’s a game point, there’s only a .35 chance she wins the next point to secure the game. If she was up 6-4 in a tiebreaker, the same decrease in probability occurs. There’s only a .35 chance she wins the tiebreaker 7-4.

A similar problem presents itself. Given player1’s p and pc, will she win the match? How confident should we be in our prediction?

We run the same model in the previous section with some minor modifications. Whenever player1 is poised to win a game, set, or match, her probability of winning the next point plummets to some pc. As in the previous section, we vary p within [.4, .6] and observe player1’s probability of winning the match. What’s different now is each curve is associated with a constant pc.

Figure 2

The blue “standard” curve represents how player1 would perform sans choking. It is the same curve depicted in Figure 1 where her probability of winning a given point is p regardless of the score. The others record what a player’s match record at a certain p would be like given her pc. If player1’s pc = .45 for instance, her performance suffers heavily. At p = .5, she has only ~40% chance of victory compared to the 50% chance observed with an identical p in the absence of choking.

Past p = .5, a .05 decrease in pc roughly corresponds to a 10% reduction in the chance of winning a match. If player1’s p = .525, and pc = .45, her chances of winning would be 62%. However, if her mental game falters and pc drops to .4, her chance of victory decreases to 53%.

Clearly, any level of choking impedes performance. If we know player’s pc is low, we should expect a rather large p to compensate. Player1’s coach might suggest addressing the root factors of unclutchness. A sports psychologist or deep reflection might increase pc, or eliminate choking altogether.

There’s a third match in Andorra and we’ve learned more about player1. She no longer chokes at this junction in her career, but her play has become streaky. Given she won the previous point in a match, there’s a probability ps she will win the next point as well. If ps = .8, for example, there’s an 80% chance she will win the next point after winning the previous one. However, streakiness goes both ways. Given she lost the previous point, there’s an 80% chance she will lose the next one as well. The first point of every game (and tiebreak) is a fresh start, though. The chance she wins that point is p. From then on, ps reigns.

To get a sense of our credence in player1’s performance, we run another simulation.

Figure 3

This is a heatmap. The color of the block occupying the (probability of winning first point, ps) coordinate corresponds to the probability of winning the match. Light colors indicate high probabilities while darker colors represent low ones. As an example, if player1 has a .42 probability of winning the first point of any given game or tiebreaker and her ps = .9, her probability of winning the match is around .3. Here, we note heatmaps favor concise representation over numerical precision. The bar on the right gives us only a general idea of what probabilities are associated with which colors.

Still, patterns are clear. Variation in ps only has noticeable consequences at the extremes. If p is low, then a high streakiness almost guarantees losing the match. Observe how the probability of victory is only ~20% when p = .4 and ps > .9. However, for any value of ps < .9, the probability of winning the match hovers around 40% if p remains fixed. Similar results occur for higher p’s. Only when ps is large do we see its influence on the chance of victory. At values of p close to .5, ps has no apparent effect. The probability of winning the match stays roughly constant as ps varies.

It might look like high ps, or streakiness, is an advantage when p is sufficiently greater than .5. This is true, but the gain is comparatively small. Recall the Kyrgyzstan model where player1’s probability of winning the next point was constant throughout the match. If p = .525, player1 had 75% chance of victory. Here, for all levels of ps, p = .525’s probability of victory hovers around 60%. Player1 is much better off winning 52.5% of points in general as opposed to embracing streakiness.

We should note streakiness as we’ve defined it “smooths” performance at low values of ps. If ps = .5, this means players have a 50% chance of winning any given point after the first. In other words, we’re saying the players are just about even after the initial point. If p = .4 in the Kyrgyzstan model, a player has almost no chance of winning. In this model, p = .4 gives an ~40% chance. What it captures at these kinds of values is the dynamics of one player frequently winning the first point, and then both players having an equiprobable chance of winning the following ones.

We take these results to Andorra. Streakiness only concerns us at the extremes. If player1 has an exceptional chance of winning the first point and is very streaky, we’re confident. If she’s dismal on first points but just as streaky, we lose faith.


I’m excited about these models for two reasons. First, they suggest other interesting questions to tackle. How do the probabilities change in 5-set matches? What about no-ad? What if a player is brilliant on break points? What happens if we incorporate a serving advantage? Can we combine several of these models? The list goes on.

The second reason is epistemological. Can models of this type provide ever provide an explanation of real-world phenomenon? I talked about the Kyrgyzstan model being insufficient to explain Pete Sampras’ dominance, yet, there are distinct reasons why people may think this is so. We could say to explain Pete Sampras’ skill, we must address specific aspects of his game. It’s necessary to observe his deft touch at net, booming serve, and flat forehand. Pete Sampras is good, the reasoning goes, because he was able to hit aces and put away volleys. Any explanation of Sampras’ skill has to begin with these factors. Under this perspective, the Kyrgyzstan model fails to give an explanation because it is too abstract. Only tracking the probability of winning any given point obscures the unique advantages Sampras had that contributed to such a high probability. Proponents of this critique believe, in principle, no idealized model can explain why a given tennis player was so successful. Such models are incapable of capturing the unique, individual aspects of a player that contributed to his or her dominance.

A second critique finds no fault with idealized models in general — just the Kyrgyzstan one. It claims idealized models can give explanations of real-world phenomena, but this one in particular is too weak to do so. A model that actually provides an explanation would take parameters like probability of winning break points, probability of winning a point on second serves, probability of winning games/sets when down or up, etc… It would be much more detailed, but it still wouldn’t directly address the unique aspects of Sampras’ tennis the prior camp requires. Explanations from the model would sound like “Sampras was great because he had a high win percentage on second-serve points,” or “Sampras was a champion because he had a high probability of saving break points.” This camp believes idealized models can supply these explanations and they’re sufficient for deep knowledge. To understand Sampras, we only need to understand his propensity to win or lose in general scenarios. We only care about his serve or volleys or movement insofar as they contribute to a high break-point save rate, for instance. The statistical measures provide the base of our understanding; everything else is secondary.

We might be partial to a certain type of explanation. Players and coaches will tend to explain matches in terms of backhands and serves where statisticians will invoke probabilities and win rates. Our intuitions are often with the players. We find it hard to believe understanding Djokovic is possible without seeing a sliding open-stance backhand winner, or a kick-serve that bounces over your head in the case of John Isner.

Are our intuitions correct? Are the modelers correct? Which level of explanation gives us the best understanding of a tennis player? Is one of these levels subordinate to the other?

Consider the ideal

Imagine a young person trying to decide what to do with her professional life. Excluding financial considerations, she might consider three principles [1].

  • The principle of approbation
    • Do the thing that earns the most social praise.
  • The principle of altruism
    • Do the thing that increases the well-being of humankind.
  • The ideal principle
    • Imagine the world is perfect and your opportunities are endless. No wars, no famine, no disease, and no obstacles preventing you from pursuing whatever you wish. Do the thing you would choose to do in this alternate world.

If our young adult is independent-minded, she will dismiss or heavily discount the principle of approbation. There are two main reasons why it might get priority over others, but neither is convincing. For one, she could think picking a plan that satisfies the principle of approbation is a good bargain. Following the principle, she could only select professions that win wide social approval (doctor/lawyer/engineer). In exchange, she gets a lifetime status boost.

The discussion could end here. Different people require different levels of praise to feel content and secure. If our young adult is the type of person that needs affirmation, yielding to the principle of approbation might be a good decision. Yet, we will continue with our assumption she is an independent thinker. Her sense of self-worth is not heavily tied to approval so she doesn’t find the trade compelling. It diminishes her freedom to choose, and, in return, she receives a good she has no dire need for.

We can also think of the principle of approbation derivatively. Our young adult might actually want to help others, so she gives precedence to the principle of altruism. However, she realizes she is in a poor position to determine the best method to go about it. She might reason that others know a lot more about helping people than she does, so listening to popular opinion might be productive. Social approval could serve as a proxy for how effective her altruism is. After all, doctors help people, and people really love doctors. Praise for professional choices is actually a sign she’s on the right path.

While tempting, she does not buy this line of thought. She acknowledges the limits to her finding the best way to help others, but she has reason to believe the crowd can’t do much better. Doctors have always been popular, but their treatments weren’t always effective. Obviously, doctors now have a much better understanding of the human body, but the point is that praise and occupational prestige may not correlate well with how effective one is at aiding others.

The principle of approbation has been dismissed. Choosing between the remaining principles might look easy. Why not choose the principle of altruism and leave the world better than you found it? It’s inexcusable, the thought goes, to yield to self-indulgence when you can heal the sick and feed the hungry. Those in favor of altruism will say we face moral obligations in our professional lives. Not only must we “do no harm,” as Hippocrates might say, but we must also alleviate the suffering around us. By being of sound mind, able-bodied, and of comfortable means, we are automatically tasked with using our individual talents to help others flourish. From this perspective, the ideal principle is irrelevant. As long as people suffer, we must rush to their aid. There is no need to even think about how you would live in a perfect world, as the world is, in fact, deeply flawed.

Despite this, I think the ideal principle is crucial. We should all have an answer to “what would you do all day in a perfect world?” To be clear, I also believe the principle of altruism should weigh heavily in informing our professional lives, but neglecting where our own preferences and inclinations might lead us in an ideal scenario is a mistake. We suppress our individuality when the question goes unasked. In the same way someone who adopts the principle of approbation is subject to external forces when deciding where to put her professional energies, the principle of altruism ties our professional lives to processes beyond our control.

Note I am well aware what we can and cannot do is generally determined by things beyond our control. It is also true the claims those suffering have on us are more legitimate than those of popular opinion. These two facts make a lack of control normal and even a consequence of being moral. My only point is the principle of altruism subjects you to additional, exogenous constraints that diminish autonomy [2].

Why should we care about autonomy? The answer is that the people who we really are, the alternate selves that are the most “us,” are the people we would be in a state of absolute freedom. Imagine tomorrow you received the ability to do whatever you want. All restrictions — financial, emotional, cultural, and otherwise — are lifted. The world is perfect (it doesn’t need your help) so you can, in good conscience, choose to do what you wish. This is absolute freedom [3].

In the real world, some decisions are made for us. An authority figure could make you choose from a small selection of alternatives, or natural circumstances might do the same. The problem is we can’t infer much about an individual based on these choices. Can we really say someone is kind if they are forced to be? Is it appropriate to call someone cruel if they had to choose between three cruel alternatives? Our intuition says no [4]. It’s easier to call someone brave and courageous if they could have been otherwise. The choices we make under favorable circumstances reflect who we really are, and the ones we might make in a state of absolute freedom do so the most [5].

When we dismiss even considering the ideal principle, it’s a failure of self-knowledge. As long as we don’t have an answer to “what would you do all day in a perfect world,” we fall short of understanding ourselves. We might grasp how the world influences us, either through approbation or altruism, but we are distinct from it and deserve independent consideration. Thinking about how we would behave in absolute freedom illuminates who we are, without the external demands and obligations layered upon us.

Lacking self-knowledge poses a deep difficulty. How can we shape our lives when it’s unclear who lives them? To me, it’s like building a house without knowing the inhabitant or writing a love letter to an unknown recipient. Even if we happen to build or write for the most extraordinary people, what we create will be uninspired. We can only address their most general features (i.e. “put a kitchen in the house” or “you have a beautiful smile”) without touching anything specific to them. Building something wonderful requires knowing who it will serve. In a certain (obvious?) way, a life first and foremost serves the person who lives it.

Thinking about ourselves is natural, but it’s unnatural to embrace it. Yet, this does not mean the ideal principle should be the only criterion that guides our lives. It is a thought experiment, necessary to consider and grapple with, but not something that should (or even can) dictate your entire life. For instance, some of our ideal lives might be out of reach (playing center for the LA Lakers) while others could be mundane and a little abhorrent (watching TV all day?). In either case, we learn something about ourselves by considering the ideal principle. It could prompt conviction (“I really like sports. Perhaps I should work in the Lakers front office”) or reassessment (“Am I really that type of person? Something needs to change”).

This does not settle the matter as to how a young person should decide where to put her professional energies. I believe the ideal principle is important, but primarily as an exercise in hypothetical reasoning whose results are used to inform a broader decision. Exactly how much weight the ideal principle deserves to guide real professional conduct is up for debate. At the very least, I think two things are clear. First, the principle of approbation should be ignored in the vast majority of cases. Second, we all need an answer to the question posed by the ideal principle. After all, it might be who you are.




[1] This is far from an exhaustive list of principles we could use to make professional decisions. At varying levels of specificity, potential principles include: the excellence principle (“do the thing you’re best at”), the aesthetic principle (“do the thing that brings the most beauty into the world”), the comfort principle (“do the thing that gives you the highest standard of living”), a smattering of ideological principles (“do the thing that furthers communism/socialism/capitalism/anarchism etc…”), the contrarian principle (“do the thing people will dislike”), the hedonistic principle (“do the thing that gives you the most sensual pleasure”), and variants of a religious principle (“do the thing God/Allah/Yahweh wants you to do”).

There are a lot of principles people might deem relevant. The three I chose are among the most general, and, I’ve observed, often crop up in actual conversations young people have about their futures (barring financial considerations)

[2] But if you choose the constraints, are they even constraints at all? I’m the one who brought them about and limited my own behavior, so aren’t they best understood as artifacts of my freedom, rather than obstacles to it?

[3] Absolute freedom is a state without hardship. If you’re concerned about the effects of hardship and struggle on personal identity, remember we enter absolute freedom tomorrow. All of our past experiences, the things that have made us “us” are preserved. In fact, I don’t think a person born and raised in absolute freedom would be much of a person at all (or at least not a very good one). Considering absolute freedom is meant to make us understand how we would behave if circumstances changed dramatically, not who we would be if our pasts were different.

[4] It is true we can observe how people react to external circumstances and make inferences that way, though. It’s the mark of a strong and magnanimous soul not to harbor spite when wronged, for instance. I’m on the fence as to whether we can really understand who a person truly “is” solely by looking at these reactions. Our ability to harbor discomfort is only a part of who we are (though a very important one) and it has reasonable limits. I’m not sure what we can infer about character from someone irascible who suffers from chronic pain.

[5] There’s a “moral luck” problem here. If we think of absolute freedom as a kind of utopia, then there’s no opportunity for courageous or kind actions, and perhaps, no possibility for courageous or kind people. A solution would be to think of absolute freedom as exactly like the regular world sans obligations. War and famine still exist but somehow our obligations to stop them disappear. Now it’s possible to be compassionate in a state of freedom by deciding to be a peacemaker or go on humanitarian missions, for example.

It gets tricky when we realize what motivates this person must be completely endogenous. Their rationale for their actions won’t appeal to the principle of altruism, because that is an external obligation that cannot exist in a state of absolute freedom. Yet, if we want to call their actions kind, they must accord with some desire for the well-being of others. It looks like we’re forced to posit an “internal” principle of altruism that operates independently of the one that creates external obligations. The strength of this internal force is the measure of how kind and compassionate someone is. Yet, how is this different from the external principle? Is the internal one best understood as a heightened sensitivity to the external principle of altruism?

The other solution is to bite the bullet and say no kind actions are possible in a state of absolute freedom, as these must be motivated by the (external) principle of altruism which doesn’t exist. This, taken in conjunction with my claims in the main body, produce strange implications. Does this mean the person who is most “you” is entirely selfish? Does altruism diminish our individuality? Broader questions about utopias are also at stake. Is being an altruist in a utopia redundant? If everyone is doing fantastic, why would you care about someone else’s well-being? Your caring won’t make them do any better (the world is perfect!).



Inflated statistics, spring admission, and the University of Southern California

A significant number of USC students do not enter as freshmen in the fall. The university offers alternative enrollment options to inflate incoming freshmen statistics and make their student-body appear higher-quality than it actually is.

Something about USC doesn’t add up.

Every fall approximately 3,200 wide-eyed freshmen matriculate. They were admitted from a pool of more than 60,000 applicants and are among the best of what high schools in the 21st-century have to offer. In 2019, the middle 50% range of their SAT scores was 1360-1530. The same stat for GPAs was 3.72 – 3.99. Roughly 20% of enrollees have rèsumès good enough to warrant merit scholarships.

This is impressive. For most of its history, USC was academically underpowered. It was better known for its football team and fraternities than serious study until the university launched a status-raising campaign in the 2000s. Now, some of the brightest high-schoolers in the country become Trojans.

But look closer. For the 2019-2020 academic year, USC claims to have around 20,500 undergraduates enrolled. If approximately 3,200 freshmen enroll every year, and that has been the case for the last 4 years, then USC should only have 3,200 * 4 = 12,800 students. In fact, if you sum the actual number of freshmen that USC reports matriculated in fall 2016, 2017, 2018, and 2019, you only get 3,068 + 3,358 + 3,401 + 3,168 = 12,995 students.

Where is everybody? If we grant that the 20,500 figure is correct, then there are roughly 7,000 students at USC who are unaccounted for on this naive model. In other words, it’s not obvious how almost 35% of the student body got into USC, or how they compare academically to their peers.

In the next section, I want to establish that the freshmen/total enrollment discrepancy at USC is real and significant compared to similar institutions. Afterward, we will discuss possible explanations for the gap.

1. The discrepancy

1.1 Methodology

The guiding thought is we should be able to get reasonably close to a university’s reported undergraduate population by counting all the students they say enroll. For instance, if a university says they enroll 250 freshmen each year, we might expect their total number of undergrads to be around 1,000. Students should graduate in 4 years, so the only people on campus should be those who enrolled 1, 2, 3, or 4 years ago.

If only college was that simple. There are good reasons why the simple calculation I just described will be inaccurate. Not everybody finishes their degree in 4 years, so students who enrolled 5 or 6 years ago might still be on campus. Matriculating class sizes might vary dramatically over that period as well. Adding a couple of numbers together also can’t account for people like dropouts and transfers who might affect the size of a student body.

We can account for all of these concerns. Many universities (including USC) publish their matriculating class sizes on their websites, either part of the Common Data Set or other statistics they distribute. The same schools also frequently publish the number of transfers they receive. As a result, we can get an exact sense of student inflow over the past 4 years.

We can also roughly approximate the number of students who take more than 4 years to graduate. Universities publish 6 and 4 year graduation rates as part of the Student Right-to-Know Act. From these figures, we can estimate the number of students in a freshmen cohort who graduate on time. We assume the rest of the students in the cohort graduate in 5 or 6 years, getting an idea of how many people who enrolled more than 4 years ago contribute to the student population.

(I acknowledge this is an overcount since some students who don’t graduate in 4 years drop out. Yet, note that overcounts are in USC’s favor. Our naive calculations show there are 7,000 missing students, so any fudgery that accounts for more undergrads helps them).

Handling dropouts who enrolled in the past 4 years is tricky but doable. Universities don’t publish the exact number of students who drop out and when, so making any kind of exact calculation is difficult. For instance, a freshman enrolling in 2015 might count towards undergrad enrollment in 2015, 2016, and 2017, but then drop out. If we knew what percent of a freshmen cohort dropped out every year, we could just “thin” their class accordingly and be done with it.

Our strategy is to perform two sets of calculations. The first assumes everybody that enrolls eventually finishes their degree. This is a “best-case scenario” and will give us an upper bound on the student body. Imagine the student who enrolls in 2015 but drops out in 2017. If we’re trying to calculate undergraduate population in 2018 under the assumption of no dropouts, she’s going to be counted even though she’s no longer enrolled. As a result, if we pretend every freshman sticks around and eventually graduates, we’re going to overshoot the number of people actually on campus by tallying people that have already left school.

The second set of calculations gives us a “worst-case scenario.” We assume everyone who will drop out does so the moment they set foot on campus. The proportion of a freshmen cohort that drops out can be approximated via published graduation rates. In our minds, those who will drop out are counted as enrolled freshmen and then disappear. If we’re doing these calculations for 2018, they will not count our hypothetical student who drops out in 2017. In fact, they wouldn’t count her in 2015, 2016, or 2017, even though she was enrolled then. Under this assumption, we get a lower bound on the student body by ignoring attendees who will eventually drop out, even if they are still enrolled.

With rough upper and lower bounds, we can be reasonably confident the number of students we can trace back to freshmen enrolled in the fall or transfers lies somewhere between the two figures. Roughly, the bounds will be computed as follows:

Upper bound = (number of freshmen enrolled over last 4 years) + (transfers from last 2 years) + (students who take 5-6 years to graduate from freshmen cohorts 5 and 6 years ago)

Lower bound = (number of freshmen expected to graduate who enrolled over the last 4 years) + (transfers from last 2 years) + (students who take 5-6 years to graduate from freshmen cohorts 5 and 6 years ago)

What’s left is to compile the data, run the numbers, and see if the bounds on the number of students we can trace back differ significantly from the number of undergrads a university says it has.

1.2  Numbers

By looking through a combination of Common Data Sets, enrollment reports, and university fact pages, I was able to gather the necessary data and compute lower and upper bounds for 8 schools, including USC. In an effort to compare apples to apples, I tried to include schools that are private and similarly sized. Data for those institutions aren’t always available, so the sample also includes public schools of similar size, and smaller, private ones (with UCLA thrown in for good measure).

Below is a table with the 8 schools and their respective reported undergraduate enrollments.

Screen Shot 2020-06-21 at 3.43.25 PM
Table 0

Using the ideas outlined in the previous section, we calculate the number of students traceable to either freshmen or transfer enrollment. The next table displays the upper and lower bounds as a percentage of the undergraduate population.

Screen Shot 2020-06-21 at 3.45.24 PM
Table 1. For details on how upper and lower bounds were calculated, consult Appendix A.

Let’s look at the University of Virginia (UVA) to start. If we add up all the students the University says have enrolled as freshmen in the past 4 years, adjust for students that enrolled 5 and 6 years ago who are taking extended time, and assume nobody drops out, we can account for 102.38% of the students on campus. If we assume all the freshmen that are going to drop out do so immediately, we can account for 97.91% of the students on campus. In this case, our upper and lower bounds contain the number of reported students. This is a sign as our method does a decent job of predicting how many undergrads a university should have given the numbers they publish.

However, this does not always happen. A percentage greater than 100 indicates an overshoot. For instance, if we assumed all the students we expected were going to drop out of Baylor did so immediately, we should expect their undergraduate population to be 114% of their current one.

As Table 1 suggests, our method does not yield pinpoint accuracy. We don’t hit actual undergraduate population numbers exactly, but two things are notable. First, our new model tends to overshoot. Half of the schools in the sample have lower bounds that are greater than stated enrollment, and the lower bounds of two more come within 8% of the actual figure. The upper bounds of 6 schools are well over 100%, or very close. This suggests there may be outflows of students I haven’t considered, leading to systemic overcounts.

The second feature is BU and USC are outliers. BU comes reasonably close in the upper bound, but its lower bound is nearly 15% below stated enrollment. USC is even worse. Its upper bound is 83.99%, which is even lower than BU’s lower bound. Remember, 83.99% as an upper bound means we can only account for that percentage of students if we make the rosy assumption nobody drops out. USC’s lower bound also dips into the 70s, which is far worse than any other school considered.

USC, and to a lesser extent, BU, have notable discrepancies between their published freshmen/transfer numbers and total enrollments. Their published student inflows do not come close to accounting for the students they have. The fact USC and BU’s freshmen/transfer enrollment numbers under predict student population — when the model overshoots considerably for other schools — suggests something is afoot.

2. Explanations

There are two general ways to account for USC and BU’s enrollment discrepancies. The first is to claim they’ve made a mistake. For one reason or another, the reasoning goes, both universities don’t have a grip on either their total enrollment or the number of freshmen/transfers that enroll every year. This could be caused by problems with their internal systems, apathy, or communication issues.

I don’t think this is plausible. For one thing, knowing how many freshmen enroll is crucial to universities. Tuition is a large source of revenue, so institutions invest a lot in ensuring incoming cohorts have the correct size and socioeconomic makeup. Unexpected freshmen yields can also lead universities to rescind acceptances, which is bad for students and administrators alike. Along the same lines, it seems unlikely a university also doesn’t know how many total undergraduates they have. Every student is a paying customer, so I’d imagine schools would know the size of a major income source.

Deceit is also a possibility, but if schools are lying about their enrollments, we have a much larger problem than can be discussed in this blog post. For that reason, I will not consider it.

The second general explanation is USC and BU have additional student inflows that aren’t matriculating freshmen or transfers. This sounds strange: doesn’t everyone enroll as either a fall freshman or a transfer? How else are you admitted to a school?

It turns out there’s a third way. USC and BU both admit applicants for the spring semester. This means a high school senior submits their application like everyone else, but instead of being invited to campus in August, the earliest they can enroll is the following January. In USC’s case, we know spring admits aren’t tallied in the freshmen numbers I used to compute the upper and lower bounds. In their matriculating freshmen reports, they are strangely specific in talking about fall admits and fall enrolls.

We can test if spring admits account for the missing students at USC. According to their admissions blog, USC enrolls between 500 and 600 spring freshmen every year. Let’s be conservative and assume the number is 500 while supposing the practice has been active for the last 4 years. We can account for this in our model by adding 500 to every fall matriculating class going back to 2016.

Table 2 demonstrates the new upper and lower bounds with this assumption. Consult Appendix A for details on how the bounds were computed.

Screen Shot 2020-06-18 at 2.26.25 PM
Table 2

There’s improvement. 93.74% as an upper bound approaches respectability, but 87.89% as a lower one is still concerning.

At this point in my investigation, I thought there has to be a table where spring admits show up in USC’s Common Data Set. It records everything from Pell Grant recipients to the number of philosophy degrees conferred, so spring admits need to be recorded somewhere, if not under the name.

That’s when the “Other first-year, degree-seeking” row in Section B of USC’s Common Data Set caught my eye. According to the definitions table in the back of the document, “Other first-year, degree-seeking” undergraduates are students that have completed fewer than 30 semester hours (units) and are seeking to graduate at the university in question. These are contrasted with “Degree-seeking, first-time, freshmen” who are undergraduates in their first year that have not attended a prior postsecondary institution. In other words, “Degree-seeking, first-time, freshmen” are traditional freshmen. “Other first-year, degree-seeking” students are freshmen that have attended a prior institution.

Two pieces of evidence that suggest this row in the Common Data Set counts spring admits. First, USC recommends spring admits to go to community college or study abroad during the fall semester. On their website, they say “most first-year spring admits choose to enroll in community college during the fall.” For the cosmopolitans (or those that can afford it), they even have fall-semester programs in places like Rome and Prague at partner universities exclusively for USC spring admits.

The second piece is the actual values in the “Other first-year, degree-seeking” row. As mentioned, USC says between 500 and 600 spring admits enroll every year. It turns out, for the last 3 years, the number of “Other’s” has been around 600, with a spike 4 years ago. If we update our upper and lower bounds by adding the number of “Other’s” to the freshmen enrollment numbers for the last 4 years, we get the following:

Screen Shot 2020-06-18 at 3.18.41 PM
Table 3

We’re much closer. Our upper bound is nearly 100%, and the lower one is a respectable 93.63%. For USC, I’m more confident than not the “Others” row approximates their spring admits. As a result, I believe USC’s policy of offering spring admission more or less explains the apparent discrepancy between matriculating freshmen numbers and total undergraduate enrollment.

If what I’m saying is correct, we can follow an identical process with BU and create better upper and lower bounds. Yet, there are slight differences that prevent this. BU’s “Other” rows are often in the low teens. This means very few freshmen have attended a prior institution before landing at BU. However, I attribute this to the nature of their spring admission policy. It appears almost all delayed admits arrive at BU as part of the College of General Studies (CGS). This is a 2-year program where students arrive in the winter, take classes, and then study abroad for the summer after their freshman year. On the CGS FAQ, they recommend students spend their gap semester volunteering, working, traveling, or taking a class. The next entry in the FAQ explicitly prohibits CGS students from enrolling in another institution for the fall semester. If students want to take non-degree courses during the fall, BU advises them to consult their CGS academic advisor.

In other words, BU does not present taking classes during fall as an attractive option. For this reason, I am not surprised the “Other” row in their Common Data Set is so low. Yet, we can still update our bounds by taking into account the number of first-year CGS students. From their website, they claim to enroll approximately 600 students annually. If we add 600 to every freshmen class going back 4 years, our new bounds are:

Screen Shot 2020-06-18 at 4.32.37 PM
Table 4

These look similar to bounds created for other institutions. Taking delayed admissions into account, we can resolve BU’s apparent discrepancy between freshmen enrollment and total undergraduate population. As mentioned, I believe the same is true of USC. Every year, both schools enroll around 600 freshmen during the second semester.

3. Motives

I believe USC and BU do this to inflate the statistics of their freshmen classes. The thought is if they can exclude academically weaker students from matriculating in the fall, their student-body will appear better and more selective than it actually is. After all, spring admits aren’t included in the fancy documents USC spins up for their “Class of 202X” promotions, and I doubt CGS statistics are included in BU materials. Based on my calculations, USC could have inflated their admit rate by ~1.3% in 2018. Consult Appendix B for the exact methodology.

Colleges have another incentive to delay admission for weaker students. US News and World Report uses the test scores and high school GPAs of first-time, first-year students who enter in the fall to calculate their rankings. If students are admitted in the spring, their statistics are irrelevant from US News’ perspective. This means spring admission is a way for schools to shield weaker students from prying eyes. Every year, the high-school performance of around 600 USC and BU freshmen is not considered when calculating college rankings. Put differently, 15% of their entering class is invisible to those who want to discern the academic quality of the average Trojan or Terrier. I would be surprised if including that 15% helped USC or BU’s cause.

Deirdre Fernandes, reporting in the Boston Globe, describes the phenomena.

Many of the students targeted for delayed admissions would have traditionally been wait listed or rejected because their test scores or grades may not have been as strong as other applicants. But since these students aren’t counted as part of the entering fall class, their academic histories don’t weigh down the school’s overall average for that particular year.

There is also a wealth dimension.

The freshmen who come in likely wouldn’t have been accepted for the traditional freshman class because their grades weren’t as strong, but they are usually wealthier and can afford to pay for a spot without relying on financial aid from the school.

Put bluntly,

“The college banks on the fact that the student wants to go there,” said Todd Weaver, a vice president with Strategies for College Inc., a Norwood-based private counseling firm. “This student might not be a best fit, but their bank account is.”

In addition to being academically weaker than traditional admits, it appears colleges also target the students that can afford to pay full freight. Observational evidence stands in favor of this point for USC. To be clear, I do not have data on USC spring admit income. Yet, of the three students who gave testimonials about their spring admit experience on USC’s delayed admission page, two went to $40,000 a year college prep high schools. This is far from damning evidence, but it is suggestive.

I acknowledge there are non-deceitful reasons why a university might offer spring admission. For instance, staggering the arrival of students allows institutions to enroll more people. Spring freshmen can replace upperclassmen that are studying abroad for the semester, which leads to efficient use of dormitory space. Personally, I believe more students should take time off between high school and college, and we can see delayed admissions as an embrace of the idea.

Perhaps university administrators have these thoughts, but the consequences for ranking and status are just too convenient. Universities live off their reputations and, notwithstanding the coronavirus, are finding it more difficult to fund themselves; we should be skeptical of professed altruistic motives. Anyone should have a hard time believing colleges engage in policies that hide low-quality admits and allow them to enroll more wealthy students for reasons other than their own advancement.

4. Normative claims

I’m going to pick on USC because it was the original subject of my investigation, though I believe everything below also applies to BU.

There’s an equality argument against USC’s spring admission policy. As described, they advantage rich, under-qualified applicants who otherwise would have little chance of being accepted. We believe wealth should have no role in allocating educational opportunity, so our ideals about merit and social mobility are violated. Hence, spring admissions policies are inconsistent with our values and should be abolished or altered. I believe this is an effective and important argument but will not pursue it at length. We all know its steps and understand how much of an issue social mobility is.

A more interesting argument concerns honesty.

Suppose you don’t mind whether private institutions lower academic standards for wealthy students. You might not believe these universities deserve tax breaks, but in principle, there’s nothing wrong with private actors imposing an income qualification on applicants. In the same way only the wealthy can buy birken bags, only the rich can get a degree from USC.

In light of this, you can still think spring admission is problematic because it functions to misrepresent the institution. Perhaps it’s within USC’s right to compromise rigor in admitting some students, but their statistics should reflect that. It’s disingenuous to tout 96th percentile SAT scores and falling acceptance rates when 15% of freshmen are not included in those figures. It’s deceptive to submit unrepresentative data to college rankings for status and prestige while slipping in hundreds of students that might be under-qualified.

I think it’s admirable USC is on such a deliberate campaign to improve itself. It’s clearly a much better institution than it was in the past, but only substantive growth should be rewarded. Its spring admissions policies are evidence it wants all the benefits of a high-powered student body while still reserving the right to lower standards for the wealthy. It cannot pick both and remain honest. If USC wants to remain a playground for the rich, so be it, though it should not pretend otherwise.

5. Conclusion

I could be wrong. It’s possible all spring admits are highly qualified, even more so than regular admits. In fact, some of them probably are [1]. It’s also possible most spring admits are low-income first-generation students, on their way up the socioeconomic ladder. Given the evidence, though, I think this is unlikely. The consequences for universities are just too convenient. I invite USC, BU, and all other universities to release statistics on spring admits. Until then, I stand by my critique.

My criticisms are also directed entirely towards institutions, not individuals. Being accepted to any college, during any semester, is a reason to celebrate. When confronted with opportunity, individuals are obliged to take it. Yet, this does not prevent debate at the institutional level about how some opportunities are allocated, or if organizations are being dishonest about who receives them.


[1] Let F(1): (1) is a spring admit and G(1): (1) is academically underqualified.

My position is not:


But rather:

∀x[P(Gx|Fx) > P(Gx)]

(with a little abuse of notation)



Appendix A: Calculations

Let’s begin with an example. Here is the excel sheet I used to calculate UVA’s figures.

Screen Shot 2020-06-16 at 10.29.30 PM
Table A1

The calculations start with the same intuition we had in the introduction: adding up freshmen enrollment numbers over the last 4 years, should reasonably approximate total undergraduate population. This happens in the “Fall matriculating class size” column. The total of 4 years of freshmen enrollment is tallied at the bottom.

The figures in the “students expected to graduate” column are calculated by multiplying the corresponding fall matriculating class size with the university’s 6-year graduation rate. UVA’s 6-year graduation rate is 95%. This means the “students expected to graduate” figure for 2017 is 3788*(.95) = 3598.6.

Transfers per year are often obtained from the latest edition of a university’s Common Data Set. Occasionally, transfer numbers aren’t available for the year 2019-2020, so in that case I assume they took in the same number of transfers as in 2018-2019. Recall that I’m assuming all transfers stay on campus for only 2 years. This means the only transfers on campus are those who arrived this year or the one prior.

I also attempt to approximate the number of students who enrolled as freshmen more than 4 years ago but are still on campus. These are the “students taking non-standard time.” To approximate the number of students from the freshmen class of 2014 that are still at UVA, I multiplied the total freshmen class by (1-[4-year graduation rate]). The rough thought is if you don’t graduate in 4 years, you will in 5 or 6. UVA’s 2014 freshmen enrollment is 3672 and their 4-year graduation rate is 89%. Hence, the number of freshmen from 2014 who are still around is 3672*(1-.89) = 403.92.

The upper bound of accounted-for students is calculated by summing the totals of “fall matriculating class size,” “transfers per year,” and “students taking non-standard time.” This assumes that every freshmen in the 4 prior classes is still around. The lower bound is calculated similarly, but the total of “fall matriculating class size” is replaced by that of “students expecting to graduate.” This calculation assumes all the students that are expected to drop out will immediately, and don’t contribute to the current undergraduate population.

The following table results:

Screen Shot 2020-06-16 at 11.15.02 PM

“Students accounted for (no dropouts)” is the upper bound, and “Students accounted for (all dropout immediately)” is the lower bound.

The full excel sheet I used can be found here. It includes additional notes on where I found enrollment data and graduation rates, and the assumptions I made when those weren’t available.


Appendix B: admit rate

Approximating how much USC inflates their admission rate is straightforward. Let’s use their published data from 2018 as an example, as this is the latest year where good data are available.

In 2018, USC admitted 8,339 students for the fall from a pool of 64,352 applicants. This translates into a 8,339/64,362 = 12.9% acceptance rate. However, in order to get a better sense of their total acceptance rate, we must factor in those they rejected for fall but admitted for spring. To my knowledge, you can’t directly apply for spring admission to USC, so the spring admits must have come from fall applications.

If what I mentioned about the “Other first-year, degree-seeking” row in the Common Data set is correct, USC had 642 spring admits enroll in 2018. Note that fewer students enroll than are admitted. Hence, the total number of spring admits is likely higher than the 642 recorded in the “Other” row. If we knew the “yield rate,” or percentage of students offered spring enrollment who took it, we could divide 642 by the rate and get the number of students accepted for the spring. To my knowledge, USC doesn’t publish that figure.

Yet, we can estimate a yield rate. Suppose it’s true the students offered spring admission to USC are academically under-whelming relative to fall admits. This means they probably would not have been accepted to USC, or schools of similar quality, under regular circumstances. As a result, even though USC offered them a spring position, it’s likely the best option they have. In other words, the choice could be between attending a #22 ranked college in the spring, or a #32 ranked college in the fall. I imagine most students opt for the former, leading to a higher yield rate.

Other factors can also influence the rate. Even though USC might be the best option for many students, it could still be unattractive to start in the spring. Students might want the entire “freshmen experience” that comes with arriving in the fall with other freshmen. Starting in the spring jeopardizes that.

It’s clear USC realizes the concern and took pains to alleviate it. As mentioned, it offers numerous foreign programs with other USC students to make spring admits feel they are not missing out. This increases the appeal of a spring enrollment.

How do we balance these competing concerns? USC’s fall 2018 yield rate was 41%. Harvard’s 2018 yield rate was 82%. I propose we think of a spring admission from USC as more attractive than a fall offer (given the spring admits’ poorer alternatives) but less attractive than Harvard (given the need to delay enrollment on campus). I think a fair figure is 75%. After all, spring admission programs are popular. In 2019, Babson College offered spring admission to 100 students and 86 took the offer. Babson is a small, specialized school, though, so I’m unwilling to read too much into their 86% yield. Still, it indicates rates should be higher rather than lower.


Using admit and application data, we can estimate USC’s actual 2018 admit rate given a 75% spring enrollment yield.

Screen Shot 2020-06-24 at 4.58.55 PM

Our assumptions entail USC is inflating their admit rate by around 1.3%. This might look paltry, but every percentage point counts in the prestige arms race.




Power in Gulliver’s Travels

No, not the Jack Black movie.

Jonathan Swift’s Gulliver’s Travels is actually a fantastic blend of adventure fantasy and social satire. It’s probably the type of book I’ll pick up later in life once I’ve seen more of the world and think it’s twice as funny/good as I do now.

In a nutshell, Gulliver’s Travels describes the journeys of Lemuel Gulliver, the most unfortunate man in the world. Over the span of 16 years, he is shipwrecked, forgotten onshore of a mysterious island, and marooned twice. After each catastrophe, he finds himself in an unknown land filled with strange inhabitants. He learns their language, adopts their customs, and reports on how their society differs from his own.

The discussion below is a suggestive summary of key parts with my analysis at the end. There are spoilers, so leave if you want to keep the surprises for yourself.

Gulliver is first shipwrecked in Lilliput, an island where everything is in miniature. Its human inhabitants are six inches tall, and their surroundings are scaled accordingly. Lilliputian cows can fit in our pockets, and their greatest metropolis is smaller than a football field.

Gulliver is an average-sized human, but a giant in their land. He is more than ten times as tall as a Lilliputian and has prodigious strength by this accord. The Emperor of Lilliput feeds and cloths Gulliver out of his own expense, and then compels him into public service. As part of this deal, Gulliver has to capture the navy of a rival empire of miniature humans, called the Blefuscans, and deliver it to Lilliputian ports. The Blesfuscans were preparing a violent invasion of Lilliput, so Gulliver justifies capturing their fleet as an act of self-defense for his adopted home.

The Emperor is overjoyed when the fleet is delivered. He confers the highest honors on Gulliver and entreats him to capture more Blefuscan vessels and even aid in a violent counter-invasion. Gulliver flatly refuses. He is content to defend Lilliput but will play no role in subjugating innocent people. The majority of the Lilliputian royal court backs this decision, but the Emperor is incensed. This begins Gulliver’s political downfall. His enemies take advantage of his disfavor with the Emperor and conspire to blind Gulliver in his sleep or kill him. Upon hearing of their plans, Gulliver flees to Blefuscu and eventually escapes to England.

Contrast this to what happens in Brobdingnag. There, Gulliver is to the Brobdingnagians what the Lilliputians were to Gulliver. The people there are more than 50 feet tall, and their buildings and animals are also scaled appropriately. Everything is incredibly dangerous to a person of Gulliver’s size, so he must be on constant guard against being crushed by a careless Brobodingnagian or carried away by a crow.

Accordingly, Gulliver is a novelty. He is exhibited as a living curiosity and toured across the country before being purchased by the queen and finding residence in her court. There, he is universally loved, but not respected, by the Brobdingnagians. They see Gulliver as a coward because he is afraid of (to them) meager heights and household flies (which are as large as birds to him). When he attempts to give the King a brief account of England, he is laughed at and stroked condescendingly for trying to make grand the history of “little people.” Nonetheless, all his needs are met by royal servants and the nobles are entertained by his company.

Comparing Gulliver’s experiences in both nations, it appears power and affection are inversely related. When he has the capacity to single-handedly defeat armies in Lilliput, Gulliver is asked to behave immorally. If he declines, he loses favor with the Emperor. If he accepts, he is seen as monstrous by the more humane members of the Lilliputian court. Gulliver loses status no matter his course of action. His power causes others to put him under conflicting obligations that are impossible to simultaneously fulfill. The result is he loses popularity and is forced to flee.

Notice Gulliver has no such worries in Brobdingnag. He’s the size of a Brobdingnagian mouse and is incapable of doing anything useful. The King, Queen, and nobles expect nothing of him except to be small and pleasant, which is easily accomplished. His obligations there are few. They are less likely to be contradictory, so he’s able to meet all of them without offending anybody. If he suddenly developed some power or faculty useful to the Brobdingnagians, I suspect Gulliver would be inundated with conflicting expectations to do this or that, and then inevitably run afoul of the group he chooses to ignore.

I’ve heard about people deliberately using this principle. A CFO I know asks salespeople to blame decisions that would upset customers on him. Conflict seems to arise when the customer wants something and the salesperson won’t provide it. If the salesperson is bound by an “evil” CFO, the customer has no reason to criticize them. The CFO understands that by appearing powerless, you preserve affection.

The major suggestion is universal love goes hand in hand with uselessness. The only certain way to avoid censure is to make sure nothing is asked of you, and the only way to make sure nothing is asked of you is to be incapable.


Probability and God

Occasionally, rare things happen to us.

You might land a competitive job (3/100), appear on the big screen at a sporting event (1/70,00), or win the lottery (1/12,271,512). It’s also possible for you to get a US green card (1/126), be struck by lightning (1/700,000), or have an idea so good it’s “like getting struck by lightning” (1/???).

Whether it’s good or bad when the improbable becomes actual, there’s always a question lurking in the background: is this evidence of anything? If what seemed impossible is staring us in the face, what can we say about it?

This question is fascinating with respect to life in the universe and God. “God” in this post will not refer to the God of the new testament, the God of the old testament, Allah,  Shiva, Mahavira, Zeus, Ra, Spinoza’s God of substance, or any other popular deity. Formal religion aside, we will be interested in the quite general question of whether a being designed the universe to support life. This designer, whether s/he exists, will be referenced as “God.” I repeat, there is nothing Judeo-Christian, Muslim, Hindu, Wiccan, etc… about my invocation of “God.” I chose the capital-g for ease of reference and because I knew it would grab your attention.


Our existence is an anomaly.  We can get an intuitive feel for this by gazing at the night sky. Billions of stars, millions of planets, and somehow, we’re alone (so far). We have yet to find evidence of even microbes in the vast expanse of the universe, so the fact beings as sophisticated as humans came about represents something uncommon and significant.

The improbability goes deeper. As it turns out, even the laws of the universe that allow life to exist are rare and unlikely to come about by chance. If we were to slightly change the basic rules of force and gravity, for instance, the resulting universe would be hostile to life. Philip Goff has examples. The following three bullets are his words.

  • The strong nuclear force has a value of 0.007. If that value had been 0.006 or less,
    the Universe would have contained nothing but hydrogen. If it had been
    0.008 or higher, the hydrogen would have fused to make heavier elements. In
    either case, any kind of chemical complexity would have been physically
    impossible. And without chemical complexity there can be no life.
  • The physical possibility of chemical complexity is also dependent on the
    masses of the basic components of matter: electrons and quarks. If the mass
    of a down quark had been greater by a factor of 3, the Universe would have
    contained only hydrogen. If the mass of an electron had been greater by a
    factor of 2.5, the Universe would have contained only neutrons: no atoms at
    all, and certainly no chemical reactions.
  • Gravity seems a momentous force but it is actually much weaker than the
    other forces that affect atoms, by about 10^36 . If gravity had been only slightly
    stronger, stars would have formed from smaller amounts of material, and
    consequently would have been smaller, with much shorter lives. A typical
    sun would have lasted around 10,000 years rather than 10 billion years, not
    allowing enough time for the evolutionary processes that produce complex
    life. Conversely, if gravity had been only slightly weaker, stars would have
    been much colder and hence would not have exploded into supernovae. This
    also would have rendered life impossible, as supernovae are the main source
    of many of the heavy elements that form the ingredients of life.

This is the cosmological equivalent of tweaking the rules of your favorite game and then finding out it is unplayable. If the laws of physics differed slightly from what they are now, life as we know it wouldn’t stand a chance. It appears every law was formulated to lie just inside the narrow range that allows complex organisms like us to exist.

When we consider the fact life is highly uncommon in our current universe, and the second-order fact that it was incredibly unlikely the fundamental structure of said universe could be compatible with even the potential for life, our existence looks even more astounding. Roger Penrose —winner of a Nobel prize in physics with Stephen Hawking— calculated the odds of a universe such as ours being created by chance as one in 10^1,200. Lee Smolin, another physicist, calculates the probability of life arising in the universe as 10^229. These estimates differ by about a thousand orders of magnitude, but their point is clear. If left to chance, nature conspires against us.

It’s natural to find these odds unsettling. “But,” someone might say, “we exist! The odds say it’s nearly impossible for us to be around, yet here we are. If something so improbable happens there has to be some explanation for it that doesn’t appeal to pure chance.” Here, we reach for God. If the universe wasn’t the result of a random process but the product of a creator with life in mind, it’s much easier to believe we exist despite the astronomical odds against us. God is a much more satisfying, and, in a certain sense, more simple, explanation than blind luck. As the reasoning goes, a low probability of life existing in the universe, coupled with the fact life actually exists, constitutes evidence of a creator.


There’s an alternative perspective to probability and God. Life being necessary, in some sense, should be evidence of a creator. If God exists, we assume she wants life to come about and will not tolerate the possibility it could be otherwise. Such a God would make it impossible for a universe to exist that cannot support life, like us.

For instance, if we discovered there was a 99.99% chance any given universe could support life, wouldn’t this mean that possible universes were optimized for our presence? What better evidence of God could there be than odds stacked in our favor? If anything, a low probability of life originating in the universe might be an indication our existence was somehow left to chance. It’s possible we would not have existed, and that is incompatible with there being a God.

These two camps, those that stress the improbability of life, and those that stress its necessity, are at odds. One claims a low probability of life arising in the universe is evidence of God, while the other asserts high probabilities are. In other words, they use opposite premises to draw identical. At first pass, one of the camps has to be wrong. After all, how can low and high probabilities both be evidence for God? Does this mean we get the evidence either way? Did I just prove the existence of God? Definitely not. Probabilistic inference appears to have gone awry, and we’re going to get to the bottom of it.

Interpreting probability (can skip if frequency-type/objective and belief-type/subjective probabilities are familiar)

There are two ways to interpret probability. The first is characterized by statements like:

“There is a 60% chance you draw a red marble out of the urn.”

“The odds of getting pocket aces is 6/1326.”

“You will only win the lottery 1 out of 12 million times.”

Here, we use probability to talk about the outcomes of repeatable chance events. In this sense, a probability tells you, on average, how frequently an outcome occurs per some number of events. “60%” in the first sentence tells us, on average, if we draw 10 marbles out of the urn 6 of them will be red. Likewise, “6/1326” in the second sentence tells us that if we play 1326 hands of poker we should expect 6 pocket aces. In each case, the probability tells us about the distribution of a certain occurrence over a number of trials. We learn something about how often a chance event yields a specific outcome. This is the frequency-type interpretation of probability.

The second interpretation of probability is characterized by statements like:

“I am 90% sure I left my keys at home.”

“The odds of getting Thai food tonight are 1/10.”

“What’s the probability Trump wins the election? I say 28.6%”

These statements are similar to the others in that they use fractions and percents to express probabilities. The similarities end there. Rather than describe the outcomes of chance events, they express subjective levels of confidence in a belief. This is called the belief-type interpretation of probability. Higher probabilities correspond to more certainty in a belief, while lower ones express doubt. For instance, saying there is a “1/10” chance of getting Thai food means you are very unsure it will happen. Saying there’s a “90%” chance you left your keys elsewhere means you’re very confident you don’t have your keys.

It’s important to note that the frequency and belief-type interpretations apply to different things. We formulate frequency-type probabilities about the outcomes of chance events, like poker hands and lottery-drawings. Belief-type probabilities do not apply to chance events. They’re used to describe our subjective degree of confidence in statements about the world, like who is going to win an election or what we are going to eat tonight.

Reconciling the two camps

In the arguments given for God, which interpretation of probability is operative?

Frequency-type looks unlikely. The creation of a universe does not appear to be the outcome of a repeatable chance event, like drawing a marble from an urn. By most scientific accounts, there was a single “Big Bang” that yielded our universe, and there will never be a similar moment of creation. Because the event is unique, it makes no sense to talk about the frequency of a certain occurrence over a number of trials. We cannot say whether a universe containing life will arise 1 out of 10^10 times as it’s impossible to create 10^10 universes and observe what happens.

Belief-type probabilities don’t run into these difficulties. It’s coherent to say you have more or less confidence God created the universe, though a bit unnatural to express the sentiment as a probability. However, philosophers wrestle with how to further interpret belief-type probabilities and discover complications. Many take belief-type probabilities as the odds an individual would set for an event to avoid being dutch-booked. This view has the advantages of being intuitive and mathematical, but the betting analogy breaks under select circumstances. Individuals might refrain from setting odds (and if we compelled them, would those odds be accurate?), and it’s not clear there’s a single, precise number that we would set the odds at to express our confidence in a proposition.

While belief-type probabilities appear to be the best choice, I’m going to ignore them. This is because my “solution” to this issue relies on a frequency-type interpretation of probability so I’m going to shamelessly ignore the alternative. We will assume the creation of our universe is the outcome of a repeatable chance event. It’s also true belief-type probabilities have been critiqued in the context of reasoning about religious hypotheses, but I will not discuss such objections.

Using frequency-type probabilities can also be somewhat legitimate. We can circumvent the objections to using it in reference to the creation of the universe with a multiverse theory. If you believe multiple universes have been created — perhaps there are 10^10 parallel universes, for example — it’s perfectly acceptable to use a frequency-type probability to describe the odds of life arising. Your statement simply expresses the odds of picking a universe with life at random out of all the created universes. Personally, I have no idea whether multiverse theories are actually plausible, but this is a potential way to justify a frequency-type interpretation.

Given the above, I don’t think the two camps are incompatible with each other. It’s possible for low and high probabilities of life to serve as evidence for God. Both parties are making valid inferences from the probabilistic evidence they have. The caveat is that I believe each can only argue for a certain type of God.

Consistent with our assumption the creation of the universe is the outcome of a repeatable chance event, imagine it is determined by the spin of a roulette wheel. Each slot in the wheel represents a possible universe, and wherever the ball lands, the universe corresponding to that slot is created. One slot might represent a universe with physical laws like our own, and compatible with life. Another slot might represent a universe so different from ours that life could never originate.

Those who think low probabilities of life are evidence of God might imagine the roulette wheel of possible universes to be enormous. There are trillions of possible slots, and only a handful of them will correspond to universes that contain life. The probability the ball lands in a slot that creates a universe containing life will be minuscule. Yet, our universe exists and contains life. Since it defied nearly-impossible odds, the reasoning goes, it must have had some assistance beyond pure chance. The “assistance” in roulette wheel terms might be thought of as God picking up the ball and deliberately placing it in a slot corresponding to life. God intervenes in the chance event, making the highly improbable, actual.

The high-probability camp’s perspective can also be thought of in terms of the roulette wheel. In this case, a high probability of life would translate into every slot in the wheel corresponding to a universe where life exists. No matter where the ball lands, a hospitable universe will be created. Chance can select any slot it desires, but the outcome will be the same. God enters the picture when we ask ourselves who made the roulette wheel and dictated the nature of possible universes. The wheel being as it is constitutes evidence of an intention to bring life about. In this instance, God creates living things by stacking the odds in our favor.

When we consider how both camps might imagine God, the tensions between them fade. High and low probabilities of life can both constitute evidence of a creator because they support different versions of her. Low probabilities imply the existence of a God that chose our universe out of innumerable alternatives. High probabilities suggest a God that creates life by making a desolate universe metaphysically impossible.

This doesn’t guarantee either type of God exists, though. Individuals may use high or low probabilities of life arising in the universe as evidence for certain types of Gods, but how effective these arguments are is an open question. At any rate, neither line of reasoning abuses probability.



pandemics and ethnic violence

We begin with two questions:

  1. Under what conditions will a population persecute an ethnic minority during and after a pandemic?
  2. Who is most likely to instigate the violence?

Their answers are important. In case you haven’t heard, a deadly coronavirus has surfaced in Wuhan, China, and has now spread around the world. Some hold Asians responsible for the pandemic and act on their prejudice. A 16-year-old Asian-American boy in the San Fernando Valley was assaulted and sent to the emergency room after being accused of having the virus. In Texas, an assailant stabbed an Asian family in line at a Sam’s Club. Asians in communities like Washington D.C. and Rockville, Maryland are purchasing firearms en masse in an attempt to protect themselves. If general answers to our questions exist they may suggest ways to relieve ethnic tensions and prevent additional violence.

We turn to medieval Europe for guidance. It experienced a horrifying pandemic followed by decades of severe antisemitism. Our best bet to understand these questions is to examine the Black Plague and the subsequent treatment of medieval Jews.

The Black Plague

Without exaggeration, the Black Plague (also called the Black Death) was the worst pandemic in human history. From 1347, when it arrived in Italy, to 1351, between 40 and 60 percent of the entire European population perished. Aggregate figures obscure the losses of individual towns. Eighty percent of residents died in some locales, effectively wiping cities off the map (Jedwab et al., 2018). France was hit so hard that it took approximately 150 years for its population to reach pre-plague levels. Medieval historians attempted to capture the devastation of the plague by describing ships sailing aimlessly on the sea, their crews dead, and towns so empty that “there was not a dog left pissing on the wall” (Lerner, 1981).

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Source: (Jedwab et al., 2018)

The statistics are scary, but the plague was also visually terrifying. After catching the disease from an infected flea an individual develops black buboes (lumps) in the groin and neck areas, vomits blood, and dies within a week. In severe cases, plague-causing bacteria circulate through the bloodstream and cause necrosis in the hands and feet, leading them to turn black and die while still attached to the body. As soon as these symptoms develop, victims usually pass within 24 hours. Seeing most of your acquaintances develop these symptoms and die was arguably more psychologically damaging than actually contracting the disease yourself.

The scientific response, if it can be called one, to the pandemic was weak. Medieval medicine was still in the throes of miasma theory, which held that disease was spread by “bad air” that emanated from decomposing matter. Still, miasma was deemed an insufficient explanation for a calamity of this size. The most educated in medieval Europe saw the plague not as a natural phenomenon beyond the grasp of modern medicine, but as a cosmic indicator of God’s wrath. Chroniclers claim the plague originated from sources as diverse as “floods of snakes and toads, snows that melted mountains, black smoke, venomous fumes, deafening thunder, lightning bolts, hailstones, and eight-legged worms that killed with their stench” all ostensibly sent from above to punish man for his sins (Cohn, 2002). A common addendum was that these were all caused in one way or another by Jews, but we’ll get to that later.

Some explanations, if squinted at, bear a passing resemblance to the secular science of today. They invoked specific constellations and the alignment of planets as the instigators of the plague, drawing out an effect from a non-divine cause. How exactly distant celestial objects caused a pandemic is unclear from their accounts, though.

In general, medieval explanations of the plague reek of desperate mysticism. They had quite literally no idea of where the disease came from, how it worked, or how to protect themselves from it.

Medieval Jews

Jewish communities were widespread in Europe by the time the plague began. In the eighth century, many Jews had become merchants and migrated from what we today call the Middle East to Muslim Spain and southern Europe. Over the next two centuries, they spread northward, eventually reaching France and southern Germany before populating the rest of the region (Botticini & Eckstein, 2003). Jews were overwhelmingly located in large urban centers and specialized in skilled professions like finance and medicine. By the 12th century, scholars estimate that as many as 95% of Jews in western Europe had left farming and taken up distinctly urban occupations (Botticini & Eckstein, 2004).

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Map indicating percent of neighboring towns with resident Jews by 1347 in a limited dataset. In other words, it does not account for every town with a Jewish population in Europe but should give you some idea of settlement patterns. The fact England is devoid of Jews is not a limitation of the data; they were expelled from the region in 1290. Map source: (Jedwab et al., 2018)

Unfortunately, the medieval period offered Jews little respite from persecution. Antisemitism was constant and institutionalized, as Christianity was the official religion of most states. Restrictions were placed on the ability of Jews to proselytize, worship, and marry. For example, in 1215, the Catholic Church declared that Jews should be differentiated from the rest of society via their dress to prevent Christians and Jews from accidentally having “sinful” intercourse. These rules eventually begot requirements that Jews wear pointed hats and distinctive badges, foreshadowing the infamous yellow patches of the Holocaust.

Medieval antisemitism was violent as well as bureaucratic. Pope Urban II fueled Christian hysteria by announcing the First Crusade in 1096, and shortly after, bands of soldiers passing through Germany on their way to wage holy war in Jerusalem killed hundreds of Jews in what became known as the Rhineland Massacres. These attacks were so brutal that there are accounts of Jewish parents hearing of a massacre in a neighboring town and killing their own children, and then themselves, rather than face the crusaders. Explanations for these massacres vary. Some scholars claim they were fueled by the desire to seize the provisions of relatively wealthy Jews in preparation for travel to the Middle East. Others attribute them to misplaced religious aggression intended for Muslims but received by Jews due to their proximity and status as “non-believers.” While there are earlier recorded instances of antisemitism, the pogroms of the First Crusade are believed to represent the first major instance of religious violence against the Jews.

Strangely, the Medievals seem to vacillate between ethnic loathing and appreciation for Jewish economic contributions. The Catholic Church forbade Christians from charging interest on loans in 1311, allowing Jews to dominate the profession. As a result, they were often the only source of credit in a town and hence were vital to nobility and the elite. This, coupled with Jews’ predilection to take up skilled trades, gave leaders a real economic incentive to encourage Jewish settlement. Rulers occasionally offered Jews “promises of security and economic opportunity” to settle in their region (Jedwab et al., 2018).

The Black Plague and Medieval Jews

As mentioned, the plague was a rapid, virulent disease with no secular explanation, and the Jews were a minority group—the only non-Christians in town—with a history of persecution. Naturally, they were blamed. Rumors circulated that Jews manufactured poison from frogs, lizards, and spiders, and dumped it in Christian wells to cause the plague. These speculations gained traction when tortured Jews “confessed” to the alleged crimes.

The results were gruesome. Adult Jews were often burned alive in the city square or in their synagogues, and their children forcibly baptized. In some towns, Jews were told they were merely going to be expelled but were then led into a wooden building that was promptly set ablaze. I will spare additional details, but these events spawned a nauseating genre of illustrations if one is curious. As the plague progressed, more than 150 towns recorded pogroms or expulsions in the five-year period between 1347 and 1351. These events, more so than the Rhineland massacres, shaped the distribution of Jewish settlement in Europe for centuries afterward.

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Black Death Jewish pogroms on a map of the Weimar Republic (early 20th century Germany). “No data” means there are no records of Jewish settlement in the area at the time of the Black Death (Voigtländer & Voth, 2012).

If we can bring ourselves to envision these pogroms, we imagine a mob of commoners whipped up into a spontaneous frenzy. Perhaps they have pitchforks. Maybe they carry clubs. Given what we know about the economic role of medieval Jews, you might impute a financial motive upon the villagers. It’s possible commoners owed some debt to the Jewish moneylenders that would be cleared if the latter died or left town. If asked what income quintile a mob member falls into, you might think that’s a strange question, and then respond the lowest. Their pitchforks indicate some type of subsistence farming, and only the poorest and least enlightened would be vulnerable to the crowd mentality that characterizes such heinous acts, you would think.

If so, it might be surprising to hear the Black Death pogroms were instigated and performed by the elite of medieval society. (Cohn, 2007) writes that “few, if any, [medieval historians] pointed to peasants, artisans, or even the faceless mob as perpetrators of the violence against the Jews in 1348 to 1351.” Bishops, dukes, and wealthy denizens were the first to spread the well-poisoning rumors and were the ones to legally condone the violence. Before even a single persecution in his nation took place, Emperor Charles IV of Bohemia had already arranged for the disposal of Jewish property and granted legal immunity to knights and patricians to facilitate the massacres. When some cities expressed skepticism at the well-poisoning allegations, aristocrats and noblemen, rather than the “rabble,” gathered at town halls to convince their governments to burn the Jews. Plague antisemitism, by most accounts, was a high-class affair.

Mayors and princes recognized the contagious nature of violence. If elites persecuted the Jews, they thought, the masses might join in and the situation could spiral out of control. As a result, the wealthy actively tried to exclude the poor from antisemitic activities. Prior to a pogrom, the wealthy would circulate rumors of well-poisoning. Those of means would then capture several Jews, torture them into “confessing,” and then alert the town government. Its notaries would record the accusations, and the matter would be presented before a court. After a (certain) guilty verdict, patrician leaders would gather the Jews and burn them in the town square or synagogue. Each step of the process was self-contained within the medieval gentry, providing no opportunity for commoners to amplify the violence beyond what was necessary. Mass persecutions often take the form of an entire society turning against a group, but the medieval elites sought to insulate a substantial amount of their population from the pogroms. Ironically, they feared religious violence left unchecked [1].

Persecutions were widespread, but not universal. (Voigtländer & Voth, 2012) say only 70 percent of towns with a Jewish population in plague-era Germany either expelled or killed their Jews. To be sure, 70 percent is a substantial figure, but the fact it is not 100 percent demonstrates that there were conditions under which ethnic violence would not ensue. What were these conditions?

In pursuing this question, (Jedwab et al., 2018) observed something strange. As plague mortality increased in some towns, the probability Jews would be persecuted actually decreased. A town where only 15 percent of inhabitants died is somehow more antisemitic than one where 40 percent did. How odd. Common sense tells us that the more severe an unexplained disaster, the stronger the incentive to resolve ambiguity and blame an outgroup. Why reserve judgment when things are the worst?

It turns out economic incentives were stronger than the desire to scapegoat. Jedwab only observed the inverse relationship between mortality and probability of persecution in towns where Jews provided moneylending services. The Jews’ unique economic role granted them a “protective effect,” changing the decision calculus of would-be persecutors. It’s true there’s still an incentive to persecute Jews since debts would be cleared if the moneylenders died, but this is a short-term gain with long-term consequences. If all Jews in a town are eliminated then future access to financial services is gone. Everyone in town would be a Christain, and thus forbidden from extending credit. As mortality increases, Jews qua moneylenders became increasingly valuable, since killing or expelling them would exacerbate the economic crisis that accompanies losing a significant fraction of your population. As a result, they were spared [2].

This is consistent with the picture we developed earlier of the upper classes undertaking plague pogroms. Often, only the wealthy utilized Jewish financial services, thus only they were sensitive to the financial implications of killing the sole bankers in town (Cohn 2007). If commoners were the major perpetrators of Black Death massacres, Jedwab and colleagues would probably not encounter evidence of a protective effect tied to Jewish occupations. Indeed, they looked for, and could not find, the protective effect in towns where Jews were doctors, artisans, or merchants. It only appeared when they provided financial services.

Persecution frequency also fell dramatically after the initial wave of the plague. The disease made semi-frequent appearances in the decades and centuries after 1347, but not one of them sparked as much violence as the first bout. A potential explanation is that many Jews had already been killed or expelled from their towns, leaving nobody to persecute. Plague severity was lower in later recurrences, so there might have been less of an incentive to persecute a minority for a mild natural disaster as opposed to a major one.

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Jewish persecutions by date. Source: (Jedwab et al., 2018)

I’ll describe a somewhat rosier phenomenon that could have contributed to this decline in persecutions. Remember that the medieval intellectual elite was clueless when it came to the causal mechanisms of the plague. Among other theories, they believed it spread via bad air, worm effluvium, frogs and toads that fell from the sky, the wrath of God, or Jewish machinations. Because Jews were the only salient member of this list present in most towns, they had borne the brunt of popular frustration and become a scapegoat [3].

Yet, science progressed slowly. By 1389, roughly 40 years after Europe’s first encounter with the plague, doctors noticed that mortality had fallen after each successive recurrence of the disease. Instead of attributing this to fewer toads in the atmosphere or less worm stench, they settled on the efficacy of human interventions. Institutions had learned how to respond —the quarantine was invented in this period— and medicine had progressed (Cohn 2007). Medievals had increasingly effective strategies for suppressing the plague and none of them involved Jews. Blaming them for subsequent  outbreaks would be downright irrational as you would be diverting time and resources away from interventions that were known to work.

I want to be clear that this did not end antisemitism in Europe. Jews for centuries were —and still are— killed over all types of non-plague related allegations like host desecration, blood libel, and killing Jesus. Yet, they enjoyed a period of relative calm after the first wave of the Black Death, in part, I believe, because their persecutors had begun to understand the actual causes of the disease.


1. Under what conditions will a population persecute a minority?

Persecutions are more likely when members of the minority in question don’t occupy an essential economic niche. Jews as moneylenders provided a vital service to members of the medieval elite, so the prospect of killing or expelling their only source of credit may have made them think twice about doing so.

2. Who is most likely to instigate the violence?

Wealthy, high-status members of medieval society instigated and undertook the Black Plague pogroms. They were responsible for spreading well-poisoning rumors, extracting “confessions,” processing and ruling on accusations, and attacking Jewish townsfolk. Some medieval elites even conspired to insulate the poor from this process for fear of the violence escalating beyond control.

How applicable are these conclusions? Can they tell us anything specific about ethnic violence and COVID-19?

Probably not. For starters, the world today looks nothing like it did during the 14th century. The Medievals may have discovered how to attenuate the effects of the plague, but it remained more or less a mystery for centuries afterward. We didn’t get germ theory until the 19th century, and it wasn’t until 1898 that Paul-Louis Simond discovered the plague was transmitted to humans through fleas.

Perhaps as a result of scientific progress, we’re also much less religious, or nature of our religiosity has changed. Very few believe hurricanes are sent by God to punish sinners, and we don’t supply theological explanations of why the ground trembles in an earthquake. We have scientific accounts of why nature misbehaves. As a result, we’re skeptical of (but not immune to) claims that a minority ethnic group is the source of all our problems. In short, we have the Enlightenment between us and the Medievals.

Cosmopolitanism is also on our side. Jews were often the only minority in a town and were indistinguishable without special markers like hats and badges. To this day, parts of Europe are still pretty ethnically homogeneous, but every continent has hubs of multiculturalism. 46% percent of people in Toronto were born outside Canada. 37 percent of Londoners hail from outside the UK. Roughly 10 percent of French residents are immigrants. All this mixing has increased our tolerance dramatically relative to historical levels.

Perhaps most importantly, COVID-19 is not even close to the plague in terms of severity. The medical, economic, and social ramifications of this pandemic are dire, but we are not facing local death rates of 80 percent. We do not expect 40 to 60 percent of our total population to die. COVID-19 is a challenge that is taxing our greatest medical minds, but we have a growing understanding of how it functions and how to treat it. It’s definitely worse than the flu, but it’s no Black Plague.

An investigation into the Black Plague and medieval Jews can provide historical perspective, but its results are not easily generalizable to the current situation. The best we can say is that when things are bad and people are ignorant of the causes, they will blame an outgroup they do not rely on economically. The cynical among us perhaps could have intuited this. Thankfully, things aren’t as bad now as they were in 1347, and we are collectively much less ignorant than our ancestors. We’ve made progress, but intolerance remains a stubborn enemy. What Asians already have, and will, endure as a result of this pandemic supports this.



Huge thanks to Michael Ioffe and Jamie Bikales for reading drafts.



[1] I draw heavily on (Cohn, 2007) in the preceding two paragraphs. It’s definitely true some pogroms were instigated and undertaken by the poor while the elites sought to protect the Jews. For instance, Pope Clement VI issued an (unheeded) papal bull absolving Jews of blame. Yet, Cohn has convinced me (an amateur) that these cases constitute a minority.

Still, the class demographics of medieval pogroms are a matter of scholarly debate. (Gottfried, 1985) describes members of Spanish royalty unsuccessfully attempting to protect their Jewish denizens. However, he does not specify whether the antisemitism was primarily instigated by the masses or regional leaders. (Jedwab et al., 2018) mentions “citizens and peasants” storming a local Jewish quarter, but whether local antisemitism was spurred by the gentry or not is also unclear. (Haverkamp, 2002) supposedly also argues for the commoner-hypothesis, but the article is written in German and thus utterly inaccessible to me.

[2] A simple alternate explanation for the inverse relation between mortality and probability of persecution is that there are fewer people left to facilitate a pogrom or expulsion at higher levels of mortality. Jedwab and colleagues aren’t convinced. They note that the plague remained in a town for an average of 5 months, and people weren’t dying simultaneously. It’s entirely possible that even at high mortality a town can muster enough people to organize a pogrom. Also, many of the persecutions were preventative. Some towns burned their Jewish population before the plague had even reached them in an attempt to avert catastrophe.

[3] God was also “present” —in the form of churches and a general religious atmosphere— in medieval Europe, so he was another popular figure to attribute the plague to. However, you can’t really blame God in a moral sense for anything he does, so adherents to this view blamed themselves. So-called “flagellants” traveled from town to town lashing themselves in an attempt to appease God’s wrath and earn salvation. This was strange and radical even by medieval standards. Pope Clement thought the movement heretical enough to ban it in 1349 (Kieckhefer 1974).



What I cited

(These are all the scholarly sources. My guideline is that if I downloaded something as a pdf and consulted it, it’ll be here. Otherwise, it’s linked in the text of the post).

Botticini, M., & Eckstein, Z. (2003, January). From Farmers to Merchants: A Human Capital Interpretation of Jewish Economic History.

Botticini, M., & Eckstein, Z. (2004, July). Jewish Occupational Selection : Education, Restrictions, or Minorities? IZA Discussion Papers, No. 1224.

Cohn, S. (2002). The Black Death: End of a Paradigm. American Historical Review .

Cohn, S. (2007). The Black Death and the Burning of Jews. Past and Present(196).

Gottfried, R. S. (1985). The Black Death: Natural and Human Disaster in Medieval Europe. Free Press.

Haverkamp, A. (2002). Geschichte der Juden im Mittelalter von der Nordsee bis zu den Su¨dalpen. Kommentiertes Kartenwerk. Hannover, Hahn.

Jedwab, R., Johnson, N. D., & Koyama, M. (2018, April). Negative Shocks and Mass Persecutions: Evidence from the Black Death. SSRN.

Kieckhefer, R. (1974). Radical tendencies in the flagellant movement of the mid-fourteenth century. Journal of Medieval and Renaissance Studies, 4(2).

Lerner, R. E. (1981, June). The Black Death and Western European Eschatological Mentalities. The American Historical Review, 533-552.

Voigtländer, N., & Voth, H.-J. (2012). PERSECUTION PERPETUATED: THE MEDIEVAL ORIGINS OF ANTI-SEMITIC VIOLENCE IN NAZI GERMANY*. The Quarterly Journal of Economics, 1339-1392.