The sausage of statistics being made

 

Nov 11 JDN 2458434

“Laws, like sausages, cease to inspire respect in proportion as we know how they are made.”

~ John Godfrey Saxe, not Otto von Bismark

Statistics are a bit like laws and sausages. There are a lot of things in statistical practice that don’t align with statistical theory. The most obvious examples are the fact that many results in statistics are asymptotic: they only strictly apply for infinitely large samples, and in any finite sample they will be some sort of approximation (we often don’t even know how good an approximation).

But the problem runs deeper than this: The whole idea of a p-value was originally supposed to be used to assess one single hypothesis that is the only one you test in your entire study.

That’s frankly a ludicrous expectation: Why would you write a whole paper just to test one parameter?

This is why I don’t actually think this so-called multiple comparisons problem is a problem with researchers doing too many hypothesis tests; I think it’s a problem with statisticians being fundamentally unreasonable about what statistics is useful for. We have to do multiple comparisons, so you should be telling us how to do it correctly.

Statisticians have this beautiful pure mathematics that generates all these lovely asymptotic results… and then they stop, as if they were done. But we aren’t dealing with infinite or even “sufficiently large” samples; we need to know what happens when your sample is 100, not when your sample is 10^29. We can’t assume that our variables are independently identically distributed; we don’t know their distribution, and we’re pretty sure they’re going to be somewhat dependent.

Even in an experimental context where we can randomly and independently assign some treatments, we can’t do that with lots of variables that are likely to matter, like age, gender, nationality, or field of study. And applied econometricians are in an even tighter bind; they often can’t randomize anything. They have to rely upon “instrumental variables” that they hope are “close enough to randomized” relative to whatever they want to study.

In practice what we tend to do is… fudge it. We use the formal statistical methods, and then we step back and apply a series of informal norms to see if the result actually makes sense to us. This is why almost no psychologists were actually convinced by Daryl Bem’s precognition experiments, despite his standard experimental methodology and perfect p < 0.05 results; he couldn’t pass any of the informal tests, particularly the most basic one of not violating any known fundamental laws of physics. We knew he had somehow cherry-picked the data, even before looking at it; nothing else was possible.

This is actually part of where the “hierarchy of sciences” notion is useful: One of the norms is that you’re not allowed to break the rules of the sciences above you, but you can break the rules of the sciences below you. So psychology has to obey physics, but physics doesn’t have to obey psychology. I think this is also part of why there’s so much enmity between economists and anthropologists; really we should be on the same level, cognizant of each other’s rules, but economists want to be above anthropologists so we can ignore culture, and anthropologists want to be above economists so they can ignore incentives.

Another informal norm is the “robustness check”, in which the researcher runs a dozen different regressions approaching the same basic question from different angles. “What if we control for this? What if we interact those two variables? What if we use a different instrument?” In terms of statistical theory, this doesn’t actually make a lot of sense; the probability distributions f(y|x) of y conditional on x and f(y|x, z) of y conditional on x and z are not the same thing, and wouldn’t in general be closely tied, depending on the distribution f(x|z) of x conditional on z. But in practice, most real-world phenomena are going to continue to show up even as you run a bunch of different regressions, and so we can be more confident that something is a real phenomenon insofar as that happens. If an effect drops out when you switch out a couple of control variables, it may have been a statistical artifact. But if it keeps appearing no matter what you do to try to make it go away, then it’s probably a real thing.

Because of the powerful career incentives toward publication and the strange obsession among journals with a p-value less than 0.05, another norm has emerged: Don’t actually trust p-values that are close to 0.05. The vast majority of the time, a p-value of 0.047 was the result of publication bias. Now if you see a p-value of 0.001, maybe then you can trust it—but you’re still relying on a lot of assumptions even then. I’ve seen some researchers argue that because of this, we should tighten our standards for publication to something like p < 0.01, but that’s missing the point; what we need to do is stop publishing based on p-values. If you tighten the threshold, you’re just going to get more rejected papers and then the few papers that do get published will now have even smaller p-values that are still utterly meaningless.

These informal norms protect us from the worst outcomes of bad research. But they are almost certainly not optimal. It’s all very vague and informal, and different researchers will often disagree vehemently over whether a given interpretation is valid. What we need are formal methods for solving these problems, so that we can have the objectivity and replicability that formal methods provide. Right now, our existing formal tools simply are not up to that task.

There are some things we may never be able to formalize: If we had a formal algorithm for coming up with good ideas, the AIs would already rule the world, and this would be either Terminator or The Culture depending on whether we designed the AIs correctly. But I think we should at least be able to formalize the basic question of “Is this statement likely to be true?” that is the fundamental motivation behind statistical hypothesis testing.

I think the answer is likely to be in a broad sense Bayesian, but Bayesians still have a lot of work left to do in order to give us really flexible, reliable statistical methods we can actually apply to the messy world of real data. In particular, tell us how to choose priors please! Prior selection is a fundamental make-or-break problem in Bayesian inference that has nonetheless been greatly neglected by most Bayesian statisticians. So, what do we do? We fall back on informal norms: Try maximum likelihood, which is like using a very flat prior. Try a normally-distributed prior. See if you can construct a prior from past data. If all those give the same thing, that’s a “robustness check” (see previous informal norm).

Informal norms are also inherently harder to teach and learn. I’ve seen a lot of other grad students flail wildly at statistics, not because they don’t know what a p-value means (though maybe that’s also sometimes true), but because they don’t really quite grok the informal underpinnings of good statistical inference. This can be very hard to explain to someone: They feel like they followed all the rules correctly, but you are saying their results are wrong, and now you can’t explain why.

In fact, some of the informal norms that are in wide use are clearly detrimental. In economics, norms have emerged that certain types of models are better simply because they are “more standard”, such as the dynamic stochastic general equilibrium models that can basically be fit to everything and have never actually usefully predicted anything. In fact, the best ones just predict what we already knew from Keynesian models. But without a formal norm for testing the validity of models, it’s been “DSGE or GTFO”. At present, it is considered “nonstandard” (read: “bad”) not to assume that your agents are either a single unitary “representative agent” or a continuum of infinitely-many agents—modeling the actual fact of finitely-many agents is just not done. Yet it’s hard for me to imagine any formal criterion that wouldn’t at least give you some points for correctly including the fact that there is more than one but less than infinity people in the world (obviously your model could still be bad in other ways).

I don’t know what these new statistical methods would look like. Maybe it’s as simple as formally justifying some of the norms we already use; maybe it’s as complicated as taking a fundamentally new approach to statistical inference. But we have to start somewhere.

How much should we give?

Nov 4 JDN 2458427

How much should we give of ourselves to others?

I’ve previously struggled with this basic question when it comes to donating money; I have written multiple posts on it now, some philosophical, some empirical, and some purely mathematical.

But the question is broader than this: We don’t simply give money. We also give effort. We also give emotion. Above all, we also give time. How much should we be volunteering? How many protest marches should we join? How many Senators should we call?

It’s easy to convince yourself that you aren’t doing enough. You can always point to some hour when you weren’t doing anything particularly important, and think about all the millions of lives that hang in the balance on issues like poverty and climate change, and then feel a wave of guilt for spending that hour watching Netflix or playing video games instead of doing one more march. This, however, is clearly unhealthy: You won’t actually make yourself into a more effective activist, you’ll just destroy yourself psychologically and become no use to anybody.

I previously argued for a sort of Kantian notion that we should commit to giving our fair share, defined as the amount we would have to give if everyone gave that amount. This is quite appealing, and if I can indeed get anyone to donate 1% of their income as a result, I will be quite glad. (If I can get 100 people to do so, that’s better than I could ever have done myself—a good example of highly cost-effective slacktivism.)

Lately I have come to believe that this is probably inadequate. We know that not everyone will take this advice, which means that by construction it won’t be good enough to actually solve global problems.

This means I must make a slightly greater demand: Define your fair share as the amount you would have to give if everyone among people who are likely to give gave that amount.

Unfortunately, this question is considerably harder. It may not even have a unique answer. The number of people willing to give an amount n is obviously dependent upon the amount x itself, and we are nowhere close to knowing what that function n(x) looks like.

So let me instead put some mathematical constraints on it, by choosing an elasticity. Instead of an elasticity of demand or elasticity of supply, we could call this an elasticity of contribution.

Presumably the elasticity is negative: The more you ask of people, the fewer people you’ll get to contribute.

Suppose that the elasticity is something like -0.5, where contribution is relatively inelastic. This means that if you increase the amount you ask for by 2%, you’ll only decrease the number of contributors by 1%. In that case, you should be like Peter Singer and ask for everything. At that point, you’re basically counting on Bill Gates to save us, because nobody else is giving anything. The total amount contributed n(x) * x is increasing in x.

On the other hand, suppose that elasticity is something like 2, where contribution is relatively elastic. This means that if you increase the amount you ask for by 2%, you will decrease the number of contributors by 4%. In that case, you should ask for very little. You’re asking everyone in the world to give 1% of their income, as I did earlier. The total amount contributed n(x) * x is now decreasing in x.

But there is also a third option: What if the elasticity is exactly -1, unit elastic? Then if you increase the amount you ask for by 2%, you’ll decrease the number of contributors by 2%. Then it doesn’t matter how much you ask for: The total amount contributed n(x) * x is constant.

Of course, there’s no guarantee that the elasticity is constant over all possible choices of x—indeed, it would be quite surprising if it were. A quite likely scenario is that contribution is inelastic for small amounts, then passes through a regime where it is nearly unit elastic, and finally it becomes elastic as you start asking for really large amounts of money.

The simplest way to model that is to just assume that n(x) is linear in x, something like n = N – k x.

There is a parameter N that sets the maximum number of people who will ever donate, and a parameter k that sets how rapidly the number of contributors drops off as the amount asked for increases.

The first-order condition for maximizing n(x) * x is then quite simple: x = N/(2k)

This actually turns out to be the precisely the point at which the elasticity of contribution is -1.

The total amount you can get under that condition is N2/(4k)

Of course, I have no idea what N and k are in real life, so this isn’t terribly helpful. But what I really want to know is whether we should be asking for more money from each person, or asking for less money and trying to get more people on board.

In real life we can sometimes do both: Ask each person to give more than they are presently giving, whatever they are presently giving. (Just be sure to run your slogans by a diverse committee, so you don’t end up with “I’ve upped my standards. Now, up yours!”) But since we’re trying to find a benchmark level to demand of ourselves, let’s ignore that for now.

About 25% of American adults volunteer some of their time, averaging 140 hours of volunteer work per year. This is about 1.6% of all the hours in a year, or 2.4% of all waking hours. Total monetary contributions in the US reached $400 billion for the first time this year; this is about 2.0% of GDP. So the balance between volunteer hours and donations is actually pretty even. It would probably be better to tilt it a bit more toward donations, but it’s really not bad. About 60% of US households made some sort of charitable contribution, though only half of these received the charitable tax deduction.

This suggests to me that the quantity of people who give is probably about as high as it’s going to get—and therefore we need to start talking more about the amount of money. We may be in the inelastic regime, where the way to increase total contributions is to demand more from each individual.

Our goal is to increase the total contribution to poverty eradication by about 1% of GDP in both the US and Europe. So if 60% of people give, and currently total contributions are about 2.0% of GDP, this means that the average contribution is about 3.3% of the contributor’s gross income. Therefore I should tell them to donate 4.3%, right? Not quite; some of them might drop out entirely, and the rest will have to give more to compensate.
Without knowing the exact form of the function n(x), I can’t say precisely what the optimal value is. But it is most likely somewhat larger than 4.3%; 5% would be a nice round number in the right general range. This would raise contributions in the US to 2.6% of GDP, or about $500 billion. That’s a 20% increase over the current level, which is large, but feasible.

Accomplishing a similar increase in Europe would then give us a total of $200 billion per year in additional funds to fight global poverty; this might not quite be enough to end world hunger (depending on which estimate you use), but it would definitely have a large impact.

I asked you before to give 1%. I am afraid I must now ask for more. Set a target of 5%. You don’t have to reach it this year; you can gradually increase your donations each year for several years (I call this “Save More Lives Tomorrow”, after Thaler’s highly successful program “Save More Tomorrow”). This is in some sense more than your fair share; I’m relying on the assumption that half the population won’t actually give anything. But ultimately this isn’t about what’s fair to us. It’s about solving global problems.

Halloween is kind of a weird holiday.

Oct 28 JDN 2458420

I suppose most holidays are weird if you look at them from an outside perspective; but I think Halloween especially so, because we don’t even seem to be clear about what we’re celebrating at this point.

Christmas is ostensibly about the anniversary of the birth of Jesus; New Year’s is about the completion of the year; Thanksgiving is about the founding of the United States and being thankful for what we have; Independence Day is about declaring independence from Great Britain.

But what’s Halloween about, again? Why do we have our children dress up in costumes and go beg candy from our neighbors?

The name comes originally from “All Hallow’s Eve”, the beginning of the three-day Christian holiday Allhallowtide of rememberance for the dead, which has merged in most Latin American countries with the traditional holiday Dia de los Muertos. But most Americans don’t actually celebrate the rest of Allhallowtide; we just do the candy and costume thing on Halloween.

The parts involving costumes and pumpkins actually seem to be drawn from Celtic folk traditions celebrating the ending of harvest season and the coming of the winter months. It’s celebrated so early because, well, in Ireland and Scotland it gets dark and cold pretty early in the year.

One tradition I sort of wish we’d kept from the Celtic festival is that of pouring molten lead into water to watch it rapidly solidify. Those guys really knew how to have a good time. It may have originated as a form of molybdomancy, which I officially declare the word of the day. Fortunately by the power of YouTube, we too can enjoy the excitement of molten lead without the usual fear of third-degree burns. The only divination ritual that we kept as a Halloween activity is the far tamer apple-bobbing.

The trick-or-treating part and especially the costume part originated in the Medieval performance art of mumming, which is also related to the modern concept of mime. Basically, these were traveling performance troupes who went around dressed up as mythological figures, did battle silently, and then bowed and passed their hats around for money. It’s like busking, basically.

The costumes were originally religious or mythological figures, then became supernatural creatures more generally, and nowadays the most popular costumes tend to be superheroes. And since apparently we didn’t want people giving out money to our children, we went for candy instead. Yet I’m sure you could right a really convincing economics paper about why candy is way less efficient, making both the parents giving, the child receiving, and the parents of the child receiving less happy than the same amount of money would (and unlike the similar argument against Christmas presents, I’m actually sort of inclined to agree; it’s not a personal gesture, and what in the world do you need with all that candy?).

So apparently we’re celebrating the end of the harvest, and also mourning the dead, and also being mimes, and also emulating pagan divination rituals, but mainly we’re dressed up like superheroes and begging for candy? Like I said, it’s kind of a weird holiday.

But maybe none of that ultimately matters. The joy of holidays isn’t really in following some ancient ritual whose religious significance is now lost on us; it’s in the togetherness we feel when we manage to all coordinate our activities and do something joyful and out of the ordinary that we don’t have to do by ourselves. I think deep down we all sort of wish we could dress up as superheroes more of the time, but society frowns upon that sort of behavior most of the year; this is our one chance to do it, so we’ll take the chance when we get it.

How to respond to dog whistles

Oct 21 JDN 2458413

Political messaging has grown extremely sophisticated. The dog whistle technique is particularly powerful one: it allows you to say the same thing to two different groups and have them each hear what they wanted to hear. The term comes from the gadget used in training canines, which emits sounds at a frequency which humans can’t hear but dogs can. Similar concepts have been around for a long time, but the word wasn’t used for this specific meaning until the 1990s.

There was once a time when politicians could literally say different things to different groups, but mass media has made that effectively impossible. When Mitt Romney tried to do this, it destroyed his (already weak) campaign. So instead they find ways to convey two different meanings, while saying the same words.

Classic examples of this include “law and order” and “states’ rights”, which have always carried hidden racist connotations, yet on their face sound perfectly reasonable. “Family values” is another one.

Trump is particularly inelegant at this; his dog whistles often seem to drop into the audible frequency range, as when he called undocumented immigrants (or possibly gang members?) “animals” and tweeted about “caravans” of immigrants, and above all when he said “they’re bringing drugs, they’re bringing crime, they’re rapists”. (Frankly, does that even count as a dog whistle?) He’s a little less obvious in his deployment of “globalist” as a probable anti-Semitic slur.

How should we respond to this kind of coded language?

It’s not as simple as you might think. It’s not always easy to tell what is a dog whistle. Someone talking about crime could be trying to insinuate something about minorities… or, they could just be talking about crime. Someone complaining about immigration could be trying to dehumanize immigrants… or, they could just want a change in our border policy. Accusations of “globalism” could be coded anti-Semitism… or they could just be nationalism.
It’s also easy to accuse someone of using dog whistles even if they probably aren’t: It is now commonplace for the right wing to argue that “common-sense gun control” means confiscating all handguns (when it in fact means universal background checks, mandatory safety classes, and perhaps assault weapon bans and magazine limits, all of which are quite popular even among gun owners), or to argue that “safe, legal, and rare” is just a Trojan horse for unrestricted free abortion (when in fact “safe, legal, and rare” is the overwhelming majority view among Americans). Indeed, it’s quite probable that many of the things that the left wing has taken as dog whistles by Trump were actually overreactions—Trump is bigoted, but not especially so by the standards of old White Republican men. The best reasons to want Trump out of office involve his authoritarianism, his corruption, and his incompetence, not his bigotry. Foreign policy and climate change should be issues that overwhelm basically everything else—these are millions of lives on the line—and they are the two issues that Trump gets most decisively wrong.

The fact that it can be difficult to tell which statements are dog-whistles is not a bug but a feature: It provides plausible deniability.

If you can structure your speech so that it will be heard by your base as supporting a strong ideological platform, but when the words are analyzed they will be innocuous enough that no one can directly prove your extremism, you can have your cake and eat it too. Even if journalists go on to point out the dog whistles in your speech, moderates on your side of the fence might not hear the same dog whistles, and then just become convinced that the journalists are overreacting. And they might even be overreacting.

Instead, I think there are two things we need to do, which are distinct but complementary.’

1. Ask for clarification.

Whether you are in a personal conversation with a friend who is spouting talking points, or a journalist interviewing a politician running for office, there will come opportunities where you can directly respond to a potential dog whistle.
Do not accuse them of using a dog whistle—even if you are confident that they are. That will only make them defensive, and make you appear to be the aggressor. Instead, ask them firmly, but calmly:

What exactly do you mean by that statement?”

If they ignore the question or try to evade it, ask again, a little more firmly. If they evade again, ask again. Keep asking until they answer you or literally force you to shut up. Be confident, but calm and poised. Now they look like the aggressor—and above all, they sound like they have something to hide.

Note also that if it turns out not to be a dog whistle, they will likely not be offended by your request and will have a perfectly reasonable clarification. For example:

“What did you mean when you said you’re worried about Muslim immigrants?”

“Well, I mean that Muslim societies often have very regressive norms surrounding gender and LGBT rights, and many Muslim immigrants have difficulty assimilating into our liberal values. I think we need to spend more effort finding ways to integrate Muslims into our community and disabuse them of harmful cultural norms.”

“What did you mean when you said you are worried about law and order?”

“I mean that gang violence in several of our inner cities is really out of control, and we need to be working on both investing more in policing and finding better methods of crime prevention in order to keep these communities safe.”

“What ‘states’ rights’ are you particularly concerned about, Senator?”

“I don’t like that the federal government thinks it can impose laws against marijuana based on an absurdly broad reading of the Interstate Commerce Clause. I don’t think it’s right that legitimate businesses in California and Colorado have to operate entirely in cash because federal regulations won’t let them put their money into banks without fear of having it confiscated.”

You may even find that you still disagree with the clarified statement, but hopefully it can be a reasonable disagreement, rather than a direct conflict over fundamental values.

2. State your own positive case.

This is one you can probably do even if you don’t actually get the opportunity to engage directly with people on the other side.

I was actually surprised to learn this, but apparently the empirical data shows that including messages of social justice in your political platform makes it more popular, even among moderates.
This means that we don’t have to respond to innuendo with innuendo—we can come out and say that we think a given policy is bad because it will hurt women or Black people. Economic populism is good too, but we don’t need to rely entirely upon that.

To be clear, we should not say that the policy is designed to hurt women or Black people—even if we think that is likely to be true—for at least two reasons: First, we can’t actually prove that, except in very rare cases, so it makes our argument inherently more tendentious; and second, it makes our whole mode of argumentation more aggressive and less charitable. We should always at least consider the possibility that our opponent’s intentions are noble, and unless the facts utterly force us to abandon that view it should probably be our working assumption.

This means that we don’t even necessarily have to come out and challenge dog whistles. We just need to make a better positive case ourselves. While they are making vague, ambiguous claims about “cleaning up our cities” and “making America great”, we can lay out explicit policy plans for reducing unemployment, poverty, and carbon emissions.

Hillary Clinton almost did this—but she didn’t do it well enough. She relied too heavily on constituents being willing to read detailed plans on her website, instead of summarizing them in concise, pithy talking points to put in headlines. Her line Because we’re going to put a lot of coal miners and coal companies out of business, right?” was indeed taken out of contextbut she should have pushed harder by making an actual slogan, like “End coal burning—save coal communities.” (I literally came up with that in five minutes. She had hundreds of professional campaign staff working for her and they couldn’t do better?) The media did butcher her statements—but she didn’t correct them by putting slogans on yard signs or giving stump speeches in Appalachia.

Indeed, the news media didn’t do her any favors—they spent literally more time talking about her emails than every actual policy issued combined, and not by a small margin. But we can’t rely on the news media—and we don’t have to, in the age of blogs and social media. Instead of assuming that everyone already agrees with us and we will win because we deserve to, we need to be doing what actually works at conveying our message and making sure that we win by the largest margin possible.

If you really want grad students to have better mental health, remove all the high-stakes checkpoints

Post 260: Oct 14 JDN 2458406

A study was recently published in Nature Biotechnology showing clear evidence of a mental health crisis among graduate students (no, I don’t know why they picked the biotechnology imprint—I guess it wasn’t good enough for Nature proper?). This is only the most recent of several studies showing exceptionally high rates of mental health issues among graduate students.

I’ve seen universities do a lot of public hand-wringing and lip service about this issue—but I haven’t seen any that were seriously willing to do what it takes to actually solve the problem.

I think this fact became clearest to me when I was required to fill out an official “Individual Development Plan” form as a prerequisite for my advancement to candidacy, which included one question about “What are you doing to support your own mental health and work/life balance?”

The irony here is absolutely excruciating, because advancement to candidacy has been overwhelmingly my leading source of mental health stress for at least the last six months. And it is only one of several different high-stakes checkpoints that grad students are expected to complete, always threatened with defunding or outright expulsion from the graduate program if the checkpoint is not met by a certain arbitrary deadline.

The first of these was the qualifying exams. Then comes advancement to candidacy. Then I have to complete and defend a second-year paper, then a third-year paper. Finally I have to complete and defend a dissertation, and then go onto the job market and go through a gauntlet of applications and interviews. I can’t think of any other time in my life when I was under this much academic and career pressure this consistently—even finishing high school and applying to college wasn’t like this.

If universities really wanted to improve my mental health, they would find a way to get rid of all that.

Granted, a single university does not have total control over all this: There are coordination problems between universities regarding qualifying exams, advancement, and dissertation requirements. One university that unilaterally tried to remove all these would rapidly lose prestige, as it would not be regarded as “rigorous” to reduce the pressure on your grad students. But that itself is precisely the problem—we have equated “rigor” with pressuring grad students until they are on the verge of emotional collapse. Universities don’t seem to know how to make graduate school difficult in the ways that would actually encourage excellence in research and teaching; they simply know how to make it difficult in ways that destroy their students psychologically.

The job market is even more complicated; in the current funding environment, it would be prohibitively expensive to open up enough faculty positions to actually accept even half of all graduating PhDs to tenure-track jobs. Probably the best answer here is to refocus graduate programs on supporting employment outside academia, recognizing both that PhD-level skills are valuable in many workplaces and that not every grad student really wants to become a professor.

But there are clearly ways that universities could mitigate these effects, and they don’t seem genuinely interested in doing so. They could remove the advancement exam, for example; you could simply advance to candidacy as a formality when your advisor decides you are ready, never needing to actually perform a high-stakes presentation before a committee—because what the hell does that accomplish anyway? Speaking of advisors, they could have a formalized matching process that starts with interviewing several different professors and being matched to the one that best fits your goals and interests, instead of expecting you to reach out on your own and hope for the best. They could have you write a dissertation, but not perform a “dissertation defense”—because, again, what can they possibly learn from forcing you to present in a high-stakes environment that they couldn’t have learned from reading your paper and talking with you about it over several months?

They could adjust or even remove funding deadlines—especially for international students. Here at UCI at least, once you are accepted to the program, you are ostensibly guaranteed funding for as long as you maintain reasonable academic progress—but then they define “reasonable progress” in such a way that you have to form an advancement committee, fill out forms, write a paper, and present before a committee all by a certain date or your funding is in jeopardy. Residents of California (which includes all US students who successfully established residency after a full year) are given more time if we need it—but international students aren’t. How is that fair?

The unwillingness of universities to take such actions clearly shows that their commitment to improving students’ mental health is paper-thin. They are only willing to help their students improve their work-life balance as long as it doesn’t require changing anything about the graduate program. They will provide us with counseling services and free yoga classes, but they won’t seriously reduce the pressure they put on us at every step of the way.
I understand that universities are concerned about protecting their prestige, but I ask them this: Does this really improve the quality of your research or teaching output? Do you actually graduate better students by selecting only the ones who can survive being emotionally crushed? Do all these arbitrary high-stakes performances actually result in greater advancement of human knowledge?

Or is it perhaps that you yourselves were put through such hazing rituals years ago, and now your cognitive dissonance won’t let you admit that it was all for naught? “This must be worth doing, or else they wouldn’t have put me through so much suffering!” Are you trying to transfer your own psychological pain onto your students, lest you be forced to face it yourself?

MSRP is tacit collusion

Oct 7 JDN 2458399

It’s been a little while since I’ve done a really straightforward economic post. It feels good to get back to that.

You are no doubt familiar with the “Manufacturer’s Suggested Retail Price” or MSRP. It can be found on everything from books to dishwashers to video games.

The MSRP is a very simple concept: The manufacturer suggests that all retailers sell it (at least the initial run) at precisely this price.

Why would they want to do that? There is basically only one possible reason: They are trying to sustain tacit collusion.

The game theory of this is rather subtle: It requires that both manufacturers and retailers engage in long-term relationships with one another, and can pick and choose who to work with based on the history of past behavior. Both of these conditions hold in most real-world situations—indeed, the fact that they don’t hold very well in the agriculture industry is probably why we don’t see MSRP on produce.

If pricing were decided by random matching with no long-term relationships or past history, MSRP would be useless. Each firm would have little choice but to set their own optimal price, probably just slightly over their own marginal cost. Even if the manufacturer suggested an MSRP, retailers would promptly and thoroughly ignore it.

This is because the one-shot Bertrand pricing game has a unique Nash equilibrium, at pricing just above marginal cost. The basic argument is as follows: If I price cheaper than you, I can claim the whole market. As long as it’s profitable for me to do that, I will. The only time it’s not profitable for me to undercut you in this way is if we are both charging just slightly above marginal cost—so that is what we shall do, in Nash equilibrium. Human beings don’t always play according to the Nash equilibrium, but for-profit corporations do so quite consistently. Humans have limited attention and moral values; corporations have accounting departments and a fanatical devotion to the One True Profit.

But the iterated Bertrand pricing game is quite different. If instead of making only one pricing decision, we make many pricing decisions over time, always with a high probability of encountering the same buyers and sellers again in the future, then I may not want to undercut your price, for fear of triggering a price war that will hurt both of our firms.

Much like how the Iterated Prisoner’s Dilemma can sustain cooperation in Nash equilibrium while the one-shot Prisoner’s Dilemma cannot, the iterated Bertrand game can sustain collusion as a Nash equilibrium.

There is in fact a vast number of possible equilibria in the iterated Bertrand game. If prices were infinitely divisible, there would be an infinite number of equilibria. In reality, there are hundreds or thousands of equilibria, depending on how finely divisible the price may be.

This makes the iterated Bertrand game a coordination gamethere are many possible equilibria, and our task is to figure out which one to coordinate on.

If we had perfect information, we could deduce what the monopoly price would be, and then all choose the monopoly price; this would be what we call “payoff dominant”, and it’s often what people actually try to choose in real-world coordination games.

But in reality, the monopoly price is a subtle and complicated thing, and might not even be the same between different retailers. So if we each try to compute a monopoly price, we may end up with different results, and then we could trigger a price war and end up driving all of our profits down. If only there were some way to communicate with one another, and say what price we all want to set?

Ah, but there is: The MSRP. Most other forms of price communication are illegal: We certainly couldn’t send each other emails and say “Let’s all charge $59.99, okay?” (When banks tried to do that with the LIBOR, it was the largest white-collar crime in history.) But for some reason economists (particularly, I note, the supposed “free market” believers of the University of Chicago) have convinced antitrust courts that MSRP is somehow different. Yet it’s obviously hardly different at all: You’ve just made the communication one-way from manufacturers to retailers, which makes it a little less reliable, but otherwise exactly the same thing.

There are all sorts of subtler arguments about how MSRP is justifiable, but as far as I can tell they all fall flat. If you’re worried about retailers not promoting your product enough, enter into a contract requiring them to promote. Proposing a suggested price is clearly nothing but an attempt to coordinate tacit—frankly not even that tacit—collusion.

MSRP also probably serves another, equally suspect, function, which is to manipulate consumers using the anchoring heuristic: If the MSRP is $59.99, then when it does go on sale for $49.99 you feel like you are getting a good deal; whereas, if it had just been priced at $49.99 to begin with, you might still have felt that it was too expensive. I see no reason why this sort of crass manipulation of consumers should be protected under the law either, especially when it would be so easy to avoid.

There are all sorts of ways for firms to tacitly collude with one another, and we may not be able to regulate them all. But the MSRP is literally printed on the box. It’s so utterly blatant that we could very easily make it illegal with hardly any effort at all. The fact that we allow such overt price communication makes a mockery of our antitrust law.

What really works against bigotry

Sep 30 JDN 2458392

With Donald Trump in office, I think we all need to be thinking carefully about what got us to this point, how we have apparently failed in our response to bigotry. It’s good to see that Kavanaugh’s nomination vote has been delayed pending investigations, but we can’t hope to rely on individual criminal accusations to derail every potentially catastrophic candidate. The damage that someone like Kavanaugh would do to the rights of women, racial minorities, and LGBT people is too severe to risk. We need to attack this problem at its roots: Why are there so many bigoted leaders, and so many bigoted voters willing to vote for them?

The problem is hardly limited to the United States; we are witnessing a global crisis of far-right ideology, as even the UN has publicly recognized.

I think the left made a very dangerous wrong turn with the notion of “call-out culture”. There is now empirical data to support me on this. Publicly calling people racist doesn’t make them less racist—in fact, it usually makes them more racist. Angrily denouncing people doesn’t change their minds—it just makes you feel righteous. Our own accusatory, divisive rhetoric is part of the problem: By accusing anyone who even slightly deviates from our party line (say, by opposing abortion in some circumstances, as 75% of Americans do?) of being a fascist, we slowly but surely push more people toward actual fascism.

Call-out culture encourages a black-and-white view of the world, where there are “good guys” (us) and “bad guys” (them), and our only job is to fight as hard as possible against the “bad guys”. It frees us from the pain of nuance, complexity, and self-reflection—at only the cost of giving up any hope of actually understanding the real causes or solving the problem. Bigotry is not something that “other” people have, which you, fine upstanding individual, could never suffer from. We are all Judy Hopps.

This is not to say we should do nothing—indeed, that would be just as bad if not worse. The rise of neofascism has been possible largely because so many people did nothing. Knowing that there is bigotry in all of us shouldn’t stop us from recognizing that some people are far worse than others, or paralyze us against constructively improving ourselves and our society. See the shades of gray without succumbing to the Fallacy of Gray.

The most effective interventions at reducing bigotry are done in early childhood; obviously, it’s far too late for that when it comes to people like Trump and Kavanaugh.

But there are interventions that can work at reducing bigotry among adults. We need to first understand where the bigotry comes from—and it doesn’t always come from the same source. We need to be willing to look carefully—yes, even sympathetically—at people with bigoted views so that we can understand them.

There are deep, innate systems in the human brain that make bigotry come naturally to us. Even people on the left who devote their lives to combating discrimination against women, racial minorities and LGBT people can still harbor bigoted attitudes toward other groups—such as rural people or Republicans. If you think that all Republicans are necessarily racist, that’s not a serious understanding of what motivates Republicans—that’s just bigotry on your part. Trump is racist. Pence is racist. One could argue that voting for them constitutes, in itself, a racist act. But that does not mean that every single Republican voter is fundamentally and irredeemably racist.

It’s also important to have conversations face-to-face. I must admit that I am personally terrible at this; despite training myself extensively in etiquette and public speaking to the point where most people perceive me as charismatic, even charming, deep down I am still a strong introvert. I dislike talking in person, and dread talking over the phone. I would much prefer to communicate entirely in written electronic communication—but the data is quite clear on this: Face-to-face conversations work better at changing people’s minds. It may be awkward and uncomfortable, but by being there in person, you limit their ability to ignore you or dismiss you; you aren’t a tweet from the void, but an actual person, sitting there in front of them.

Speak with friends and family members. This, I know, can be especially awkward and painful. In the last few years I have lost connections with friends who were once quite close to me as a result of difficult political conversations. But we must speak up, for silence becomes complicity. And speaking up really can work.

Don’t expect people to change their entire worldview overnight. Focus on small, concrete policy ideas. Don’t ask them to change who they are; ask them to change what they believe. Ask them to justify and explain their beliefs—and really listen to them when they do. Be open to the possibility that you, too might be wrong about something.

If they say “We should deport all illegal immigrants!”, point out that whenever we try this, a lot of fields go unharvested for lack of workers, and ask them why they are so concerned about illegal immigrants. If they say “Illegal immigrants come here and commit crimes!” point them to the statistical data showing that illegal immigrants actually commit fewer crimes on average than native-born citizens (probably because they are more afraid of what happens if they get caught).

If they are concerned about Muslim immigrants influencing our culture in harmful ways, first, acknowledge that there are legitimate concerns about Islamic cultural values (particularly toward women and LGBT people)but then point out that over 90% of Muslim-Americans are proud to be American, and that welcoming people is much more effective at getting them to assimilate into our culture than keeping them out and treating them as outsiders.

If they are concerned about “White people getting outnumbered”, first point out that White people are still over 70% of the US population, and in most rural areas there are only a tiny fraction of non-White people. Point out that Census projections showing the US will be majority non-White by 2045 are based on naively extrapolating current trends, and we really have no idea what the world will look like almost 30 years from now. Next, ask them why they worry about being “outnumbered”; get them to consider that perhaps racial demographics don’t have to be a matter of zero-sum conflict.

After you’ve done this, you will feel frustrated and exhausted, and the relationship between you and the person you’re trying to convince will be strained. You will probably feel like you have accomplished absolutely nothing to change their mind—but you are wrong. Even if they don’t acknowledge any change in their beliefs, the mere fact that you sat down and asked them to justify what they believe, and presented calm, reasonable, cogent arguments against those beliefs will have an effect. It will be a small effect, difficult for you to observe in that moment. But it will still be an effect.

Think about the last time you changed your mind about something important. (I hope you can remember such a time; none of us were born being right about everything!) Did it happen all at once? Was there just one, single knock-down argument that convinced you? Probably not. (On some mathematical and scientific questions I’ve had that experience: Oh, wow, yeah, that proof totally demolishes what I believed. Well, I guess I was wrong. But most beliefs aren’t susceptible to such direct proof.) More likely, you were presented with arguments from a variety of sources over a long span of time, gradually chipping away at what you thought you knew. In the moment, you might not even have admitted that you thought any differently—even to yourself. But as the months or years went by, you believed something quite different at the end than you had at the beginning.

Your goal should be to catalyze that process in other people. Don’t take someone who is currently a frothing neo-Nazi and expect them to start marching with Black Lives Matter. Take someone who is currently a little bit uncomfortable about immigration, and calm their fears. Don’t take someone who thinks all poor people are subhuman filth and try to get them to support a basic income. Take someone who is worried about food stamps adding to our national debt, and show them how it is a small portion of our budget. Don’t take someone who thinks global warming was made up by the Chinese and try to get them to support a ban on fossil fuels. Take someone who is worried about gas prices going up as a result of carbon taxes and show them that carbon offsets would add only about $100 per person per year while saving millions of lives.

And if you’re ever on the other side, and someone has just changed your mind, even a little bit—say so. Thank them for opening your eyes. I think a big part of why we don’t spend more time trying to honestly persuade people is that so few people acknowledge us when we do.