heuristics and biases

The confidence game

PNRJ core principles, ethics, heuristics and biases, personal, politics , , , , , , , , , , ,

Dec 14 JDN 2461024

Our society rewards confidence. Indeed, it seems to do so without limit: The more confident you are, the more successful you will be, the more prestige you will gain, the more power you will have, the more money you will make. It doesn’t seem to matter whether your confidence is justified; there is no punishment for overconfidence and no reward for humility.

If you doubt this, I give you Exhibit A: President Donald Trump.

He has nothing else going for him. He manages to epitomize almost every human vice and lack in almost every human virtue. He is ignorant, impulsive, rude, cruel, incurious, bigoted, incompetent, selfish, xenophobic, racist, and misogynist. He has no empathy, no understanding of justice, and little capacity for self-control. He cares nothing for truth and lies constantly, even to the point of pathology. He has been convicted of multiple felonies. His businesses routinely go bankrupt, and he saves his wealth mainly through fraud and lawsuits. He has publicly admitted to sexually assaulting adult women, and there is mounting evidence that he has also sexually assaulted teenage girls. He is, in short, one of the worst human beings in the world. He does not have the integrity or trustworthiness to be an assistant manager at McDonald’s, let alone President of the United States.

But he thinks he’s brilliant and competent and wise and ethical, and constantly tells everyone around him that he is—and millions of people apparently believe him.

To be fair, confidence is not the only trait that our society rewards. Sometimes it does actually reward hard work, competence, or intellect. But in fact it seems to reward these virtues less consistently than it rewards confidence. And quite frankly I’m not convinced our society rewards honesty at all; liars and frauds seem to be disproportionately represented among the successful.

This troubles me most of all because confidence is not a virtue.

There is nothing good about being confident per se. There is virtue in notbeing underconfident, because underconfidence prevents you from taking actions you should take. But there is just as much virtue in not being overconfident, because overconfidence makes you take actions you shouldn’t—and if anything, is the more dangerous of the two. Yet our culture appears utterly incapable of discerning whether confidence is justifiable—even in the most blatantly obvious cases—and instead rewards everyone all the time for being as confident as they can possibly be.

In fact, the most confident people are usually less competent than the most humble people—because when you really understand something, you also understand how much you don’t understand.

We seem totally unable to tell whether someone who thinks they are right is actually right; and so, whoever thinks they are right is assumed to be right, all the time, every time.

Some of this may even be genetic, a heuristic that perhaps made more sense in our ancient environment. Even quite young children already are more willing to trust confident answers than hesitant ones, in multiple experiments.

Studies suggest that experts are just as overconfident as anyone else, but to be frank, I think this is because you don’t get to be called an expert unless you’re overconfident; people with intellectual humility are filtered out by the brutal competition of academia before they can get tenure.

I guess this is also personal for me.

I am not a confident person. Temperamentally, I just feel deeply uncomfortable going out on a limb and asserting things when I’m not entirely certain of them. I also have something of a complex about ever being perceived as arrogant or condescending, maybe because people often seem to perceive me that way even when I am actively trying to do the opposite. A lot of people seem to take you as condescending when you simply acknowledge that you have more expertise on something than they do.

I am also apparently a poster child for Impostor Syndrome. I once went to an Impostor Syndrome with a couple dozen other people where they played a bingo game for Impostor Syndrome traits and behaviors—and won. I once went to a lecture by George Akerlof where he explained that he attributed his Nobel Prize more to luck and circumstances than any particular brilliance on his part—and I guarantee you, in the extremely unlikely event I ever win a prize like that, I’ll say the same.

Compound this with the fact that our society routinely demands confidence in situations where absolutely no one could ever justify being confident.

Consider a job interview, when they ask you: “Why are you the best candidate for this job?” I couldn’t possibly know that. No one in my position could possibly know that. I literally do not know who your other candidates are in order to compare myself to them. I can tell you why I am qualified, but that’s all I can do. I could be the best person for the job, but I have no idea if I am. It’s your job to figure that out, with all the information in front of you—and I happen to know that you’re actually terrible at it, even with all that information I don’t have access to. If I tell you I know I’m the best person for the job, I am, by construction, either wildly overconfident or lying. (And in my case, it would definitely be lying.)

In fact, if I were a hiring manager, I would probably disqualify anyone who told me they were the best person for the job—because the one thing I now know about them is that they are either overconfident or willing to lie. (But I’ll probably never be a hiring manager.)

Likewise, I’ve been often told when pitching creative work to explain why I am the best or only person who could bring this work to life, or to provide accurate forecasts of how much the work would sell if published. I almost certainly am not the best or only person who could do anything—only a handful of people on Earth could realistically say that they are, and they’ve all already won Oscars or Emmys or Nobel Prizes. Accurate sales forecasts for creative works are so difficult that even Disney Corporation, an ever-growing conglomerate media superpower with billions of dollars to throw at the problem and even more billions of dollars at stake in getting it right, still routinely puts out films that are financial failures.


They casually hand you impossible demands and then get mad at you when you say you can’t meet them. And then they go pick someone else who claims to be able to do the impossible.

There is some hope, however.

Some studies suggest that people can sometimes recognize and punish overconfidence—though, again, I don’t see how that can be reconciled with the success of Donald Trump. In this study of evaluating expert witnesses, the most confident witnesses were rated as slightly less reliable than the moderately-confident ones, but both were far above the least-confident ones.

Surprisingly simple interventions can make intellectual humility more salient to people, and make them more willing to trust people who express doubt—who are, almost without exception, the more trustworthy people.

But somehow, I think I have to learn to express confidence I don’t feel, because that’s how you succeed in our society.

How to be a deontological consequentialist

PNRJ cognitive science, core principles, ethics, heuristics and biases, politics, public policy , , , , , , , , , ,

Dec 7 JDN 2461017

As is commonly understood, there are two main branches of normative ethics:

  • Deontology, on which morality consists in following rules and fulfilling obligations, and
  • Consequentialism, on which morality consists in maximizing good consequences.

The conflict between them has raged for centuries, with Kantians leading the deontologists and utilitarians leading the consequentialists. Both theories seem to have a lot of good points, but neither can decisively defeat the other.

I think this is because they are both basically correct.

In their strongest forms, deontology and consequentialism are mutually contradictory; but it turns out that you can soften each of them a little bit, and the results become compatible.

To make deontology a little more consequentialist, let’s ask a simple question:

What makes a rule worth following?

I contend that the best answer we have is “because following that rule would make the world better off than not following that rule”. (Even Kantians pretty much have to admit this: What maxim could you will to be an absolute law? Only a law that would yield good outcomes.)

That is, the ultimate justification of a sound deontology would be fundamentally consequentialist.

But lest the consequentialists get too smug, we can also ask them another question, which is a bit subtler:

How do you know which actions will ultimately have good consequences?

Sure, if we were omniscient beings who could perfectly predict the consequences of our actions across the entire galaxy on into the indefinite future, we could be proper act utilitarians who literally choose every single action according to a calculation of the expected utility.

But in practice, we have radical uncertainty about the long-term consequences of our actions, and can generally only predict the immediate consequences.

That leads to the next question:

Would you really want to live in a world where people optimized immediate consequences?

I contend that you would not, that such a world actually sounds like a dystopian nightmare.

Immediate consequences say that if a healthy person walks into a hospital and happens to have compatible organs for five people who need donations, we should kill that person, harvest their organs, and give them to the donors. (This is the organ transplant variant of the Trolley Problem.)

Basically everyone recognizes that this is wrong. But why is it wrong? That’s thornier. One pretty convincing case is that a systematic policy of this kind would undermine trust in hospitals and destroy the effectiveness of healthcare in general, resulting in disastrous consequences far outweighing the benefit of saving those five people. But those aren’t immediate consequences, and indeed, it’s quite difficult to predict exactly how many crazy actions like this it would take to undermine people’s trust in hospitals, just how much it would undermine that trust, or exactly what the consequences of that lost trust would be.

So it seems like it’s actually better to have a rule about this.

This makes us into rule utilitarians, who instead of trying to optimize literally every single action—which requires information we do not have and never will—we instead develop a system of rules that we can follow, heuristics that will allow us to get better outcomes generally even if they can’t be guaranteed to produce the best possible outcome in any particular case.

That is, the output of a sophisticated consequentialism is fundamentally deontological.

We have come at the question of normative ethics from two very different directions, but the results turned out basically the same:

We should follow the rules that would have the best consequences.

The output of our moral theory is rules, like deontology; but its fundamental justification is based on outcomes, like consequentialism.

In my experience, when I present this account to staunch deontologists, they are pretty much convinced by it. They’re prepared to give up the fundamental justification to consequences if it allows them to have their rules.

The resistance I get is mainly from staunch consequentialists, who insist that it’s not so difficult to optimize individual actions, and so we should just do that instead of making all these rules.

So it is to those consequentialists, particularly those who say “rule utilitarianism collapses into act utilitarianism”, to whom the rest of the post is addressed.

First, let me say that I agree.

In the ideal case of omniscient, perfectly-benevolent, perfectly-rational agents, rule utilitarianism mathematically collapses into act utilitarianism. That is a correct theorem.

However, we do not live in the ideal case of omniscient, perfectly-benevolent, perfectly-rational agents. We are not even close to that ideal case; we will never be close to that ideal case. Indeed, I think part of the problem here is that you fail to fully grasp the depth and width of the chasm between here and there. Even a galactic civilization of a quintillion superhuman AIs would still not be close to that ideal case.

Quite frankly, humans aren’t even particularly good at forecasting what will make themselves happy.

There are massive errors and systematic biases in human affective forecasting.

One of the post important biases is impact bias: People systematically overestimate the impact of individual events on their long-term happiness. Some of this seems to be just due to focus: Paying attention to a particular event exaggerates its importance in your mind, and makes it harder for you to recall other events that might push your emotions in a different direction. Another component is called immune neglect: people fail to account for their own capacity to habituate to both pleasant and unpleasant experiences. (This effect is often overstated: It’s a common misconception that lottery winners are no happier than they were before. No, they absolutely are happier, on average; they’re just not as much happier as they predicted themselves to be.)

People also use inconsistent time discounting: $10 today is judged as better than $11 tomorrow, but $10 in 364 days is not regarded as better than $11 in 365 days—so if I made a decision a year ago, I’d want to change it now. (The correct answer, by the way, is to take the $11; a discount rate of 10% per day is a staggering 120,000,000,000,000,000% APR—seriously; check it yourself—so you’d better not be discounting at that rate, unless you’re literally going to die before tomorrow.)

Now, compound that with the fact that different human beings come at the world from radically different perspectives and with radically different preferences.

How good do you think we are at predicting what will make other people happy?

Damn right: We’re abysmal.

Basically everyone assumes that what they want and what they would feel is also what other people will want and feel—which, honestly, explains a lot about politics. As a result, my prediction of your feelings is more strongly correlated with my prediction of my feelings than it is with your actual feelings.

The impact bias is especially strong when forecasting other people’s feelings in response to our own actions: We tend to assume that other people care more about what we do than they actually care—and this seems to be a major source of social anxiety.

People also tend to overestimate the suffering of others, and are generally willing to endure more pain than they are willing to inflict upon others. (This one seems like it might be a good thing!)

Even when we know people well, we can still be totally blindsided by their emotional reactions. We’re just really awful at this.

Does this just mean that morality is hopeless? We have no idea what we’re doing?

Fortunately, no. Because while no individual can correctly predict or control the outcomes of particular actions, the collective action of well-designed institutions can in fact significantly improve the outcomes of policy.

This is why we have things like the following:

  • Laws
  • Courts
  • Regulations
  • Legislatures
  • Constitutions
  • Newspapers
  • Universities

These institutions—which form the backbone of liberal democracy—aren’t simply arbitrary. They are the result of hard-fought centuries, a frothing, volatile, battle-tested mix of intentional design and historical evolution.

Are these institutions optimal? Good heavens, no!

But we have no idea what optimal institutions look like, and probably never will. (Those galaxy-spanning AIs will surely have a better system than this; but even theirs probably won’t be optimal.) Instead, what we are stuck with are the best institutions we’ve come up with so far.

Moreover, we do have very clear empirical evidence at this point that some form of liberal democracy with a mixed economy is the best system we’ve got so far. One can reasonably debate whether Canada is doing better or worse than France, or whether the system in Denmark could really be scaled to the United States, or just what the best income tax rates are; but there is a large, obvious, and important difference between life in a country like Canada or Denmark and life in a country like Congo or Afghanistan.

Indeed, perhaps there is no better pair to compare than North and South Korea: Those two countries are right next to each other, speak the same language, and started in more or less the same situation; but the south got good institutions and the north got bad ones, and now the difference between them couldn’t be more stark. (Honestly, this is about as close as we’re ever likely to get of a randomized controlled experiment in macroeconomics.)

People in South Korea now live about as well as some of the happiest places in the world; their GDP per capita PPP is about $65,000 per year, roughly the same as Canada. People in North Korea live about as poorly as it is possible for humans to live, subject to totalitarian oppression and living barely above subsistence; their GDP per capita PPP is estimated to be $600 per year—less than 1% as much.

The institutions of South Korea are just that much better.

Indeed, there’s one particular aspect of good institutions that seems really important, yet is actually kind of hard to justify in act-utilitarian terms:

Why is freedom good?

A country’s level of freedom is almost perfectly correlated with its overall level of happiness and development. (Yes, even on this measure, #ScandinaviaIsBetter.)

But why? In theory, letting people do whatever they want could actually lead to really bad outcomes—and indeed, occasionally it does. There’s even a theorem that liberty is incompatible with full Pareto-efficiency. But all the countries with the happiest people seem to have a lot of liberty, and indeed the happiest ones seem to have the most. How come?

My answer:

Personal liberty is a technology for heuristic utility maximization.

In the ideal case, we wouldn’t really need personal liberty; you could just compel everyone to do whatever is optimal all the time, and that would—by construction—be optimal. It might even be sort of nice: You don’t need to make any difficult decisions, you can just follow the script and know that everything will turn out for the best.

But since we don’t know what the optimal choice is—even in really simple cases, like what you should eat for lunch tomorrow—we can’t afford to compel people in this way. (It would also be incredibly costly to implement such totalitarian control, but that doesn’t stop some governments from trying!)

Then there are disagreements: What I think is optimal may not be what you think is optimal, and in truth we’re probably both wrong (but one of us may be less wrong).

And that’s not even getting into conflicts of interest: We aren’t just lacking in rationality, we’re also lacking in benevolence. Some people are clearly much more benevolent than others, but none of us are really 100% selfless. (Sadly, I think some people are 100% selfish.)

In fact, this is a surprisingly deep question:

Would the world be better if we were selfless?

Could there be actually some advantage in aggregate to having some degree of individual self-interest?

Here are some ways that might hold, just off the top of my head:

  • Partial self-interest supports an evolutionary process of moral and intellectual development that otherwise would be stalled or overrun by psychopaths—see my post on Rousseaus and Axelrods
  • Individuals have much deeper knowledge of their own preferences than anyone else’s, and thus can optimize them much better. (Think about it: This is true even of people you know very well. Otherwise, why would we ever need to ask our spouses one of the most common questions in any marriage: “Honey, what do you want for dinner tonight?”)
  • Self-interest allows for more efficient economic incentives, and thus higher overall productivity.

Of course, total selfishness is clearly not optimal—that way lies psychopathy. But some degree of selfishness might actually be better for long-term aggregate outcomes than complete altruism, and this is to some extent an empirical question.

Personal liberty solves a lot of these problems: Since people are best at knowing their own preferences, let people figure out on their own what’s good for them. Give them the freedom to live the kind of life they want to live, within certain reasonable constraints to prevent them from causing great harm to others or suffering some kind of unrecoverable mistake.

This isn’t exactly a new idea; it’s basically the core message of John Stuart Mill’s On Liberty (which I consider a good candidate for the best book every written—seriously, it beats the Bible by a light-year). But by putting it in more modern language, I hope to show that deontology and consequentialism aren’t really so different after all.

And indeed, for all its many and obvious flaws, freedom seems to work pretty well—at least as well as anything we’ve tried.

On foxes and hedgehogs, part II

PNRJ heuristics and biases, politics, statistics , , , , , , , , , , , , ,

Aug 3 JDN 2460891

In last week’s post I described Philip E. Tetlock’s experiment showing that “foxes” (people who are open-minded and willing to consider alternative views) make more accurate predictions than “hedgehogs” (people who are dogmatic and conform strictly to a single ideology).

As I explained at the end of the post, he, uh, hedges on this point quite a bit, coming up with various ways that the hedgehogs might be able to redeem themselves, but still concluding that in most circumstances, the foxes seem to be more accurate.

Here are my thoughts on this:

I think he went too easy on the hedgehogs.

I consider myself very much a fox, and I honestly would never assign a probability of 0% or 100% to any physically possible event. Honestly I consider it a flaw in Tetlock’s design that he included those as options but didn’t include probabilities I would assign, like 1%, 0.1%, or 0.01%.

He only let people assign probabilities in 10% increments. So I guess if you thought something was 3% likely, you’re supposed to round to 0%? That still feels terrible. I’d probably still write 10%. There weren’t any questions like “Aliens from the Andromeda Galaxy arrive to conquer our planet, thus rendering all previous political conflicts moot”, but man, had there been, I’d still be tempted to not put 0%. I guess I would put 0% for that though? Because in 99.999999% of cases, I’d get it right—it wouldn’t happen—and I’d get more points. But man, even single-digit percentages? I’d mash the 10% button. I am pretty much allergic to overconfidence.

In fact, I think in my mind I basically try to use a logarithmic score, which unlike a Brier score, severely (technically, infinitely) punishes you for saying that something impossible happened or something inevitable didn’t. Like, really, if you’re doing it right, that should never, ever happen to you. If you assert that something has 0% probability and it happens, you have just conclusively disproven your worldview. (Admittedly it’s possible you could fix it with small changes—but a full discussion of that would get us philosophically too far afield. “outside the scope of this paper”.)

So honestly I think he was too lenient on overconfidence by using a Brier score, which does penalize this kind of catastrophic overconfidence, but only by a moderate amount. If you say that something has a 0% chance and then it happens, you get a Brier score of -1. But if you say that something has a 50% chance and then it happens (which it would, you know, 50% of the time), you’d get a Brier score of -0.25. So even absurd overconfidence isn’t really penalized that badly.

Compare this to a logarithmic rule: Say 0% and it happens, and you get negative infinity. You lose. You fail. Go home. Your worldview is bad and you should feel bad. This should never happen to you if you have a coherent worldview (modulo the fact that he didn’t let you say 0.01%).

So if I had designed this experiment, I would have given finer-grained options at the extremes, and then brought the hammer down on anybody who actually asserted a 0% chance of an event that actually occurred. (There’s no need for the finer-grained options elsewhere; over millennia of history, the difference between 0% and 0.1% is whether it won’t happen or it will—quite relevant for, say, full-scale nuclear war—while the difference between 40% and 42.1% is whether it’ll happen every 2 to 3 years or… every 2 to 3 years.)

But okay, let’s say we stick with the Brier score, because infinity is scary.

  1. About the adjustments:
    1. The “value adjustments” are just absolute nonsense. Those would be reasons to adjust your policy response, via your utility function—they are not a reason to adjust your probability. Yes, a nuclear terrorist attack would be a really big deal if it happened and we should definitely be taking steps to prevent that; but that doesn’t change the fact that the probability of one happening is something like 0.1% per year and none have ever happened. Predicting things that don’t happen is bad forecasting, even if the things you are predicting would be very important if they happened.
    2. The “difficulty adjustments” are sort of like applying a different scoring rule, so that I’m more okay with; but that wasn’t enough to make the hedgehogs look better than the foxes.
    3. The “fuzzy set” adjustments could be legitimate, but only under particular circumstances. Being “almost right” is only valid if you clearly showed that the result was anomalous because of some other unlikely event, and—because the timeframe was clearly specified in the questions—“might still happen” should still get fewer points than accurately predicting that it hasn’t happened yet. Moreover, it was very clear that people only ever applied these sort of changes when they got things wrong; they rarely if ever said things like “Oh, wow, I said that would happen and it did, but for completely different reasons that I didn’t expect—I was almost wrong there.” (Crazy example, but if the Soviet Union had been taken over by aliens, “the Soviet Union will fall” would be correct—but I don’t think you could really attribute that to good political prediction.)
  2. The second exercise shows that even the foxes are not great Bayesians, and that some manipulations can make people even more inaccurate than before; but the hedgehogs also perform worse and also make some of the same crazy mistakes and still perform worse overall than the foxes, even in that experiment.
  3. I guess he’d call me a “hardline neopositivist”? Because I think that your experiment asking people to predict things should require people to, um, actually predict things? The task was not to get the predictions wrong but be able to come up with clever excuses for why they were wrong that don’t challenge their worldview. The task was to not get the predictions wrong. Apparently this very basic level of scientific objectivity is now considered “hardline neopositivism”.

I guess we can reasonably acknowledge that making policy is about more than just prediction, and indeed maybe being consistent and decisive is advantageous in a game-theoretic sense (in much the same way that the way to win a game of Chicken is to very visibly throw away your steering wheel). So you could still make a case for why hedgehogs are good decision-makers or good leaders.

But I really don’t see how you weasel out of the fact that hedgehogs are really bad predictors. If I were running a corporation, or a government department, or an intelligence agency, I would want accurate predictions. I would not be interested in clever excuses or rich narratives. Maybe as leaders one must assemble such narratives in order to motivate people; so be it, there’s a division of labor there. Maybe I’d have a separate team of narrative-constructing hedgehogs to help me with PR or something. But the people who are actually analyzing the data should be people who are good at making accurate predictions, full stop.

And in fact, I don’t think hedgehogs are good decision-makers or good leaders. I think they are good politicians. I think they are good at getting people to follow them and believe what they say. But I do not think they are actually good at making the decisions that would be the best for society.

Indeed, I think this is a very serious problem.

I think we systematically elect people to higher office—and hire them for jobs, and approve them for tenure, and so on—because they express confidence rather than competence. We pick the people who believe in themselves the most, who (by regression to the mean if nothing else) are almost certainly the people who are most over-confident in themselves.

Given that confidence is easier to measure than competence in most areas, it might still make sense to choose confident people if confidence were really positively correlated with competence, but I’m not convinced that it is. I think part of what Tetlock is showing us is that the kind of cognitive style that yields high confidence—a hedgehog—simply is not the kind of cognitive style that yields accurate beliefs—a fox. People who are really good at their jobs are constantly questioning themselves, always open to new ideas and new evidence; but that also means that they hedge their bets, say “on the other hand” a lot, and often suffer from Impostor Syndrome. (Honestly, testing someone for Impostor Syndrome might be a better measure of competence than a traditional job interview! Then again, Goodhart’s Law.)

Indeed, I even see this effect within academic science; the best scientists I know are foxes through and through, but they’re never the ones getting published in top journals and invited to give keynote speeches at conferences. The “big names” are always hedgehog blowhards with some pet theory they developed in the 1980s that has failed to replicate but somehow still won’t die.

Moreover, I would guess that trustworthiness is actually pretty strongly inversely correlated to confidence—“con artist” is short for “confidence artist”, after all.

Then again, I tried to find rigorous research comparing openness (roughly speaking “fox-ness”) or humility to honesty, and it was surprisingly hard to find. Actually maybe the latter is just considered an obvious consensus in the literature, because there is a widely-used construct called honesty-humility. (In which case, yeah, my thinking on trustworthiness and confidence is an accepted fact among professional psychologists—but then, why don’t more people know that?)

But that still doesn’t tell me if there is any correlation between honesty-humility and openness.

I did find these studies showing that both honesty-humility and openness are both positively correlated with well-being, both positively correlated with cooperation in experimental games, and both positively correlated with being left-wing; but that doesn’t actually prove they are positively correlated with each other. I guess it provides weak evidence in that direction, but only weak evidence. It’s entirely possible for A to be positively correlated with both B and C but B and C are uncorrelated or negatively correlated. (Living in Chicago is positively correlated with being a White Sox fan and positively correlated with being a Cubs fan, but being a White Sox fan is not positively correlated with being a Cubs fan!)

I also found studies showing that higher openness predicts less right-wing authoritarianism and higher honesty predicts less social conformity; but that wasn’t the question either.

Here’s a factor analysis specifically arguing for designing measures of honesty-humility so that they don’t correlate with other personality traits, so it can be seen as its own independent personality trait. There are some uncomfortable degrees of freedom in designing new personality metrics, which may make this sort of thing possible; and then by construction honesty-humility and openness would be uncorrelated, because any shared components were parceled out to one trait or the other.

So, I guess I can’t really confirm my suspicion here; maybe people who think like hedgehogs aren’t any less honest, or are even more honest, than people who think like foxes. But I’d still bet otherwise. My own life experience has been that foxes are honest and humble while hedgehogs are deceitful and arrogant.

Indeed, I believe that in systematically choosing confident hedgehogs as leaders, the world economy loses tens of trillions of dollars a year in inefficiencies. In fact, I think that we could probably end world hunger if we only ever put leaders in charge who were both competent and trustworthy.

Of course, in some sense that’s a pipe dream; we’re never going to get all good leaders, just as we’ll never get zero death or zero crime.

But based on how otherwise-similar countries have taken wildly different trajectories based on differences in leadership, I suspect that even relatively small changes in that direction could have quite large impacts on a society’s outcomes: South Korea isn’t perfect at picking its leaders; but surely it’s better than North Korea, and indeed that seems like one of the primary things that differentiates the two countries. Botswana is not a utopian paradise, but it’s a much nicer place to live than Nigeria, and a lot of the difference seems to come down to who is in charge, or who has been in charge for the last few decades.

And I could put in a jab here about the current state of the United States, but I’ll resist. If you read my blog, you already know my opinions on this matter.

Bayesian updating with irrational belief change

PNRJ cognitive science, core principles, critique of neoclassical economics, ethics, heuristics and biases, personal, tribal paradigm , , , , , , , , , , , , , , , , , , , , , , , , ,

Jul 27 JDN 2460884

For the last few weeks I’ve been working at a golf course. (It’s a bit of an odd situation: I’m not actually employed by the golf course; I’m contracted by a nonprofit to be a “job coach” for a group of youths who are part of a work program that involves them working at the golf course.)

I hate golf. I have always hated golf. I find it boring and pointless—which, to be fair, is my reaction to most sports—and also an enormous waste of land and water. A golf course is also a great place for oligarchs to arrange collusion.

But I noticed something about being on the golf course every day, seeing people playing and working there: I feel like I hate it a bit less now.

This is almost certainly a mere-exposure effect: Simply being exposed to something many times makes it feel familiar, and that tends to make you like it more, or at least dislike it less. (There are some exceptions: repeated exposure to trauma can actually make you more sensitive to it, hating it even more.)

I kinda thought this would happen. I didn’t really want it to happen, but I thought it would.

This is very interesting from the perspective of Bayesian reasoning, because it is a theorem (though I cannot seem to find anyone naming the theorem; it’s like a folk theorem, I guess?) of Bayesian logic that the following is true:

The prior expectation of the posterior is the expectation of the prior.

The prior is what you believe before observing the evidence; the posterior is what you believe afterward. This theorem describes a relationship that holds between them.

This theorem means that, if I am being optimally rational, I should take into account all expected future evidence, not just evidence I have already seen. I should not expect to encounter evidence that will change my beliefs—if I did expect to see such evidence, I should change my beliefs right now!

This might be easier to grasp with an example.

Suppose I am trying to predict whether it will rain at 5:00 pm tomorrow, and I currently estimate that the probability of rain is 30%. This is my prior probability.

What will actually happen tomorrow is that it will rain or it won’t; so my posterior probability will either be 100% (if it rains) or 0% (if it doesn’t). But I had better assign a 30% chance to the event that will make me 100% certain it rains (namely, I see rain), and a 70% chance to the event that will make me 100% certain it doesn’t rain (namely, I see no rain); if I were to assign any other probabilities, then I must not really think the probability of rain at 5:00 pm tomorrow is 30%.

(The keen Bayesian will notice that the expected variance of my posterior need not be the variance of my prior: My initial variance is relatively high (it’s actually 0.3*0.7 = 0.21, because this is a Bernoulli distribution), because I don’t know whether it will rain or not; but my posterior variance will be 0, because I’ll know the answer once it rains or doesn’t.)

It’s a bit trickier to analyze, but this also works even if the evidence won’t make me certain. Suppose I am trying to determine the probability that some hypothesis is true. If I expect to see any evidence that might change my beliefs at all, then I should, on average, expect to see just as much evidence making me believe the hypothesis more as I see evidence that will make me believe the hypothesis less. If that is not what I expect, I should really change how much I believe the hypothesis right now!

So what does this mean for the golf example?

Was I wrong to hate golf quite so much before, because I knew that spending time on a golf course might make me hate it less?

I don’t think so.

See, the thing is: I know I’m not perfectly rational.

If I were indeed perfectly rational, then anything I expect to change my beliefs is a rational Bayesian update, and I should indeed factor it into my prior beliefs.

But if I know for a fact that I am not perfectly rational, that there are things which will change my beliefs in ways that make them deviate from rational Bayesian updating, then in fact I should not take those expected belief changes into account in my prior beliefs—since I expect to be wrong later, updating on that would just make me wrong now as well. I should only update on the expected belief changes that I believe will be rational.

This is something that a boundedly-rational person should do that neither a perfectly-rational nor perfectly-irrational person would ever do!

But maybe you don’t find the golf example convincing. Maybe you think I shouldn’t hate golf so much, and it’s not irrational for me to change my beliefs in that direction.


Very well. Let me give you a thought experiment which provides a very clear example of a time when you definitely would think your belief change was irrational.


To be clear, I’m not suggesting the two situations are in any way comparable; the golf thing is pretty minor, and for the thought experiment I’m intentionally choosing something quite extreme.

Here’s the thought experiment.

A mad scientist offers you a deal: Take this pill and you will receive $50 million. Naturally, you ask what the catch is. The catch, he explains, is that taking the pill will make you staunchly believe that the Holocaust didn’t happen. Take this pill, and you’ll be rich, but you’ll become a Holocaust denier. (I have no idea if making such a pill is even possible, but it’s a thought experiment, so bear with me. It’s certainly far less implausible than Swampman.)

I will assume that you are not, and do not want to become, a Holocaust denier. (If not, I really don’t know what else to say to you right now. It happened.) So if you take this pill, your beliefs will change in a clearly irrational way.

But I still think it’s probably justifiable to take the pill. This is absolutely life-changing money, for one thing, and being a random person who is a Holocaust denier isn’t that bad in the scheme of things. (Maybe it would be worse if you were in a position to have some kind of major impact on policy.) In fact, before taking the pill, you could write out a contract with a trusted friend that will force you to donate some of the $50 million to high-impact charities—and perhaps some of it to organizations that specifically fight Holocaust denial—thus ensuring that the net benefit to humanity is positive. Once you take the pill, you may be mad about the contract, but you’ll still have to follow it, and the net benefit to humanity will still be positive as reckoned by your prior, more correct, self.

It’s certainly not irrational to take the pill. There are perfectly-reasonable preferences you could have (indeed, likely dohave) that would say that getting $50 million is more important than having incorrect beliefs about a major historical event.

And if it’s rational to take the pill, and you intend to take the pill, then of course it’s rational to believe that in the future, you will have taken the pill and you will become a Holocaust denier.

But it would be absolutely irrational for you to become a Holocaust denier right now because of that. The pill isn’t going to provide evidence that the Holocaust didn’t happen (for no such evidence exists); it’s just going to alter your brain chemistry in such a way as to make you believe that the Holocaust didn’t happen.

So here we have a clear example where you expect to be more wrong in the future.

Of course, if this really only happens in weird thought experiments about mad scientists, then it doesn’t really matter very much. But I contend it happens in reality all the time:

  • You know that by hanging around people with an extremist ideology, you’re likely to adopt some of that ideology, even if you really didn’t want to.
  • You know that if you experience a traumatic event, it is likely to make you anxious and fearful in the future, even when you have little reason to be.
  • You know that if you have a mental illness, you’re likely to form harmful, irrational beliefs about yourself and others whenever you have an episode of that mental illness.

Now, all of these belief changes are things you would likely try to guard against: If you are a researcher studying extremists, you might make a point of taking frequent vacations to talk with regular people and help yourself re-calibrate your beliefs back to normal. Nobody wants to experience trauma, and if you do, you’ll likely seek out therapy or other support to help heal yourself from that trauma. And one of the most important things they teach you in cognitive-behavioral therapy is how to challenge and modify harmful, irrational beliefs when they are triggered by your mental illness.

But these guarding actions only make sense precisely because the anticipated belief change is irrational. If you anticipate a rational change in your beliefs, you shouldn’t try to guard against it; you should factor it into what you already believe.

This also gives me a little more sympathy for Evangelical Christians who try to keep their children from being exposed to secular viewpoints. I think we both agree that having more contact with atheists will make their children more likely to become atheists—but we view this expected outcome differently.

From my perspective, this is a rational change, and it’s a good thing, and I wish they’d factor it into their current beliefs already. (Like hey, maybe if talking to a bunch of smart people and reading a bunch of books on science and philosophy makes you think there’s no God… that might be because… there’s no God?)

But I think, from their perspective, this is an irrational change, it’s a bad thing, the children have been “tempted by Satan” or something, and thus it is their duty to protect their children from this harmful change.

Of course, I am not a subjectivist. I believe there’s a right answer here, and in this case I’m pretty sure it’s mine. (Wouldn’t I always say that? No, not necessarily; there are lots of matters for which I believe that there are experts who know better than I do—that’s what experts are for, really—and thus if I find myself disagreeing with those experts, I try to educate myself more and update my beliefs toward theirs, rather than just assuming they’re wrong. I will admit, however, that a lot of people don’t seem to do this!)

But this does change how I might tend to approach the situation of exposing their children to secular viewpoints. I now understand better why they would see that exposure as a harmful thing, and thus be resistant to actions that otherwise seem obviously beneficial, like teaching kids science and encouraging them to read books. In order to get them to stop “protecting” their kids from the free exchange of ideas, I might first need to persuade them that introducing some doubt into their children’s minds about God isn’t such a terrible thing. That sounds really hard, but it at least clearly explains why they are willing to fight so hard against things that, from my perspective, seem good. (I could also try to convince them that exposure to secular viewpoints won’t make their kids doubt God, but the thing is… that isn’t true. I’d be lying.)

That is, Evangelical Christians are not simply incomprehensibly evil authoritarians who hate truth and knowledge; they quite reasonably want to protect their children from things that will harm them, and they firmly believe that being taught about evolution and the Big Bang will make their children more likely to suffer great harm—indeed, the greatest harm imaginable, the horror of an eternity in Hell. Convincing them that this is not the case—indeed, ideally, that there is no such place as Hell—sounds like a very tall order; but I can at least more keenly grasp the equilibrium they’ve found themselves in, where they believe that anything that challenges their current beliefs poses a literally existential threat. (Honestly, as a memetic adaptation, this is brilliant. Like a turtle, the meme has grown itself a nigh-impenetrable shell. No wonder it has managed to spread throughout the world.)

Quantifying stereotypes

PNRJ cognitive science, core principles, ethics, heuristics and biases, politics, public policy, tribal paradigm , , , , , , , , , , , , ,

Jul 6 JDN 2460863

There are a lot of stereotypes in the world, from the relatively innocuous (“teenagers are rebellious”) to the extremely harmful (“Black people are criminals”).

Most stereotypes are not true.

But most stereotypes are not exactly false, either.

Here’s a list of forty stereotypes, all but one of which I got from this list of stereotypes:

(Can you guess which one? I’ll give you a hint: It’s a group I belong to and a stereotype I’ve experienced firsthand.)

  1. “Children are always noisy and misbehaving.”
  2. “Kids can’t understand complex concepts.”
  3. “Children are tech-savvy.”
  4. “Teenagers are always rebellious.”
  5. “Teenagers are addicted to social media.”
  6. “Adolescents are irresponsible and careless.”
  7. “Adults are always busy and stressed.”
  8. “Adults are responsible.”
  9. “Adults are not adept at using modern technologies.”
  10. “Elderly individuals are always grumpy.”
  11. “Old people can’t learn new skills, especially related to technology.”
  12. “The elderly are always frail and dependent on others.”
  13. “Women are emotionally more expressive and sensitive than men.”
  14. “Females are not as good at math or science as males.”
  15. “Women are nurturing, caring, and focused on family and home.”
  16. “Females are not as assertive or competitive as men.”
  17. “Men do not cry or express emotions openly.”
  18. “Males are inherently better at physical activities and sports.”
  19. “Men are strong, independent, and the primary breadwinners.”
  20. “Males are not as good at multitasking as females.”
  21. “African Americans are good at sports.”
  22. “African Americans are inherently aggressive or violent.”
  23. “Black individuals have a natural talent for music and dance.”
  24. “Asians are highly intelligent, especially in math and science.”
  25. “Asian individuals are inherently submissive or docile.”
  26. “Asians know martial arts.”
  27. “Latinos are uneducated.”
  28. “Hispanic individuals are undocumented immigrants.”
  29. “Latinos are inherently passionate and hot-tempered.”
  30. “Middle Easterners are terrorists.”
  31. “Middle Eastern women are oppressed.”
  32. “Middle Eastern individuals are inherently violent or aggressive.”
  33. “White people are privileged and unacquainted with hardship.”
  34. “White people are racist.”
  35. “White individuals lack rhythm in music or dance.”
  36. “Gay men are excessively flamboyant.”
  37. “Gay men have lisps.”
  38. “Lesbians are masculine.”
  39. “Bisexuals are promiscuous.”
  40. “Trans people get gender-reassignment surgery.”

If you view the above 40 statements as absolute statements about everyone in the category (the first-order operator “for all”), they are obviously false; there are clear counter-examples to every single one. If you view them as merely saying that there are examples of each (the first-order operator “there exists”), they are obviously true, but also utterly trivial, as you could just as easily find examples from other groups.

But I think there’s a third way to read them, which may be more what most people actually have in mind. Indeed, it kinda seems uncharitable not to read them this third way.

That way is:

“This is more true of the group I’m talking about than it is true of other groups.”

And that is not only a claim that can be true, it is a claim that can be quantified.

Recall my new favorite effect size measure, because it’s so simple and intuitive; I’m not much for the official name probability of superiority (especially in this context!), so I’m gonna call it the more down-to-earth chance of being higher.

It is exactly what it sounds like: If you compare a quantity X between group A and group B, what is the chance that the person in group A has a higher value of X?

Let’s start at the top: If you take one randomly-selected child, and one randomly-selected adult, what is the chance that the child is one who is more prone to being noisy and misbehaving?

Probably pretty high.

Or let’s take number 13: If you take one randomly-selected woman and one randomly-selected man, what is the chance that the woman is the more emotionally expressive one?

Definitely more than half.

Or how about number 27: If you take one randomly-selected Latino and one randomly-selected non-Latino (especially if you choose a White or Asian person), what is the chance that the Latino is the less-educated one?

That one I can do fairly precisely: Since 95% of White Americans have completed high school but only 75% of Latino Americans have, while 28% of Whites have a bachelor’s degree and only 21% of Latinos do, the probability of the White person being at least as educated as the Latino person is about 82%.

I don’t know the exact figures for all of these, and I didn’t want to spend all day researching 40 different stereotypes, but I am quite prepared to believe that at least all of the following exhibit a chance of being higher that is over 50%:

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 15, 16, 17, 18, 19, 21, 24, 26, 27, 28, 29, 30, 31, 33, 34, 36, 37, 38, 40.

You may have noticed that that’s… most of them. I had to shrink the font a little to fit them all on one line.

I think 30 is an important one to mention, because while terrorists are a tiny proportion of the Middle Eastern population, they are in fact a much larger proportion of that population than they are of most other populations, and it doesn’t take that many terrorists to make a place dangerous. The Middle East is objectively a more dangerous place for terrorism than most other places, and only India and sub-Saharan Africa close (and both of which are also largely driven by Islamist terrorism). So while it’s bigoted to assume that any given Muslim or Middle Easterner is a terrorist, it is an objective fact that a disproportionate share of terrorists are Middle Eastern Muslims. Part of what I’m trying to do here is get people to more clearly distinguish between those two concepts, because one is true and the other is very, very false.

40 also deserves particular note, because the chance of being higher is almost certainly very close to 100%. While most trans people don’t get gender-reassignment surgery, virtually all people who get gender-reassignment surgery are trans.

Then again, you could see this as a limitation of the measure, since we might expect a 100% score to mean “it’s true of everyone in the group”, when here it simply means “if we ask people whether they have had gender-reassignment surgery, the trans people sometimes say yes and the cis people always say no.”


We could talk about a weak or strict chance of being higher: The weak chance is the chance of being greater than or equal to (which is the normal measure), while the strict chance is the chance of being strictly greater. In this case, the weak chance is nearly 100%, while the strict chance is hard to estimate but probably about 33% based on surveys.

This doesn’t mean that all stereotypes have some validity.

There are some stereotypes here, including a few pretty harmful ones, for which I’m not sure how the statistics would actually shake out:
10, 14, 22, 23, 25, 32, 35, 39

But I think we should be honestly prepared for the possibility that maybe there is some statistical validity to some of these stereotypes too, and instead of simply dismissing the stereotypes as false—or even bigoted—we should instead be trying to determine how true they are, and also look at why they might have some truth to them.

My proposal is to use the chance of being higher as a measure of the truth of a stereotype.

A stereotype is completely true if it has a chance of being higher of 100%.

It is completely false if it has a chance of being higher of 50%.

And it is completely backwards if it has a chance of being higher of 0%.

There is a unique affine transformation that does this: 2X-1.

100% maps to 100%, 50% maps to 0%, and 0% maps to -100%.

With discrete outcomes, the difference between weak and strong chance of being higher becomes very important. With a discrete outcome, you can have a 100% weak chance but a 1% strong chance, and honestly I’m really not sure whether we should say that stereotype is true or not.

For example, for the claim “trans men get bottom surgery”, the figures would be 100% and 6% respectively. The vast majority of trans men don’t get bottom surgery—but cis men almost never do. (Unless I count penis enlargement surgery? Then the numbers might be closer than you’d think, at least in the US where the vast majority of such surgery is performed.)

And for the claim “Middle Eastern Muslims are terrorists”, well, given two random people of whatever ethnicity or religion, they’re almost certainly not terrorists—but if it one of them is, it’s probably the Middle Eastern Muslim. It may be better in this case to talk about the conditional chance of being higher: If you have two random people, you know that one is a terrorist and one isn’t, and one is a Middle Eastern Muslim and one isn’t, how likely is it that the Middle Eastern Muslim is the terrorist? Probably about 80%. Definitely more than 50%, but also not 100%. So that’s the sense in which the stereotype has some validity. It’s still the case that 99.999% of Middle Eastern Muslims aren’t terrorists, and so it remains bigoted to treat every Middle Eastern Muslim you meet like a terrorist.

We could also work harder to more clearly distinguish between “Middle Easterners are terrorists” and “terrorists are Middle Easterners”; the former is really not true (99.999% are not), but the latter kinda is (the plurality of the world’s terrorists are in the Middle East).

Alternatively, for discrete traits we could just report all four probabilities, which would be something like this: 99.999% of Middle Eastern Muslims are not terrorists, and 0.001% are; 99.9998% of other Americans are not terrorists, and 0.0002% are. Compared to Muslim terrorists in the US, White terrorists actually are responsible for more attacks and a similar number of deaths, but largely because there just are a lot more White people in America.

These issues mainly arise when a trait is discrete. When the trait is itself quantitative (like rebelliousness, or math test scores), this is less of a problem, and the weak and strong chances of being higher are generally more or less the same.


So instead of asking whether a stereotype is true, we could ask: How true is it?

Using measures like this, we will find that some stereotypes probably have quite high truth levels, like 1 and 4; but others, if they are true at all, must have quite low truth levels, like 14; if there’s a difference, it’s a small difference!

The lower a stereotype’s truth level, the less useful it is; indeed, by this measure, it directly predicts how accurate you’d be at guessing someone’s score on the trait if you knew only the group they belong to. If you couldn’t really predict, then why are you using the stereotype? Get rid of it.

Moreover, some stereotypes are clearly more harmful than others.

Even if it is statistically valid to say that Black people are more likely to commit crimes in the US than White people (it is), the kind of person who goes around saying “Black people are criminals” is (1) smearing all Black people with the behavior of a minority of them, and (2) likely to be racist in other ways. So we have good reason to be suspect of people who say such things, even if there may be a statistical kernel of truth to their claims.

But we might still want to be a little more charitable, a little more forgiving, when people express stereotypes. They may make what sounds like a blanket absolute “for all” statement, but actually intend something much milder—something that might actually be true. They might not clearly grasp the distinction between “Middle Easterners are terrorists” and “terrorists are Middle Easterners”, and instead of denouncing them as a bigot immediately, you could try taking the time to listen to what they are saying and carefully explain what’s wrong with it.

Failing to be charitable like this—as we so often do—often feels to people like we are dismissing their lived experience. All the terrorists they can think of were Middle Eastern! All of the folks they know with a lisp turned out to be gay! Lived experience is ultimately anecdotal, but it still has a powerful effect on how people think (too powerful—see also availability heuristic), and it’s really not surprising that people would feel we are treating them unjustly if we immediately accuse them of bigotry simply for stating things that, based on their own experience, seem to be true.

I think there’s another harm here as well, which is that we damage our own credibility. If I believe that something is true and you tell me that I’m a bad person for believing it, that doesn’t make me not believe it—it makes me not trust you. You’ve presented yourself as the sort of person who wants to cover up the truth when it doesn’t fit your narrative. If you wanted to actually convince me that my belief is wrong, you could present evidence that might do that. (To be fair, this doesn’t always work; but sometimes it does!) But if you just jump straight to attacking my character, I don’t want to talk to you anymore.

How to teach people about vaccines

PNRJ ethics, heuristics and biases, science and academia , , , , , , ,

May 25 JDN 2460821

Vaccines are one of the greatest accomplishments in human history. They have saved hundreds of millions of lives with minimal cost and almost no downside at all. (For everyone who suffers a side effect from a vaccine, I guarantee you: Someone else would have had it much worse from the disease if they hadn’t been vaccinated.)

It’s honestly really astonishing just how much good vaccines have done for humanity.

Thus, it’s a bit of a mystery how there are so many people who oppose vaccines.

But this mystery becomes a little less baffling in light of behavioral economics. People assess the probability of an event mainly based on the availability heuristic: How many examples can they think of when it happened?

Precisely because vaccines have been so effective at preventing disease, we have now reached a point where diseases that were once commonplace are now virtually eradicated. Thus, parents considering whether to vaccinate their children think about whether they know anyone who has gotten sick from that disease, and they can’t think of anyone, so they assume that it’s not a real danger. Then, someone comes along and convinces them (based on utter lies that have been thoroughly debunked) that vaccines cause autism, and they get scared about autism, because they can think of someone they know who has autism.

But of course, the reason that they can’t think of anyone who died from measles or pertussis is because of the vaccines. So I think we need an educational campaign that makes these rates more vivid for people, which plays into the availability heuristic instead of against it.

Here’s my proposal for a little educational game that might help:

It functions quite similarly to a classic tabletop RPG like Dungeons & Dragons, only here the target numbers are based on real figures.


Gather a group of at least 100 people. (Too few, and the odds become small enough that you may get no examples of some diseases.)

Each person needs 3 10-sided dice. Preferably they would be different colors or somehow labeled, because we want one to represent the 100s digit, one the 10s digit, and one the 1s digit. (The numbers you can roll thus range uniformly from 0 to 999.) In TTRPG parlance, this is called a d1000.

Give each person a worksheet that looks like this:

DiseaseBefore vaccine: Caught?Before vaccine: Died?After vaccine: Caught?After vaccine: Died?
Diptheria



Measles



Mumps



Pertussis



Polio



Rubella



Smallpox



Tetanus



Hep A



Hep B



Pneumococca



Varicella



In the first round, use the figures for before the vaccine. In the second round, use the figures for after the vaccine.

For each disease in each round, there will be a certain roll that people need to get in order to either not contract the disease: Roll that number or higher, and you are okay; roll below it, and you catch the disease.


Likewise, there will be a certain roll they need to get to survive if they contract it: Roll that number or higher, and you get sick but survive; roll below it, and you die.

Each time, name a disease, and then tell people what they need to roll to not catch it.

Have them all roll, and if they catch it, check off that box.

Then, for everyone who catches it, have them roll again to see if they survive it. If they die, check that box.

Based on the historical incidences which I have converted into lifetime prevalences, the target numbers are as follows:

DiseaseBefore vaccine: Roll to not catchBefore vaccine: Roll to surviveAfter vaccine: Roll to not catchAfter vaccine: Roll to survive
Diptheria138700
Measles244100
Mumps66020
Pertussis1232042
Polio208900
Rubella191190
Smallpox201200
Tetanus1800171
Hep A37141
Hep B22444
Pneumococca1910311119
Varicella95011640

What you should expect to see for a group of 100 is something like this (of course the results are random, so it won’t be this exactly):

DiseaseBefore vaccine: Number caughtBefore vaccine: Number diedAfter vaccine: Number caughtAfter vaccine: Number died
Diptheria1000
Measles24000
Mumps7000
Pertussis12100
Polio2000
Rubella2000
Smallpox2000
Tetanus0000
Hep A4000
Hep B2000
Pneumococca2111
Varicella950160

You’ll find that not a lot of people have checked those “dead” boxes either before or after the vaccine. So if you just look at death rates, the difference may not seem that stark.

(Of course, over a world as big as ours, it adds up: The difference between the 0.25% death rate of pertussis before the vaccine and 0% today is 20 million people—roughly the number of people who live in the New York City metro area.)

But I think people will notice that a lot more people got sick in the “before-vaccine” world than the “after-vaccine” world. Moreover, those that did get sick will find themselves rolling the dice on dying; they’ll probably be fine, but you never know for sure.

Make sure people also notice that (except for pneumococca), if you do get sick, the roll you need to survive is a lot higher without the vaccine. (If anyone does get unlucky enough to get tetanus in the first round, they’re probably gonna die!)

If anyone brings up autism, you can add an extra round where you roll for that too.

The supposedly “epidemic” prevalence of autism today is… 3.2%.

(Honestly I expected higher than that, but then, I hang around with a lot of queer and neurodivergent people. (So the availability heuristic got me too!))

Thus, what’s the roll to not get autism? 32.

Even with the expansive diagnostic criteria that include a lot of borderline cases like yours truly, you still only need to roll 32 on this d1000 to not get autism.

This means that only about 3 people in your group of 100 should end up getting autism, most likely fewer than the number who were saved from getting measles, mumps, and rubella by the vaccine, comparable to the number saved from getting most of the other diseases—and almost certainly fewer than the number saved from getting varicella.

So even if someone remains absolutely convinced that vaccines cause autism, you can now point out that vaccines also clearly save billions of people from getting sick and millions from dying.

Also, there are different kinds of autism. Some forms might not even be considered a disability if society were more accommodating; others are severely debilitating.

Recently clinicians have started to categorize “profound autism”, the kind that is severely debilitating. This constitutes about 25% of children with autism—but it’s a falling percentage over time, because broader diagnostic criteria are including more people as autistic, but not changing the number who are severely debilitated. (It is controversial exactly what should constitute “profound autism”, but I do think the construct is useful; there’s a big difference between someone like me who can basically function normally with some simple accommodations, and someone who never even learns to talk.)

So you can have the group do another roll, specifically for profound autism; that target number is now only 8.

There’s also one more demonstration you can do.

Aggregating over all these diseases, we can find the overall chance of dying from any of these diseases before and after the vaccine.

Have everyone roll for that, too:

Before the vaccines, the target number is 8. Afterward, it is 1.

If autism was brought up, make that comparison explicit.

Even if 100% of autism cases were caused by vaccines (which, I really must say, is ridiculous, as there’s no credible evidence that vaccines cause autism at all) that would still mean the following:

You are trading off a 32 in 1000 chance of your child being autistic and an 8 in 1000 chance of your child being profoundly autistic, against a 7 in 1000 chance of your child dying.

If someone is still skeptical of vaccines at this point, you should ask them point-blank:

Do you really think that being autistic is one-fifth as bad as dying?

Do you really think that being profoundly autistic is as bad as dying?

A knockdown proof of social preferences

PNRJ core principles, critique of neoclassical economics, experimental economics, heuristics and biases, tribal paradigm , , , , , ,

Apr 27 JDN 2460793

In economics jargon, social preferences basically just means that people care about what happens to people other than themselves.

If you are not an economist, it should be utterly obvious that social preferences exist:

People generally care the most about their friends and family, less but still a lot about their neighbors and acquaintances, less but still moderately about other groups they belong to such as those delineated by race, gender, religion, and nationality (or for that matter alma mater), and less still but not zero about any randomly-selected human being. Most of us even care about the welfare of other animals, though we can be curiously selective about this: Abuse that would horrify most people if done to cats or dogs passes more or less ignored when it is committed against cows, pigs, and chickens.

For some people, there are also groups for which there seem to be negative social preferences, sometimes called “spiteful preferences”, but that doesn’t really seem to capture it: I think we need a stronger word like hatredfor whatever emotion human beings feel when they are willing and eager to participate in genocide. Yet even that is still a social preference: If you want someone to suffer or die, you do care about what happens to them.

But if you are an economist, you’ll know that the very idea of social preferences remains controversial, even after it has been clearly and explictly demonstrated by numerous randomized controlled experiments. (I will never forget the professor who put “altruism” in scare quotes in an email reply he sent me.)

Indeed, I have realized that the experimental evidence is so clear, so obvious, that it surprises me that I haven’t seen anyone present the really overwhelming knockdown evidence that ought to convince any reasonable skeptic. So that is what I have decided to do today.

Consider the following four economics experiments:

Dictator 1Participant 1 chooses an allocation of $20, dividing it between themself and Participant 2. Whatever allocation Participant 1 chooses, Participant 2 must accept. Both participants get their allocated amounts.
Dictator 2Participant 1 chooses an allocation of $20, choosing how much they get. Participant 1 gets their allocated amount. The rest of the money is burned.
Ultimatum 1Participant 1 chooses an allocation of $20, dividing it between themself and Participant 2. Participant 2 may choose to accept or reject this allocation; if they accept, both participants get their allocated amounts. If they reject, both participants get nothing.
Ultimatum 2Participant 1 chooses an allocation of $20, dividing it between themself and Participant 2. Participant 2 may choose to accept or reject this allocation; if they accept, both participants get their allocated amounts. If they reject, Participant 2 gets nothing, but Participant 1 still gets the allocated amount.

Dictator 1 and Ultimatum 1 are the standard forms of the Dictator Game and Ultimatum Game, which are experiments that have been conducted dozens if not hundreds of times and are the subject of a huge number of papers in experimental economics.

These experiments clearly demonstrate the existence of social preferences. But I think even most behavioral economists don’t quite seem to grasp just how compelling that evidence is.

This is because they have generally failed to compare against my other two experiments, Dictator 2 and Ultimatum 2.

If social preferences did not exist, Participant 1 would be completely indifferent about what happened to the money that they themself did not receive.

In that case, Dictator 1 and Dictator 2 should show the same result: Participant 1 chooses to get $20.

Likewise, Ultimatum 1 and Ultimatum 2 should show the same result: Participant 1 chooses to get $19, offering only $1 to Participant 2, and Participant 2 accepts. This is the outcome that is “rational” in the hyper-selfish neoclassical sense.

Much ink has already been spilled over the fact that these are not the typical outcomes of Dictator 1 and Ultimatum 1. Far more likely is that Participant 1 offers something close to $10, or even $10 exactly, in both games; and in Ultimatum 1, in the unlikely event that Participant 1 should offer only $1 or $2, Participant 2 will typically reject.

But what I’d like to point out today is that the “rational” neoclassical outcome is what would happen in Dictator 2 and Ultimatum 2, and that this is so obvious we probably don’t even need to run the experiments (but we might as well, just to be sure).

In Dictator 1, the money that Participant 1 doesn’t keep goes to Participant 2, and so they are deciding how to weigh their own interests against those of another. But in Dictator 2, Participant 1 is literally just deciding how much free money they will receive. The other money doesn’t go to anyone—not even back to the university conducting the experiment. It’s just burned. It provides benefit to no one. So the rational choice is in fact obvious: Take all of the free money. (Technically, burning money and thereby reducing the money supply would have a miniscule effect of reducing future inflation across the entire economy. But even the full $20 would be several orders of magnitude too small for anyone to notice—and even a much larger amount like $10 billion would probably end up being compensated by the actions of the Federal Reserve.)

Likewise, in both Ultimatum 1 and Ultimatum 2, the money that Participant 1 doesn’t keep will go to Participant 2. Their offer will thus probably be close to $10. But what I really want to focus in on is Participant 2’s choice: If they are offered only $1 or $2, will they accept? Neoclassical theory says that the “rational” choice is to accept it. But in Ultimatum 1, most people will reject it. Are they being irrational?

If they were simply being irrational—failing to maximize their own payoff—then they should reject just as often in Ultimatum 2. But I contend that they would in fact accept far more offers in Ultimatum 2 than they did in Ultimatum 1. Why? Because rejection doesn’t stop Participant 1 from getting what they demanded. There is no way to punish Participant 1 for an unfair offer in Ultimatum 2: It is literally just a question of whether you get $1 or $0.

Like I said, I haven’t actually run these experiments. I’m not sure anyone has. But these results seem very obvious, and I would be deeply shocked if they did not turn out the way I expect. (Perhaps as shocked as so many neoclassical economists were when they first saw the results of experiments on Dictator 1 and Ultimatum 1!)

Thus, Dictator 2 and Ultimatum 2 should have outcomes much more like what neoclassical economics predicts than Dictator 1 and Ultimatum 1.

Yet the only difference—the only difference—between Dictator 1 and Dictator 2, and between Ultimatum 1 and Ultimatum 2, is what happens to someone else’s payoff when you make your decision. Your own payoff is exactly identical.

Thus, behavior changes when we change only the effects on the payoffs of other people; therefore people care about the payoffs of others; therefore social preferences exist.

QED.

Of course this still leaves the question of what sort of social preferences people have, and why:

  • Why are some people more generous than others? Why are people sometimes spiteful—or even hateful?
  • Is it genetic? Is it evolutionary? Is it learned? Is it cultural? Likely all of the above.
  • Are people implicitly thinking of themselves as playing in a broader indefinitely iterated game called “life” and using that to influence their decisions? Quite possibly.
  • Is maintaining a reputation of being a good person important to people? In general, I’m sure it is, but I don’t think it can explain the results of these economic experiments by itself—especially in versions where everything is completely anonymous.

But given the stark differences between Dictator 1 versus Dictator 2 and Ultimatum 1 versus Ultimatum 2 (and really, feel free to run the experiments!), I don’t think anyone can reasonably doubt that social preferences do, in fact, exist.

If you ever find someone who does doubt social preferences, point them to this post.

Adverse selection and all-you-can-eat

PNRJ core principles, heuristics and biases, market failure, public policy , , , ,

Jul 7 JDN 2460499

The concept of adverse selection is normally associated with finance and insurance, and they certainly do have a lot of important applications there. But finance and insurance are complicated (possibly intentionally?) and a lot of people are intimidated by them, and it turns out there’s a much simpler example of this phenomenon, which most people should find familiar:

All-you-can-eat meals.

At most restaurants, you buy a specific amount of food: One cheeseburger, one large order of fries. But at some, you have another option: You can buy an indeterminate amount of food, as much as you are able to eat at one sitting.

Now think about this from the restaurant’s perspective: How do you price an all-you-can-eat meal and turn a profit? Your cost obviously depends on how much food you need to prepare, but you don’t know exactly how much each customer is going to eat.

Fortunately, you don’t need to! You only need to know how much people will eat on average. As long as the average customer’s meal is worth less than what they paid for it, you will continue to make a profit, even though some customers end up eating more than what they paid for.

Insurance works the same way: Some people will cash in on their insurance, costing the company money; but most will not, providing the company with revenue. In fact, you could think of an all-you-can-eat-meal as a form of food insurance.

So, all you need to do is figure out how much an average person eats in one meal, and price based on that, right?

Wrong. Here’s the problem: The people who eat at your restaurant aren’t a random sample of people. They are specifically the kind of people who eat at all-you-can-eat restaurants.

Someone who eats very little probably won’t want to go to your restaurant very much, because they’ll have to pay a high price for very little food. But someone with a big appetite will go to your restaurant frequently, because they get to eat a large amount of food for that same price.

This means that, on average, your customers will end up eating more than what an average restaurant customer eats. You’ll have to raise the price accordingly—which will make the effect even stronger.

This can end in one of two ways: Either an equilibrium is reached where the price is pretty high and most of the customers have big appetites, or no equilibrium is reached, and the restaurant either goes bankrupt or gets rid of its all-you-can-eat policy.

But there’s basically no way to get the outcome that seems the best, which is a low price and a wide variety of people attending the restaurant. Those who eat very little just won’t show up.

That’s adverse selection. Because there’s no way to charge people who eat more a higher price (other than, you know, not being all-you-can-eat), people will self-select by choosing whether or not to attend, and the people who show up at your restaurant will be the ones with big appetites.

The same thing happens with insurance. Say we’re trying to price health insurance; we don’t just need to know the average medical expenses of our population, even if we know a lot of specific demographic information. People who are very healthy may choose not to buy insurance, leaving us with only the less-healthy people buying our insurance—which will force us to raise the price of our insurance.

Once again, you’re not getting a random sample; you’re getting a sample of the kind of people who buy health insurance.

Obamacare was specifically designed to prevent this, by imposing a small fine on people who choose not to buy health insurance. The goal was to get more healthy people buying insurance, in order to bring the cost down. It worked, at least for awhile—but now that individual mandate has been nullified, so adverse selection will once again rear its ugly head. Had our policymakers better understood this concept, they might not have removed the individual mandate.

Another option might occur to you, analogous to the restaurant: What if we just didn’t offer insurance, and made people pay for all their own healthcare? This would be like the restaurant ending its all-you-can-eat policy and charging for each new serving. Most restaurants do that, so maybe it’s the better option in general?

There are two problems here, one ethical, one economic.

The ethical problem is that people don’t deserve to be sick or injured. They didn’t choose those things. So it isn’t fair to let them suffer or bear all the costs of getting better. As a society, we should share in those costs. We should help people in need. (If you don’t already believe this, I don’t know how to convince you of it. But hopefully most people do already believe this.)

The economic problem is that some healthcare is rarely needed, but very expensive. That’s exactly the sort of situation where insurance makes sense, to spread the cost around. If everyone had to pay for their own care with no insurance at all, then most people who get severe illnesses simply wouldn’t be able to afford it. They’d go massively into debt, go bankrupt—people already do, even with insurance!—and still not even get much of the care they need. It wouldn’t matter that we have good treatments for a lot of cancers now; they are all very expensive, so most people with cancer would be unable to pay for them, and they’d just die anyway.

In fact, the net effect of such a policy would probably be to make us all poorer, because a lot of illness and disability would go untreated, making our workforce less productive. Even if you are very healthy and never need health insurance, it may still be in your own self-interest to support a policy of widespread health insurance, so that sick people get treated and can go back to work.

A world without all-you-can-eat restaurants wouldn’t be so bad. But a world without health insurance would be one in which millions of people suffer needlessly because they can’t afford healthcare.

Everyone includes your mother and Los Angeles

PNRJ cognitive science, computer science, core principles, current events, ethics, futurism, heuristics and biases, politics, public policy , , , , , ,

Apr 28 JDN 2460430

What are the chances that artificial intelligence will destroy human civilization?

A bunch of experts were surveyed on that question and similar questions, and half of respondents gave a probability of 5% or more; some gave probabilities as high as 99%.

This is incredibly bizarre.

Most AI experts are people who work in AI. They are actively participating in developing this technology. And yet more than half of them think that the technology they are working on right now has a more than 5% chance of destroying human civilization!?

It feels to me like they honestly don’t understand what they’re saying. They can’t really grasp at an intuitive level just what a 5% or 10% chance of global annihilation means—let alone a 99% chance.

If something has a 5% chance of killing everyone, we should consider that at least as bad as something that is guaranteed to kill 5% of people.

Probably worse, in fact, because you can recover from losing 5% of the population (we have, several times throughout history). But you cannot recover from losing everyone. So really, it’s like losing 5% of all future people who will ever live—which could be a very large number indeed.

But let’s be a little conservative here, and just count people who already, currently exist, and use 5% of that number.

5% of 8 billion people is 400 million people.

So anyone who is working on AI and also says that AI has a 5% chance of causing human extinction is basically saying: “In expectation, I’m supporting 20 Holocausts.”

If you really think the odds are that high, why aren’t you demanding that any work on AI be tried as a crime against humanity? Why aren’t you out there throwing Molotov cocktails at data centers?

(To be fair, Eliezer Yudkowsky is actually calling for a global ban on AI that would be enforced by military action. That’s the kind of thing you should be doing if indeed you believe the odds are that high. But most AI doomsayers don’t call for such drastic measures, and many of them even continue working in AI as if nothing is wrong.)

I think this must be scope neglect—or something even worse.

If you thought a drug had a 99% chance of killing your mother, you would never let her take the drug, and you would probably sue the company for making it.

If you thought a technology had a 99% chance of destroying Los Angeles, you would never even consider working on that technology, and you would want that technology immediately and permanently banned.

So I would like to remind anyone who says they believe the danger is this great and yet continues working in the industry:

Everyone includes your mother and Los Angeles.

If AI destroys human civilization, that means AI destroys Los Angeles. However shocked and horrified you would be if a nuclear weapon were detonated in the middle of Hollywood, you should be at least that shocked and horrified by anyone working on advancing AI, if indeed you truly believe that there is at least a 5% chance of AI destroying human civilization.

But people just don’t seem to think this way. Their minds seem to take on a totally different attitude toward “everyone” than they would take toward any particular person or even any particular city. The notion of total human annihilation is just so remote, so abstract, they can’t even be afraid of it the way they are afraid of losing their loved ones.

This despite the fact that everyone includes all your loved ones.

If a drug had a 5% chance of killing your mother, you might let her take it—but only if that drug was the best way to treat some very serious disease. Chemotherapy can be about that risky—but you don’t go on chemo unless you have cancer.

If a technology had a 5% chance of destroying Los Angeles, I’m honestly having trouble thinking of scenarios in which we would be willing to take that risk. But the closest I can come to it is the Manhattan Project. If you’re currently fighting a global war against fascist imperialists, and they are also working on making an atomic bomb, then being the first to make an atomic bomb may in fact be the best option, even if you know that it carries a serious risk of utter catastrophe.

In any case, I think one thing is clear: You don’t take that kind of serious risk unless there is some very large benefit. You don’t take chemotherapy on a whim. You don’t invent atomic bombs just out of curiosity.

Where’s the huge benefit of AI that would justify taking such a huge risk?

Some forms of automation are clearly beneficial, but so far AI per se seems to have largely made our society worse. ChatGPT lies to us. Robocalls inundate us. Deepfakes endanger journalism. What’s the upside here? It makes a ton of money for tech companies, I guess?

Now, fortunately, I think 5% is too high an estimate.

(Scientific American agrees.)

My own estimate is that, over the next two centuries, there is about a 1% chance that AI destroys human civilization, and only a 0.1% chance that it results in human extinction.

This is still really high.

People seem to have trouble with that too.

“Oh, there’s a 99.9% chance we won’t all die; everything is fine, then?” No. There are plenty of other scenarios that would also be very bad, and a total extinction scenario is so terrible that even a 0.1% chance is not something we can simply ignore.

0.1% of people is still 8 million people.

I find myself in a very odd position: On the one hand, I think the probabilities that doomsayers are giving are far too high. On the other hand, I think the actions that are being taken—even by those same doomsayers—are far too small.

Most of them don’t seem to consider a 5% chance to be worthy of drastic action, while I consider a 0.1% chance to be well worthy of it. I would support a complete ban on all AI research immediately, just from that 0.1%.

The only research we should be doing that is in any way related to AI should involve how to make AI safer—absolutely no one should be trying to make it more powerful or apply it to make money. (Yet in reality, almost the opposite is the case.)

Because 8 million people is still a lot of people.

Is it fair to treat a 0.1% chance of killing everyone as equivalent to killing 0.1% of people?

Well, first of all, we have to consider the uncertainty. The difference between a 0.05% chance and a 0.015% chance is millions of people, but there’s probably no way we can actually measure it that precisely.

But it seems to me that something expected to kill between 4 million and 12 million people would still generally be considered very bad.

More importantly, there’s also a chance that AI will save people, or have similarly large benefits. We need to factor that in as well. Something that will kill 4-12 million people but also save 15-30 million people is probably still worth doing (but we should also be trying to find ways to minimize the harm and maximize the benefit).

The biggest problem is that we are deeply uncertain about both the upsides and the downsides. There are a vast number of possible outcomes from inventing AI. Many of those outcomes are relatively mundane; some are moderately good, others are moderately bad. But the moral question seems to be dominated by the big outcomes: With some small but non-negligible probability, AI could lead to either a utopian future or an utter disaster.

The way we are leaping directly into applying AI without even being anywhere close to understanding AI seems to me especially likely to lean toward disaster. No other technology has ever become so immediately widespread while also being so poorly understood.

So far, I’ve yet to see any convincing arguments that the benefits of AI are anywhere near large enough to justify this kind of existential risk. In the near term, AI really only promises economic disruption that will largely be harmful. Maybe one day AI could lead us into a glorious utopia of automated luxury communism, but we really have no way of knowing that will happen—and it seems pretty clear that Google is not going to do that.

Artificial intelligence technology is moving too fast. Even if it doesn’t become powerful enough to threaten our survival for another 50 years (which I suspect it won’t), if we continue on our current path of “make money now, ask questions never”, it’s still not clear that we would actually understand it well enough to protect ourselves by then—and in the meantime it is already causing us significant harm for little apparent benefit.

Why are we even doing this? Why does halting AI research feel like stopping a freight train?

I dare say it’s because we have handed over so much power to corporations.

The paperclippers are already here.

Bundling the stakes to recalibrate ourselves

PNRJ cognitive science, heuristics and biases, personal , , , , , , , , , ,

Mar 31 JDN 2460402

In a previous post I reflected on how our minds evolved for an environment of immediate return: An immediate threat with high chance of success and life-or-death stakes. But the world we live in is one of delayed return: delayed consequences with low chance of success and minimal stakes.

We evolved for a world where you need to either jump that ravine right now or you’ll die; but we live in a world where you’ll submit a hundred job applications before finally getting a good offer.

Thus, our anxiety system is miscalibrated for our modern world, and this miscalibration causes us to have deep, chronic anxiety which is pathological, instead of brief, intense anxiety that would protect us from harm.

I had an idea for how we might try to jury-rig this system and recalibrate ourselves:

Bundle the stakes.

Consider job applications.

The obvious way to think about it is to consider each application, and decide whether it’s worth the effort.

Any particular job application in today’s market probably costs you 30 minutes, but you won’t hear back for 2 weeks, and you have maybe a 2% chance of success. But if you fail, all you lost was that 30 minutes. This is the exact opposite of what our brains evolved to handle.

So now suppose if you think of it in terms of sending 100 job applications.

That will cost you 30 times 100 minutes = 50 hours. You still won’t hear back for weeks, but you’ve spent weeks, so that won’t feel as strange. And your chances of success after 100 applications are something like 1-(0.98)^100 = 87%.

Even losing 50 hours over a few weeks is not the disaster that falling down a ravine is. But it still feels a lot more reasonable to be anxious about that than to be anxious about losing 30 minutes.

More importantly, we have radically changed the chances of success.

Each individual application will almost certainly fail, but all 100 together will probably succeed.

If we were optimally rational, these two methods would lead to the same outcomes, by a rather deep mathematical law, the linearity of expectation:
E[nX] = n E[X]

Thus, the expected utility of doing something n times is precisely n times the expected utility of doing it once (all other things equal); and so, it doesn’t matter which way you look at it.

But of course we aren’t perfectly rational. We don’t actually respond to the expected utility. It’s still not entirely clear how we do assess probability in our minds (prospect theory seems to be onto something, but it’s computationally harder than rational probability, which means it makes absolutely no sense to evolve it).

If instead we are trying to match up our decisions with a much simpler heuristic that evolved for things like jumping over ravines, our representation of probability may be very simple indeed, something like “definitely”, “probably”, “maybe”, “probably not”, “definitely not”. (This is essentially my categorical prospect theory, which, like the stochastic overload model, is a half-baked theory that I haven’t published and at this point probably never will.)

2% chance of success is solidly “probably not” (or maybe something even stronger, like “almost definitely not”). Then, outcomes that are in that category are presumably weighted pretty low, because they generally don’t happen. Unless they are really good or really bad, it’s probably safest to ignore them—and in this case, they are neither.

But 87% chance of success is a clear “probably”; and outcomes in that category deserve our attention, even if their stakes aren’t especially high. And in fact, by bundling them, we have even made the stakes a bit higher—likely making the outcome a bit more salient.

The goal is to change “this will never work” to “this is going to work”.

For an individual application, there’s really no way to do that (without self-delusion); maybe you can make the odds a little better than 2%, but you surely can’t make them so high they deserve to go all the way up to “probably”. (At best you might manage a “maybe”, if you’ve got the right contacts or something.)

But for the whole set of 100 applications, this is in fact the correct assessment. It will probably work. And if 100 doesn’t, 150 might; if 150 doesn’t, 200 might. At no point do you need to delude yourself into over-estimating the odds, because the actual odds are in your favor.

This isn’t perfect, though.

There’s a glaring problem with this technique that I still can’t resolve: It feels overwhelming.

Doing one job application is really not that big a deal. It accomplishes very little, but also costs very little.

Doing 100 job applications is an enormous undertaking that will take up most of your time for multiple weeks.

So if you are feeling demotivated, asking you to bundle the stakes is asking you to take on a huge, overwhelming task that surely feels utterly beyond you.

Also, when it comes to this particular example, I even managed to do 100 job applications and still get a pretty bad outcome: My only offer was Edinburgh, and I ended up being miserable there. I have reason to believe that these were exceptional circumstances (due to COVID), but it has still been hard to shake the feeling of helplessness I learned from that ordeal.

Maybe there’s some additional reframing that can help here. If so, I haven’t found it yet.

But maybe stakes bundling can help you, or someone out there, even if it can’t help me.