# Why are humans so bad with probability?

Apr 29 JDN 2458238

In previous posts on deviations from expected utility and cumulative prospect theory, I’ve detailed some of the myriad ways in which human beings deviate from optimal rational behavior when it comes to probability.

This post is going to be a bit different: Yes, we behave irrationally when it comes to probability. Why?

Why aren’t we optimal expected utility maximizers?
This question is not as simple as it sounds. Some of the ways that human beings deviate from neoclassical behavior are simply because neoclassical theory requires levels of knowledge and intelligence far beyond what human beings are capable of; basically anything requiring “perfect information” qualifies, as does any game theory prediction that involves solving extensive-form games with infinite strategy spaces by backward induction. (Don’t feel bad if you have no idea what that means; that’s kind of my point. Solving infinite extensive-form games by backward induction is an unsolved problem in game theory; just this past week I saw a new paper presented that offered a partial potential solutionand yet we expect people to do it optimally every time?)

I’m also not going to include questions of fundamental uncertainty, like “Will Apple stock rise or fall tomorrow?” or “Will the US go to war with North Korea in the next ten years?” where it isn’t even clear how we would assign a probability. (Though I will get back to them, for reasons that will become clear.)

No, let’s just look at the absolute simplest cases, where the probabilities are all well-defined and completely transparent: Lotteries and casino games. Why are we so bad at that?

Lotteries are not a computationally complex problem. You figure out how much the prize is worth to you, multiply it by the probability of winning—which is clearly spelled out for you—and compare that to how much the ticket price is worth to you. The most challenging part lies in specifying your marginal utility of wealth—the “how much it’s worth to you” part—but that’s something you basically had to do anyway, to make any kind of trade-offs on how to spend your time and money. Maybe you didn’t need to compute it quite so precisely over that particular range of parameters, but you need at least some idea how much \$1 versus \$10,000 is worth to you in order to get by in a market economy.

Casino games are a bit more complicated, but not much, and most of the work has been done for you; you can look on the Internet and find tables of probability calculations for poker, blackjack, roulette, craps and more. Memorizing all those probabilities might take some doing, but human memory is astonishingly capacious, and part of being an expert card player, especially in blackjack, seems to involve memorizing a lot of those probabilities.

Furthermore, by any plausible expected utility calculation, lotteries and casino games are a bad deal. Unless you’re an expert poker player or blackjack card-counter, your expected income from playing at a casino is always negative—and the casino set it up that way on purpose.

Why, then, can lotteries and casinos stay in business? Why are we so bad at such a simple problem?

Clearly we are using some sort of heuristic judgment in order to save computing power, and the people who make lotteries and casinos have designed formal models that can exploit those heuristics to pump money from us. (Shame on them, really; I don’t fully understand why this sort of thing is legal.)

In another previous post I proposed what I call “categorical prospect theory”, which I think is a decently accurate description of the heuristics people use when assessing probability (though I’ve not yet had the chance to test it experimentally).

But why use this particular heuristic? Indeed, why use a heuristic at all for such a simple problem?

I think it’s helpful to keep in mind that these simple problems are weird; they are absolutely not the sort of thing a tribe of hunter-gatherers is likely to encounter on the savannah. It doesn’t make sense for our brains to be optimized to solve poker or roulette.

The sort of problems that our ancestors encountered—indeed, the sort of problems that we encounter, most of the time—were not problems of calculable probability risk; they were problems of fundamental uncertainty. And they were frequently matters of life or death (which is why we’d expect them to be highly evolutionarily optimized): “Was that sound a lion, or just the wind?” “Is this mushroom safe to eat?” “Is that meat spoiled?”

In fact, many of the uncertainties most important to our ancestors are still important today: “Will these new strangers be friendly, or dangerous?” “Is that person attracted to me, or am I just projecting my own feelings?” “Can I trust you to keep your promise?” These sorts of social uncertainties are even deeper; it’s not clear that any finite being could ever totally resolve its uncertainty surrounding the behavior of other beings with the same level of intelligence, as the cognitive arms race continues indefinitely. The better I understand you, the better you understand me—and if you’re trying to deceive me, as I get better at detecting deception, you’ll get better at deceiving.

Personally, I think that it was precisely this sort of feedback loop that resulting in human beings getting such ridiculously huge brains in the first place. Chimpanzees are pretty good at dealing with the natural environment, maybe even better than we are; but even young children can outsmart them in social tasks any day. And once you start evolving for social cognition, it’s very hard to stop; basically you need to be constrained by something very fundamental, like, say, maximum caloric intake or the shape of the birth canal. Where chimpanzees look like their brains were what we call an “interior solution”, where evolution optimized toward a particular balance between cost and benefit, human brains look more like a “corner solution”, where the evolutionary pressure was entirely in one direction until we hit up against a hard constraint. That’s exactly what one would expect to happen if we were caught in a cognitive arms race.

What sort of heuristic makes sense for dealing with fundamental uncertainty—as opposed to precisely calculable probability? Well, you don’t want to compute a utility function and multiply by it, because that adds all sorts of extra computation and you have no idea what probability to assign. But you’ve got to do something like that in some sense, because that really is the optimal way to respond.

So here’s a heuristic you might try: Separate events into some broad categories based on how frequently they seem to occur, and what sort of response would be necessary.

Some things, like the sun rising each morning, seem to always happen. So you should act as if those things are going to happen pretty much always, because they do happen… pretty much always.

Other things, like rain, seem to happen frequently but not always. So you should look for signs that those things might happen, and prepare for them when the signs point in that direction.

Still other things, like being attacked by lions, happen very rarely, but are a really big deal when they do. You can’t go around expecting those to happen all the time, that would be crazy; but you need to be vigilant, and if you see any sign that they might be happening, even if you’re pretty sure they’re not, you may need to respond as if they were actually happening, just in case. The cost of a false positive is much lower than the cost of a false negative.

And still other things, like people sprouting wings and flying, never seem to happen. So you should act as if those things are never going to happen, and you don’t have to worry about them.

This heuristic is quite simple to apply once set up: It can simply slot in memories of when things did and didn’t happen in order to decide which category they go in—i.e. availability heuristic. If you can remember a lot of examples of “almost never”, maybe you should move it to “unlikely” instead. If you get a really big number of examples, you might even want to move it all the way to “likely”.

Another large advantage of this heuristic is that by combining utility and probability into one metric—we might call it “importance”, though Bayesian econometricians might complain about that—we can save on memory space and computing power. I don’t need to separately compute a utility and a probability; I just need to figure out how much effort I should put into dealing with this situation. A high probability of a small cost and a low probability of a large cost may be equally worth my time.

How might these heuristics go wrong? Well, if your environment changes sufficiently, the probabilities could shift and what seemed certain no longer is. For most of human history, “people walking on the Moon” would seem about as plausible as sprouting wings and flying away, and yet it has happened. Being attacked by lions is now exceedingly rare except in very specific places, but we still harbor a certain awe and fear before lions. And of course availability heuristic can be greatly distorted by mass media, which makes people feel like terrorist attacks and nuclear meltdowns are common and deaths by car accidents and influenza are rare—when exactly the opposite is true.

How many categories should you set, and what frequencies should they be associated with? This part I’m still struggling with, and it’s an important piece of the puzzle I will need before I can take this theory to experiment. There is probably a trade-off between more categories giving you more precision in tailoring your optimal behavior, but costing more cognitive resources to maintain. Is the optimal number 3? 4? 7? 10? I really don’t know. Even I could specify the number of categories, I’d still need to figure out precisely what categories to assign.

# Are some ideas too ridiculous to bother with?

Apr 22 JDN 2458231

There are an astonishing number of ideas that satisfy two apparently-contrary conditions:

1. They are so obviously ridiculous that even a few minutes of honest, rational consideration of evidence that is almost universally available will immediately refute them;
2. They are believed by tens or hundreds of millions of otherwise-intelligent people.

Young-Earth Creationism is probably the most alarming, seeing as it grips the minds of some 38% of Americans.

What should we do when faced with such ideas? This is something I’ve struggled with before.

I’ve spent a lot of time and effort trying to actively address and refute them—but I don’t think I’ve even once actually persuaded someone who believes these ideas to change their mind. This doesn’t mean my time and effort were entirely wasted; it’s possible that I managed to convince bystanders, or gained some useful understanding, or simply improved my argumentation skills. But it does seem likely that my time and effort were mostly wasted.

It’s tempting, therefore, to give up entirely, and just let people go on believing whatever nonsense they want to believe. But there’s a rather serious downside to that as well: Thirty-eight percent of Americans.

These people vote. They participate in community decisions. They make choices that affect the rest of our lives. Nearly all of those Creationists are Evangelical Christians—and White Evangelical Christians voted overwhelmingly in favor of Donald Trump. I can’t be sure that changing their minds about the age of the Earth would also change their minds about voting for Trump, but I can say this: If all the Creationists in the US had simply not voted, Hillary Clinton would have won the election.

And let’s not leave the left wing off the hook either. Jill Stein is a 9/11 “Truther”, and pulled a lot of fellow “Truthers” to her cause in the election as well. Had all of Jill Stein’s votes gone to Hillary Clinton instead, again Hillary would have won, even if all the votes for Trump had remained the same. (That said, there is reason to think that if Stein had dropped out, most of those folks wouldn’t have voted at all.)

Therefore, I don’t think it is safe to simply ignore these ridiculous beliefs. We need to do something; the question is what.

We could try to censor them, but first of all that violates basic human rights—which should be a sufficient reason not to do it—and second, it probably wouldn’t even work. Censorship typically leads to radicalization, not assimilation.

We could try to argue against them. Ideally this would be the best option, but it has not shown much effect so far. The kind of person who sincerely believes that the Earth is 6,000 years old (let alone that governments are secretly ruled by reptilian alien invaders) isn’t the kind of person who is highly responsive to evidence and rational argument.

In fact, there is reason to think that these people don’t actually believe what they say the same way that you and I believe things. I’m not saying they’re lying, exactly. They think they believe it; they want to believe it. They believe in believing it. But they don’t actually believe it—not the way that I believe that cyanide is poisonous or the way I believe the sun will rise tomorrow. It isn’t fully integrated into the way that they anticipate outcomes and choose behaviors. It’s more of a free-floating sort of belief, where professing a particular belief allows them to feel good about themselves, or represent their status in a community.

To be clear, it isn’t that these beliefs are unimportant to them; on the contrary, they are in some sense more important. Creationism isn’t really about the age of the Earth; it’s about who you are and where you belong. A conventional belief can be changed by evidence about the world because it is about the world; a belief-in-belief can’t be changed by evidence because it was never really about that.

But if someone’s ridiculous belief is really about their identity, how do we deal with that? I can’t refute an identity. If your identity is tied to a particular social group, maybe they could ostracize you and cause you to lose the identity; but an outsider has no power to do that. (Even then, I strongly suspect that, for instance, most excommunicated Catholics still see themselves as Catholic.) And if it’s a personal identity not tied to a particular group, even that option is unavailable.

Where, then, does that leave us? It would seem that we can’t change their minds—but we also can’t afford not to change their minds. We are caught in a terrible dilemma.

I think there might be a way out. It’s a bit counter-intuitive, but I think what we need to do is stop taking them seriously as beliefs, and start treating them purely as announcements of identity.

So when someone says something like, “The Rothschilds run everything!”, instead of responding as though this were a coherent proposition being asserted, treat it as if someone had announced, “Boo! I hate the Red Sox!” Belief in the Rothschild conspiracies isn’t a well-defined set of propositions about the world; it’s an assertion of membership in a particular sort of political sect that is vaguely left-wing and anarchist. You don’t really think the Rothschilds rule everything. You just want to express your (quite justifiable) anger at how our current political system privileges the rich.

Likewise, when someone says they think the Earth is 6,000 years old, you could try to present the overwhelming scientific evidence that they are wrong—but it might be more productive, and it is certainly easier, to just think of this as a funny way of saying “I’m an Evangelical Christian”.

Will this eliminate the ridiculous beliefs? Not immediately. But it might ultimately do so, in the following way: By openly acknowledging the belief-in-belief as a signaling mechanism, we can open opportunities for people to develop new, less pathological methods of signaling. (Instead of saying you think the Earth is 6,000 years old, maybe you could wear a funny hat, like Orthodox Jews do. Funny hats don’t hurt anybody. Everyone loves funny hats.) People will always want to signal their identity, and there are fundamental reasons why such signals will typically be costly for those who use them; but we can try to make them not so costly for everyone else.

This also makes arguments a lot less frustrating, at least at your end. It might make them more frustrating at the other end, because people want their belief-in-belief to be treated like proper belief, and you’ll be refusing them that opportunity. But this is not such a bad thing; if we make it more frustrating to express ridiculous beliefs in public, we might manage to reduce the frequency of such expression.

# Today would be my father’s birthday.

Apr 15 JDN 2458224

When this post goes live, it will be April 15, 2018. My father was born April 15, 1954 and died August 31, 2017, so this is the first time we will be celebrating his birthday without him.

I’m not sure that grief ever really goes away. The shock of the unexpected death fades eventually, and at last you can accept that this has really happened and make it a part of your life. But the sum total of all missed opportunities for life events you could have had together only continues to increase.

There are many cliches about this sort of thing: “Death is a part of life.” “Everything happens for a reason.” It’s all making excuses for the dragon. If we could find a way to make people stop dying, we ought to do it. The other consequences are things we could figure out later.

But, alas, we can’t, at least not in general. We have managed to cure or vaccinate against a wide variety of diseases, and as a result people do, on average, live longer than ever before in human history. But none of us live “on average”—and sometimes you get a very unlucky draw.

Yet somehow, we do learn to go on. I’m not sure how. I guess it’s a kind of desensitization: Right after my father’s death, any reminder of him was painful. But over time, that pain began to lessen. Each new reminder hurts a little less than the last, until eventually the pain is mild enough that it can mostly be ignored. It never really goes away, I think; but eventually it is below your just-noticeable-difference.

I had hoped to do more with this post. I had hoped that reflecting on the grief I’ve felt for the last several months would allow me to find some greater insight that I could share. Instead, I find myself re-writing the same sentences over and over again, trying in vain to express something that might help me, or help someone else who is going through similar grief. I keep looking for ways to distract myself, other things to think about—anything but this. Maybe there are no simple insights, no way for words to shorten the process that everyone must go through.

# The extreme efficiency of environmental regulation—and the extreme inefficiency of war

Apr 8 JDN 2458217

Insofar as there has been any coherent policy strategy for the Trump administration, it has largely involved three things:

1. Increase investment in military, incarceration, and immigration enforcement
2. Redistribute wealth from the poor and middle class to the rich
3. Remove regulations that affect business, particularly environmental regulations

The human cost of such a policy strategy is difficult to overstate. Literally millions of people will die around the world if such policies continue. This is almost the exact opposite of what our government should be doing.

This is because military is one of the most wasteful and destructive forms of government investment, while environmental regulation is one of the most efficient and beneficial. The magnitude of these differences is staggering.

First of all, it is not clear that the majority of US military spending provides any marginal benefit. It could quite literally be zero. The US spends more on military than the next ten countries combined.

I think it’s quite reasonable to say that the additional defense benefit becomes negligible once you exceed the sum of spending from all plausible enemies. China, Russia, and Saudi Arabia together add up to about \$350 billion per year. Current US spending is \$610 billion per year. (And this calculation, by the way, requires them all to band together, while simultaneously all our NATO allies completely abandon us.) That means we could probably cut \$260 billion per year without losing anything.

What about the remaining \$350 billion? I could be extremely generous here, and assume that nuclear weapons, alliances, economic ties, and diplomacy all have absolutely no effect, so that without our military spending we would be invaded and immediately lose, and that if we did lose a war with China or Russia it would be utterly catastrophic and result in the deaths of 10% of the US population. Since in this hypothetical scenario we are only preventing the war by the barest margin, each year of spending only adds 1 year to the lives of the war’s potential victims. That means we are paying some \$350 billion per year to add 1 year to the lives of 32 million people. That is a cost of about \$11,000 per QALY. If it really is saving us from being invaded, that doesn’t sound all that unreasonable. And indeed, I don’t favor eliminating all military spending.

Of course, the marginal benefit of additional spending is still negligible—and UN peacekeeping is about twice as cost-effective as US military action, even if we had to foot the entire bill ourselves.

Alternatively, I could consider only the actual, documented results of our recent military action, which has resulted in over 280,000 deaths in Iraq and 110,000 in Afghanistan, all for little or no apparent gain. Life expectancy in these countries is about 70 in Iraq and 60 in Afghanistan. Quality of life there is pretty awful, but people are also greatly harmed by war without actually dying in it, so I think a fair conversion factor is about 60 QALY per death. That’s a loss of 23.4 MQALY. The cost of the Iraq War was about \$1.1 trillion, while the cost of the Afghanistan War was about a further \$1.1 trillion. This means that we paid \$94,000 per lost QALY. If this is right, we paid enormous amounts to destroy lives and accomplished nothing at all.

Somewhere in between, we could assume that cutting the military budget greatly would result in the US being harmed in a manner similar to World War 2, which killed about 500,000 Americans. Paying \$350 billion per year to gain 500,000 QALY per year is a price of \$700,000 per QALY. I think this is about right; we are getting some benefit, but we are spending an enormous amount to get it.

Now let’s compare that to the cost-effectiveness of environmental regulation.

Since 1990, the total cost of implementing the regulations in the Clean Air Act was about \$65 billion. That’s over 28 years, so less than \$2.5 billion per year. Compare that to the \$610 billion per year we spend on the military.

Yet the Clean Air Act saves over 160,000 lives every single year. And these aren’t lives extended one more year as they were in the hypothetical scenario where we are just barely preventing a catastrophic war; most of these people are old, but go on to live another 20 years or more. That means we are gaining 3.2 MQALY for a price of \$2.5 billion. This is a price of only \$800 per QALY.

From 1970 to 1990, the Clean Air Act cost more to implement: about \$520 billion (so, you know, less than one year of military spending). But its estimated benefit was to save over 180,000 lives per year, and its estimated economic benefit was \$22 trillion.

Look at those figures again, please. Even under very pessimistic assumptions where we would be on the verge of war if not for our enormous spending, we’re spending at least \$11,000 and probably more like \$700,000 on the military for each QALY gained. But environmental regulation only costs us about \$800 per QALY. That’s a factor of at least 14 and more likely 1000. Environmental regulation is probably about one thousand times as cost-effective as military spending.

And I haven’t even included the fact that there is a direct substitution here: Climate change is predicted to trigger thousands if not millions of deaths due to military conflict. Even if national security were literally the only thing we cared about, it would probably still be more cost-effective to invest in carbon emission reduction rather than building yet another aircraft carrier. And if, like me, you think that a child who dies from asthma is just as important as one who gets bombed by China, then the cost-benefit analysis is absolutely overwhelming; every \$60,000 spent on war instead of environmental protection is a statistical murder.

This is not even particularly controversial among economists. There is disagreement about specific environmental regulations, but the general benefits of fighting climate change and keeping air and water clean are universally acknowledged. There is disagreement about exactly how much military spending is necessary, but you’d be hard-pressed to find an economist who doesn’t think we could cut our military substantially with little or no risk to security.

# Reasonableness and public goods games

Apr 1 JDN 2458210

There’s a very common economics experiment called a public goods game, often used to study cooperation and altruistic behavior. I’m actually planning on running a variant of such an experiment for my second-year paper.

The game is quite simple, which is part of why it is used so frequently: You are placed into a group of people (usually about four), and given a little bit of money (say \$10). Then you are offered a choice: You can keep the money, or you can donate some of it to a group fund. Money in the group fund will be multiplied by some factor (usually about two) and then redistributed evenly to everyone in the group. So for example if you donate \$5, that will become \$10, split four ways, so you’ll get back \$2.50.

Donating more to the group will benefit everyone else, but at a cost to yourself. The game is usually set up so that the best outcome for everyone is if everyone donates the maximum amount, but the best outcome for you, holding everyone else’s choices constant, is to donate nothing and keep it all.

Yet it is a very robust finding that most people do neither of those things. There’s still a good deal of uncertainty surrounding what motivates people to donate what they do, but certain patterns that have emerged:

1. Most people donate something, but hardly anyone donates everything.
2. Increasing the multiplier tends to smoothly increase how much people donate.
3. The number of people in the group isn’t very important, though very small groups (e.g. 2) behave differently from very large groups (e.g. 50).
4. Letting people talk to each other tends to increase the rate of donations.
5. Repetition of the game, or experience from previous games, tends to result in decreasing donation over time.
6. Economists donate less than other people.

Number 6 is unfortunate, but easy to explain: Indoctrination into game theory and neoclassical economics has taught economists that selfish behavior is efficient and optimal, so they behave selfishly.

Number 3 is also fairly easy to explain: Very small groups allow opportunities for punishment and coordination that don’t exist in large groups. Think about how you would respond when faced with 2 defectors in a group of 4 as opposed to 10 defectors in a group of 50. You could punish the 2 by giving less next round; but punishing the 10 would end up punishing 40 others who had contributed like they were supposed to.

Number 4 is a very interesting finding. Game theory says that communication shouldn’t matter, because there is a unique Nash equilibrium: Donate nothing. All the promises in the world can’t change what is the optimal response in the game. But in fact, human beings don’t like to break their promises, and so when you get a bunch of people together and they all agree to donate, most of them will carry through on that agreement most of the time.

Number 5 is on the frontier of research right now. There are various theoretical accounts for why it might occur, but none of the models proposed so far have much predictive power.

But my focus today will be on findings 1 and 2.

If you’re not familiar with the underlying game theory, finding 2 may seem obvious to you: Well, of course if you increase the payoff for donating, people will donate more! It’s precisely that sense of obviousness which I am going to appeal to in a moment.

In fact, the game theory makes a very sharp prediction: For N players, if the multiplier is less than N, you should always contribute nothing. Only if the multiplier becomes larger than N should you donate—and at that point you should donate everything. The game theory prediction is not a smooth increase; it’s all-or-nothing. The only time game theory predicts intermediate amounts is on the knife-edge at exactly equal to N, where each player would be indifferent between donating and not donating.

But it feels reasonable that increasing the multiplier should increase donation, doesn’t it? It’s a “safer bet” in some sense to donate \$1 if the payoff to everyone is \$3 and the payoff to yourself is \$0.75 than if the payoff to everyone is \$1.04 and the payoff to yourself is \$0.26. The cost-benefit analysis comes out better: In the former case, you can gain up to \$2 if everyone donates, but would only lose \$0.25 if you donate alone; but in the latter case, you would only gain \$0.04 if everyone donates, and would lose \$0.74 if you donate alone.

I think this notion of “reasonableness” is a deep principle that underlies a great deal of human thought. This is something that is sorely lacking from artificial intelligence: The same AI that tells you the precise width of the English Channel to the nearest foot may also tell you that the Earth is 14 feet in diameter, because the former was in its database and the latter wasn’t. Yes, WATSON may have won on Jeopardy, but it (he?) also made a nonsensical response to the Final Jeopardy question.

Human beings like to “sanity-check” our results against prior knowledge, making sure that everything fits together. And, of particular note for public goods games, human beings like to “hedge our bets”; we don’t like to over-commit to a single belief in the face of uncertainty.

I think this is what best explains findings 1 and 2. We don’t donate everything, because that requires committing totally to the belief that contributing is always better. We also don’t donate nothing, because that requires committing totally to the belief that contributing is always worse.

And of course we donate more as the payoffs to donating more increase; that also just seems reasonable. If something is better, you do more of it!

These choices could be modeled formally by assigning some sort of probability distribution over other’s choices, but in a rather unconventional way. We can’t simply assume that other people will randomly choose some decision and then optimize accordingly—that just gives you back the game theory prediction. We have to assume that our behavior and the behavior of others is in some sense correlated; if we decide to donate, we reason that others are more likely to donate as well.

Stated like that, this sounds irrational; some economists have taken to calling it “magical thinking”. Yet, as I always like to point out to such economists: On average, people who do that make more money in the games. Economists playing other economists always make very little money in these games, because they turn on each other immediately. So who is “irrational” now?

Indeed, if you ask people to predict how others will behave in these games, they generally do better than the game theory prediction: They say, correctly, that some people will give nothing, most will give something, and hardly any will give everything. The same “reasonableness” that they use to motivate their own decisions, they also accurately apply to forecasting the decisions of others.

Of course, to say that something is “reasonable” may be ultimately to say that it conforms to our heuristics well. To really have a theory, I need to specify exactly what those heuristics are.

“Don’t put all your eggs in one basket” seems to be one, but it’s probably not the only one that matters; my guess is that there are circumstances in which people would actually choose all-or-nothing, like if we said that the multiplier was 0.5 (so everyone giving to the group would make everyone worse off) or 10 (so that giving to the group makes you and everyone else way better off).

“Higher payoffs are better” is probably one as well, but precisely formulating that is actually surprisingly difficult. Higher payoffs for you? For the group? Conditional on what? Do you hold others’ behavior constant, or assume it is somehow affected by your own choices?

And of course, the theory wouldn’t be much good if it only worked on public goods games (though even that would be a substantial advance at this point). We want a theory that explains a broad class of human behavior; we can start with simple economics experiments, but ultimately we want to extend it to real-world choices.