How (not) to destroy an immoral market

Jul 29 JDN 2458329

In this world there are people of primitive cultures, with a population that is slowly declining, trying to survive a constant threat of violence in the aftermath of colonialism. But you already knew that, of course.

What you may not have realized is that some of these people are actively hunted by other people, slaughtered so that their remains can be sold on the black market.

I am referring of course to elephants. Maybe those weren’t the people you first had in mind?

Elephants are not human in the sense of being Homo sapiens; but as far as I am concerned, they are people in a moral sense.

Elephants take as long to mature as humans, and spend most of their childhood learning. They are born with brains only 35% of the size of their adult brains, much as we are born with brains 28% the size of our adult brains. Their encephalization quotients range from about 1.5 to 2.4, comparable to chimpanzees.

Elephants have problem-solving intelligence comparable to chimpanzees, cetaceans, and corvids. Elephants can pass the “mirror test” of self-identification and self-awareness. Individual elephants exhibit clearly distinguishable personalities. They exhibit empathy toward humans and other elephants. They can think creatively and develop new tools.

Elephants distinguish individual humans or elephants by sight or by voice, comfort each other when distressed, and above all mourn their dead. The kind of mourning behaviors elephants exhibit toward the remains of their dead family members have only been observed in humans and chimpanzees.

On a darker note, elephants also seek revenge. In response to losing loved ones to poaching or collisions with trains, elephants have orchestrated organized counter-attacks against human towns. This is not a single animal defending itself, as almost any will do; this is a coordinated act of vengeance after the fact. Once again, we have only observed similar behaviors in humans, great apes, and cetaceans.

Huffington Post backed off and said “just kidding” after asserting that elephants are people—but I won’t. Elephants are people. They do not have an advanced civilization, to be sure. But as far as I am concerned they display all the necessary minimal conditions to be granted the fundamental rights of personhood. Killing an elephant is murder.

And yet, the ivory trade continues to be profitable. Most of this is black-market activity, though it was legal in some places until very recently; China only restored their ivory trade ban this year, and Hong Kong’s ban will not take full effect until 2021. Some places are backsliding: A proposal (currently on hold) by the US Fish and Wildlife Service under the Trump administration would also legalize some limited forms of ivory trade.
With this in mind, I can understand why people would support the practice of ivory-burning, symbolically and publicly destroying ivory by fire so that no one can buy it. Two years ago, Kenya organized a particularly large ivory-burning that set ablaze 105 tons of elephant tusk and 1.35 tons of rhino horn.

But as economist, when I first learned about ivory-burning, it seemed like a really, really bad idea.

Why? Supply and demand. By destroying supply, you have just raised the market price of ivory. You have therefore increased the market incentives for poaching elephants and rhinos.

Yet it turns out I was wrong about this, as were many other economists. I looked at the empirical research, and changed my mind substantially. Ivory-burning is not such a bad idea after all.

Here was my reasoning before: If I want to reduce the incentives to produce something, what do I need to do? Lower the price. How do I do that? I need to increase the supply. Economists have made several proposals for how to do that, and until I looked at the data I would have expected them to work; but they haven’t.

The best way to increase supply is to create synthetic ivory that is cheap and very difficult to tell apart from the real thing. This has been done, but it didn’t work. For some reason, sellers try to hide the expensive real ivory in with the cheap synthetic ivory. I admit I actually have trouble understanding this; if you can’t sell it at full price, why even bother with the illegal real ivory? Maybe their customers have methods of distinguishing the two that the regulators don’t? If so, why aren’t the regulators using those methods? Another concern with increasing the supply of ivory is that it might reduce the stigma of consuming ivory, thereby also increasing the demand.

A similar problem has arisen with so-called “ghost ivory”; for obvious reasons, existing ivory products were excluded from the ban imposed in 1947, lest the government be forced to confiscate millions of billiard balls and thousands of pianos. Yet poachers have learned ways to hide new, illegal ivory and sell it as old, legal ivory.

Another proposal was to organize “sustainable ivory harvesting”, which based on past experience with similar regulations is unlikely to be enforceable. Moreover, this is not like sustainable wood harvesting, where our only concern is environmental. I for one care about the welfare of individual elephants, and I don’t think they would want to be “harvested”, sustainably or otherwise.
There is one way of doing “sustainable harvesting” that might not be so bad for the elephants, which would be to set up a protected colony of elephants, help them to increase their population, and then when elephants die of natural causes, take only the tusks and sell those as ivory, stamped with an official seal as “humanely and sustainably produced”. Even then, elephants are among a handful of species that would be offended by us taking their ancestors’ remains. But if it worked, it could save many elephant lives. The bigger problem is how expensive such a project would be, and how long it would take to show any benefit; elephant lifespans are about half as long as ours, (except in zoos, where their mortality rate is much higher!) so a policy that might conceivably solve a problem in 30 to 40 years doesn’t really sound so great. More detailed theoretical and empirical analysis has made this clear: you just can’t get ivory fast enough to meet existing demand this way.

In any case, China’s ban on all ivory trade had an immediate effect at dropping the price of ivory, which synthetic ivory did not. Before that, strengthened regulations in the US (particularly in New York and California) had been effective at reducing ivory sales. The CITES treaty in 1989 that banned most international ivory trade was followed by an immediate increase in elephant populations.

The most effective response to ivory trade is an absolutely categorical ban with no loopholes. To fight “ghost ivory”, we should remove exceptions for old ivory, offering buybacks for any antiques with a verifiable pedigree and a brief period of no-penalty surrender for anything with no such records. The only legal ivory must be for medical and scientific purposes, and its sourcing records must be absolutely impeccable—just as we do with human remains.

Even synthetic ivory must also be banned, at least if it’s convincing enough that real ivory could be hidden in it. You can make something you call “synthetic ivory” that serves a similar consumer function, but it must be different enough that it can be easily verified at customs inspections.

We must give no quarter to poachers; Kenya was right to impose a life sentence for aggravated poaching. The Tanzanian proposal to “shoot to kill” was too extreme; summary execution is never acceptable. But if indeed someone currently has a weapons pointed at an elephant and refuses to drop it, I consider it justifiable to shoot them, just as I would if that weapon were aimed at a human.

The need for a categorical ban is what makes the current US proposal dangerous. The particular exceptions it carves out are not all that large, but the fact that it carves out exceptions at all makes enforcement much more difficult. To his credit, Trump himself doesn’t seem very keen on the proposal, which may mean that it is dead in the water. I don’t get to say this often, but so far Trump seems to be making the right choice on this one.

Though the economic theory predicted otherwise, the empirical data is actually quite clear: The most effective way to save elephants from poaching is an absolutely categorical ban on ivory.

Ivory-burning is a signal of commitment to such a ban. Any ivory we find being sold, we will burn. Whoever was trying to sell it will lose their entire investment. Find more, and we will burn that too.

Self-fulfilling norms

Post 242: Jun 10 JDN 2458280

Imagine what it would be like to live in a country with an oppressive totalitarian dictator. For millions of people around the world, this is already reality. For us in the United States, it’s becoming more terrifyingly plausible all the time.

You would probably want to get rid of this dictator. And even if you aren’t in the government yourself, there are certainly things you could do to help with that: Join protests, hide political dissenters in your basement, publish refutations of the official propaganda on the Internet. But all of these things carry great risks. How do you know whether it’s worth the risk?

Well, a very important consideration in that reasoning is how many other people agree with you. In the extreme case where everyone but the dictator agrees with you, overthrowing him should be no problem. In the other extreme case where nobody agrees with you, attempting to overthrow him will inevitably result in being imprisoned and tortured as a political prisoner. Everywhere in between, your probability of success increases as the number of people who agree with you increases.

But how do you know how many people agree with you? You can’t just ask them—simply asking someone “Do you support the dictator?” is a dangerous thing to do in a totalitarian society. Simply by asking around, you could get yourself into a lot of trouble. And if people think you might be asking on behalf of the government, they’re always going to say they support the dictator whether or not they do.

If you believe that enough people would support you, you will take action against the dictator. But if you don’t believe that, you won’t take the chance. Now, consider the fact that many other people are in the same position: They too would only take action if they believed others would.

You are now in what’s called a coordination game. The best decision for you depends upon what everyone else decides. There are two equilibrium outcomes of this game: In one, you all keep your mouths shut and the dictator continues to oppress you. In the other, you all rise up together and overthrow the dictator. But if you take an action out of equilibrium, that could be very bad for you: If you rise up against the dictator without support, you’ll be imprisoned and tortured. If you support the dictator while others try to overthrow him, you might be held responsible for some of his crimes once the coup d’etat is complete.

And what about people who do support the dictator? They might still be willing to go along with overthrowing him, if they saw the writing on the wall. But if they think the dictator can still win, they will stand with him. So their beliefs, also, are vital in deciding whether to try to overthrow the dictator.

This results in a self-fulfilling norm. The dictator can be overthrown, if and only if enough people believe that the dictator can be overthrown.

There are much more mundane examples of of self-fulfilling norms. Most of our traffic laws are actually self-fulfilling norms as much as they are real laws; enforcement is remarkably weak, particularly when you compare it to the rate of compliance. Most of us have driven faster than the speed limit or run a red light on occasion; but how often do you drive on the wrong side of the road, or stop on green and go on red? It is best to drive on the right side of the road if, and only if, everyone believes it is best to drive on the right side of the road. That’s a self-fulfilling norm.

Self-fulfilling norms are a greatly underappreciated force in global history. We often speak as though historical changes are made by “great men”—powerful individuals who effect chance through their charisma or sheer force of will. But that power didn’t exist in a vacuum. For good (Martin Luther King) or for ill (Adolf Hitler), “great men” only have their power because they can amass followers. The reason they can amass followers is that a large number of people already agree with them—but are too afraid to speak up, because they are trapped in a self-fulfilling norm. The primary function of a great leader is to announce—at great personal risk—views that they believe others already hold. If indeed they are correct, then they can amass followers by winning the coordination game. If they are wrong, they may suffer terribly at the hands of a populace that hates them.

There is persuasion involved, but typically it’s not actually persuading people to believe that something is right; it’s persuading people to actually take action, convincing them that there is really enough chance of succeeding that it is worth the risk. Because of the self-fulfilling norm, this is a very all-or-nothing affair; do it right and you win, but do it wrong and your whole movement collapses. You essentially need to know exactly what battles you can win, so that you only fight those battles.

The good news is that information technology may actually make this easier. Honest assessment of people’s anonymous opinions is now easier than ever. Large-scale coordination of activity with relative security is now extremely easy, as we saw in the Arab Spring. This means that we are entering an era of rapid social change, where self-fulfilling norms will rise and fall at a rate never before seen.

In the best-case scenario, this means we get rid of all the bad norms and society becomes much better.

In the worst-case scenario, we may find out that most people actually believe in the bad norms, and this makes those norms all the more entrenched.

Only time will tell.

How do people think about probability?

Nov 27, JDN 2457690

(This topic was chosen by vote of my Patreons.)

In neoclassical theory, it is assumed (explicitly or implicitly) that human beings judge probability in something like the optimal Bayesian way: We assign prior probabilities to events, and then when confronted with evidence we infer using the observed data to update our prior probabilities to posterior probabilities. Then, when we have to make decisions, we maximize our expected utility subject to our posterior probabilities.

This, of course, is nothing like how human beings actually think. Even very intelligent, rational, numerate people only engage in a vague approximation of this behavior, and only when dealing with major decisions likely to affect the course of their lives. (Yes, I literally decide which universities to attend based upon formal expected utility models. Thus far, I’ve never been dissatisfied with a decision made that way.) No one decides what to eat for lunch or what to do this weekend based on formal expected utility models—or at least I hope they don’t, because that point the computational cost far exceeds the expected benefit.

So how do human beings actually think about probability? Well, a good place to start is to look at ways in which we systematically deviate from expected utility theory.

A classic example is the Allais paradox. See if it applies to you.

In game A, you get $1 million dollars, guaranteed.
In game B, you have a 10% chance of getting $5 million, an 89% chance of getting $1 million, but now you have a 1% chance of getting nothing.

Which do you prefer, game A or game B?

In game C, you have an 11% chance of getting $1 million, and an 89% chance of getting nothing.

In game D, you have a 10% chance of getting $5 million, and a 90% chance of getting nothing.

Which do you prefer, game C or game D?

I have to think about it for a little bit and do some calculations, and it’s still very hard because it depends crucially on my projected lifetime income (which could easily exceed $3 million with a PhD, especially in economics) and the precise form of my marginal utility (I think I have constant relative risk aversion, but I’m not sure what parameter to use precisely), but in general I think I want to choose game A and game C, but I actually feel really ambivalent, because it’s not hard to find plausible parameters for my utility where I should go for the gamble.

But if you’re like most people, you choose game A and game D.

There is no coherent expected utility by which you would do this.

Why? Either a 10% chance of $5 million instead of $1 million is worth risking a 1% chance of nothing, or it isn’t. If it is, you should play B and D. If it’s not, you should play A and C. I can’t tell you for sure whether it is worth it—I can’t even fully decide for myself—but it either is or it isn’t.

Yet most people have a strong intuition that they should take game A but game D. Why? What does this say about how we judge probability?
The leading theory in behavioral economics right now is cumulative prospect theory, developed by the great Kahneman and Tversky, who essentially founded the field of behavioral economics. It’s quite intimidating to try to go up against them—which is probably why we should force ourselves to do it. Fear of challenging the favorite theories of the great scientists before us is how science stagnates.

I wrote about it more in a previous post, but as a brief review, cumulative prospect theory says that instead of judging based on a well-defined utility function, we instead consider gains and losses as fundamentally different sorts of thing, and in three specific ways:

First, we are loss-averse; we feel a loss about twice as intensely as a gain of the same amount.

Second, we are risk-averse for gains, but risk-seeking for losses; we assume that gaining twice as much isn’t actually twice as good (which is almost certainly true), but we also assume that losing twice as much isn’t actually twice as bad (which is almost certainly false and indeed contradictory with the previous).

Third, we judge probabilities as more important when they are close to certainty. We make a large distinction between a 0% probability and a 0.0000001% probability, but almost no distinction at all between a 41% probability and a 43% probability.

That last part is what I want to focus on for today. In Kahneman’s model, this is a continuous, monotonoic function that maps 0 to 0 and 1 to 1, but systematically overestimates probabilities below but near 1/2 and systematically underestimates probabilities above but near 1/2.

It looks something like this, where red is true probability and blue is subjective probability:

cumulative_prospect
I don’t believe this is actually how humans think, for two reasons:

  1. It’s too hard. Humans are astonishingly innumerate creatures, given the enormous processing power of our brains. It’s true that we have some intuitive capacity for “solving” very complex equations, but that’s almost all within our motor system—we can “solve a differential equation” when we catch a ball, but we have no idea how we’re doing it. But probability judgments are often made consciously, especially in experiments like the Allais paradox; and the conscious brain is terrible at math. It’s actually really amazing how bad we are at math. Any model of normal human judgment should assume from the start that we will not do complicated math at any point in the process. Maybe you can hypothesize that we do so subconsciously, but you’d better have a good reason for assuming that.
  2. There is no reason to do this. Why in the world would any kind of optimization system function this way? You start with perfectly good probabilities, and then instead of using them, you subject them to some bizarre, unmotivated transformation that makes them less accurate and costs computing power? You may as well hit yourself in the head with a brick.

So, why might it look like we are doing this? Well, my proposal, admittedly still rather half-baked, is that human beings don’t assign probabilities numerically at all; we assign them categorically.

You may call this, for lack of a better term, categorical prospect theory.

My theory is that people don’t actually have in their head “there is an 11% chance of rain today” (unless they specifically heard that from a weather report this morning); they have in their head “it’s fairly unlikely that it will rain today”.

That is, we assign some small number of discrete categories of probability, and fit things into them. I’m not sure what exactly the categories are, and part of what makes my job difficult here is that they may be fuzzy-edged and vary from person to person, but roughly speaking, I think they correspond to the sort of things psychologists usually put on Likert scales in surveys: Impossible, almost impossible, very unlikely, unlikely, fairly unlikely, roughly even odds, fairly likely, likely, very likely, almost certain, certain. If I’m putting numbers on these probability categories, they go something like this: 0, 0.001, 0.01, 0.10, 0.20, 0.50, 0.8, 0.9, 0.99, 0.999, 1.

Notice that this would preserve the same basic effect as cumulative prospect theory: You care a lot more about differences in probability when they are near 0 or 1, because those are much more likely to actually shift your category. Indeed, as written, you wouldn’t care about a shift from 0.4 to 0.6 at all, despite caring a great deal about a shift from 0.001 to 0.01.

How does this solve the above problems?

  1. It’s easy. Not only don’t you compute a probability and then recompute it for no reason; you never even have to compute it precisely. Just get it within some vague error bounds and that will tell you what box it goes in. Instead of computing an approximation to a continuous function, you just slot things into a small number of discrete boxes, a dozen at the most.
  2. That explains why we would do it: It’s easy. Our brains need to conserve their capacity, and they did especially in our ancestral environment when we struggled to survive. Rather than having to iterate your approximation to arbitrary precision, you just get within 0.1 or so and call it a day. That saves time and computing power, which saves energy, which could save your life.

What new problems have I introduced?

  1. It’s very hard to know exactly where people’s categories are, if they vary between individuals or even between situations, and whether they are fuzzy-edged.
  2. If you take the model I just gave literally, even quite large probability changes will have absolutely no effect as long as they remain within a category such as “roughly even odds”.

With regard to 2, I think Kahneman may himself be able to save me, with his dual process theory concept of System 1 and System 2. What I’m really asserting is that System 1, the fast, intuitive judgment system, operates on these categories. System 2, on the other hand, the careful, rational thought system, can actually make use of proper numerical probabilities; it’s just very costly to boot up System 2 in the first place, much less ensure that it actually gets the right answer.

How might we test this? Well, I think that people are more likely to use System 1 when any of the following are true:

  1. They are under harsh time-pressure
  2. The decision isn’t very important
  3. The intuitive judgment is fast and obvious

And conversely they are likely to use System 2 when the following are true:

  1. They have plenty of time to think
  2. The decision is very important
  3. The intuitive judgment is difficult or unclear

So, it should be possible to arrange an experiment varying these parameters, such that in one treatment people almost always use System 1, and in another they almost always use System 2. And then, my prediction is that in the System 1 treatment, people will in fact not change their behavior at all when you change the probability from 15% to 25% (fairly unlikely) or 40% to 60% (roughly even odds).

To be clear, you can’t just present people with this choice between game E and game F:

Game E: You get a 60% chance of $50, and a 40% chance of nothing.

Game F: You get a 40% chance of $50, and a 60% chance of nothing.

People will obviously choose game E. If you can directly compare the numbers and one game is strictly better in every way, I think even without much effort people will be able to choose correctly.

Instead, what I’m saying is that if you make the following offers to two completely different sets of people, you will observe little difference in their choices, even though under expected utility theory you should.
Group I receives a choice between game E and game G:

Game E: You get a 60% chance of $50, and a 40% chance of nothing.

Game G: You get a 100% chance of $20.

Group II receives a choice between game F and game G:

Game F: You get a 40% chance of $50, and a 60% chance of nothing.

Game G: You get a 100% chance of $20.

Under two very plausible assumptions about marginal utility of wealth, I can fix what the rational judgment should be in each game.

The first assumption is that marginal utility of wealth is decreasing, so people are risk-averse (at least for gains, which these are). The second assumption is that most people’s lifetime income is at least two orders of magnitude higher than $50.

By the first assumption, group II should choose game G. The expected income is precisely the same, and being even ever so slightly risk-averse should make you go for the guaranteed $20.

By the second assumption, group I should choose game E. Yes, there is some risk, but because $50 should not be a huge sum to you, your risk aversion should be small and the higher expected income of $30 should sway you.

But I predict that most people will choose game G in both cases, and (within statistical error) the same proportion will choose F as chose E—thus showing that the difference between a 40% chance and a 60% chance was in fact negligible to their intuitive judgments.

However, this doesn’t actually disprove Kahneman’s theory; perhaps that part of the subjective probability function is just that flat. For that, I need to set up an experiment where I show discontinuity. I need to find the edge of a category and get people to switch categories sharply. Next week I’ll talk about how we might pull that off.