A Crumby Deal

David Byrne was once trapped beside me on a plane for over five hours, an ordeal he has probably blocked out of his mind if it ever registered at all. For me, it was a delightful and unforgettable experience. We spent the entire flight talking about the human brain and human behavior, a subject we discovered we both had a passion for that was outside our paid area of expertise.

David was working on his “Theater of the Mind” project at the time — where he combines immersive theater with established psychology experiments. At a conference we were both attending that weekend, he was planning on a live demonstration of a very popular game theory experiment called the Ultimatum Game. It was one I’d read up on many times over the years, frequently popping up in books and other papers about fairness and game theory. The Ultimatum Game goes like this:

One person (The Proposer) is given a sum of money — let’s say $100, which I believe is the amount David used on stage. The Proposer divides this pool of money into two piles however they like. It could even be one pile of $100 and a big pile of nothing. They designate one of the piles as “theirs” and offer the other pile to Subject B (The Responder).

The Responder’s entire role in the Ultimatum Game is to decide whether or not the deal goes through. If they refuse their pile, neither person gets any money at all (it goes back to the folks running the experiment). If the Responder agrees with the split, then both people walk away a little richer.

This experiment was first proposed in the 60s, but wasn’t really performed and analyzed until the 80s. Since then it has become a staple of classrooms and labs around the world, with thousands of variations of the experiment each looking for unique angles (such as: do fraternal twins offer and accept different splits than identical twins?).

In its basic form, where the subjects are unrelated and don’t know one another, offers from the Proposer of less than 30% are usually rejected by the Responder. This means the person accepting the split is choosing to forego any money at all in order to punish an offer they deem unfair. And this is what the Ultimatum Game is ostensibly designed to search for. What is our innate sense of fairness? How much inequality will we tolerate?

In groups that know one another or have frequent contact or relations (a small office group, a family, a fraternity), the Proposer often creates a nearly 50/50 split, which is then happily accepted. Two friends or colleagues walk away a little richer. One of the interesting findings from the Ultimatum Game is that people playing it for the very first time with complete strangers — even if the Proposer and Responder will never see one another or have any contact whatsoever — usually stay within a 50/50 to 70/30 range. First-time Proposers rarely offer anything insulting like 95/5 or 90/10. Having never done or heard of the experiment, their intuition informs them not to push their luck. Perhaps they place themselves (consciously or subconsciously) in the Responder’s seat for a moment and realize that they would reject an unfair offer. Or perhaps most of us, deep down, are generally fair people.

These are the ideas I took away from my reading up on the Ultimatum Game over the years. I found the experiment interesting but not mind-shattering. My thoughts tended to linger on other experiments. Until my flight with David. Until I watched him perform the experiment on stage. I suppose it was just that I had three or four days to mull this one experiment over and over. Because something didn’t sit quite right with me, something about how the experiment is performed and what we read into the results. The problem, I realized, is that we could never truly test the limits of what is actually being studied here. And what is being studied here is not at all what researchers for decades have assumed.

The problem goes back to the original version of this experiment in the 80s, where the sum of money being divided was something like €20. It’s always a small sum, because the experiment only works if you let the Proposer and Responder keep the money. There needs to be actual skin in the game. Experimenters don’t have unlimited resources, and they need to run hundreds or thousands of iterations of the game to get meaningful amounts of data, so the pot size is generally small.

What the Ultimatum Game is measuring, then, is not our innate sense of fairness, but rather what amount of money we are willing to part with in order to impose fairness on others. We are measuring the cost of fairness.

Take a college student at a university (the subject of most psychology experiments, alas). A Proposer offers them a 90/10 split. Ten bucks would buy a slice of pizza and beer and leave enough to tip the cute waiter at the local hangout. But this student isn’t completely broke. They have some cash in the bank, parents who pay their tuition, a part-time job that gives them some spending money. For $10, they could also give a big middle finger to whatever anonymous asshat is trying to walk away with $90. No thank you. They choose to reject this offer, punishing the lack of decorum and fairness. I mean — for $30 they might have been tempted, but they would’ve still be upset. For $30, they could ask the waiter to go see a movie or something.

Okay, now imagine the same experiment but it’s not college students with full bellies and positive bank accounts. It’s two homeless men down on their luck who haven’t had a decent meal in days. One homeless Proposer offers 90/10. The homeless Responder is just as pissed as any college student would be. It’s a bum deal. But $10 is $10. That’s food in my stomach. That’ll get me through another day. I don’t know when I’m going to see $10 again. Many of us would take this deal.

The failure of the Ultimatum Game is that it doesn’t offer meaningful amounts of money. In practice, it simply can’t. No experimenter could afford to. But where practice is impossible, hypotheticals are useful. So let’s run a different version of the game in our heads, one in which we raise the stakes until college students (and middle-aged college drop-outs like me) feel the same weight of the experiment as the homeless above.

Let’s imagine a pot size of $100,000. The Proposer offers the same 90/10 split, which in thousands of experiments people have been deemed unfair, rejecting a measly offer of $1 or $10. But now it’s $10,000 being offered. Yes, they realize the Proposer is going to keep $90,000. Oh yeah, you bet they are upset at this offer. Why not go 50/50? They tell themselves that they would have gone 50/50. They’d yell at this person if the experiment wasn’t being performed anonymously (much less hypothetically). But ten grand is more than they make in a month after taxes. That’s a vacation. It’s paying off a credit card. It’s two months of living expenses with a little left over to invest. Boy, they’d love nothing more than to punish the unfairness of this offer, but that’s too much money to give up. They accept the offer. Wouldn’t you?

If not, let’s say the pot size is now a million dollars. The Proposer suggests $900,000 to themselves and $100,000 to you. It’s still unfair, but that’s one hundred grand you get to keep. Almost nobody in their right mind would reject that offer.

And yet, in thousands of Ultimatum Games run over the last 40 years, the 90/10 split is rarely offered and almost always rejected. That’s because the price being paid to reject unfairness is tolerable. Raise the stakes, and suddenly the same unfairness is accepted, however angry it makes us. Which leads us to this:

Red and orange represent the top 10% in the US. Combined, they own nearly 75% of all there is to own. The bottom 50% of Americans is represented by that teal sliver which almost disappears around 2008. The top 1% are twenty times as wealthy as the bottom half of the US. Oh, and the gap is both growing and accelerating.

This kind of distribution is seen elsewhere, but it is worse in the US than in Europe. We tend to align more with India, Russia, and China than we do Europe when it comes to how we tolerate income inequality. (It’s worth noting that India has a very powerful caste system that permeates the entire culture. Inequality is not just tolerated there but in many ways enshrined and celebrated).

*Note that this graph measures income, which is different than wealth. Wealth tends to be even more unevenly distributed than income, mostly due to low inheritance taxes. It’s easier to sit on amassed wealth than to go out and compete in the market for real wages.

Here’s another graph to ponder:

In the last 50 years, the top 20% of earners have seen a nearly 10% raise, coming at the expense of the other 80%, which have all seen their share of income fall. The middle quintile have seen the greatest erosion. This is the “disappearance of the middle class” you may have heard about. What’s actually happening is the haves and have-nots are growing further apart. You see blame being tossed about, and anger is on the rise, but the blame is difficult to accurately assign. People vote against their own interests. Many don’t vote at all. And no party offers clear and radical solutions to this growing problem.

Historically, things have not gone well when wealth disparity grows too much. Sometimes there are uprisings, as seen in Cuba in the 50s. The disparity in wealth there between those in the city and those in the countryside grew to such a state that revolutionaries like Castro were able to topple the haves and take it all for themselves. Same thing has happened in Russia more than once, and in France and Britain. It’s happened thousands of times and will keep happening, because the structures that create income inequality are both ratcheting and compounding. They go one direction and they feed on themselves.

They go one direction, because power once seized is difficult to relinquish. They feed on themselves because those in power tend to change the rules to gain more power (or they skirt the rules, take advantage of loopholes only they can afford, or get away with breaking the law). Get angry all you want, it doesn’t change anything. It’s human psychology. It’s game theory. And one thing we’ve learned from millions of psychology experiments is that if you change the roles, you get the same results. Let the guards become the prisoners or vice versa, and you get the same behavior. Let the Proposer and Responder switch sides, and it doesn’t matter. If you were a billionaire, you would most likely nudge things — even subconsciously — in a way that rewards being a billionaire. Self-interest is a very difficult thing to buck.

Making things more difficult is that perceived wealth is far from actual wealth. This graph breaks my heart:

There’s a lot going on here. The first thing that jumps out is that folks think being wealthy is a lot more common than it actually is. People assume that earning a million dollars a year is something that quite a few people do, when almost no one does. Fewer than half a percent of the US population earns over a million dollars a year. If you know 200 randomly distributed people, then you might know one person who fits the bill. (Of course, we don’t know randomly distributed people. We know people mostly in our realm of income, which is one of the sources of confusion here).

We overestimate how many wealthy people there are while underestimating how many people are living in poverty. This may be part of why people vote against their own interests. They think moving up to where the rules will one day favor them will be easier than it actually is. (There are other, less flattering reasons that I’ve blogged about here at times). What’s wild is that income inequality is getting worse — and accelerating — all while we are unaware of how bad it’s gotten. We think income is more evenly distributed than it actually is.

Let’s return to the Ultimatum Game. If I offered you $100,000 a year (after taxes, guaranteed), but it meant that thousands of people would get millions of dollars from that same pool, would you accept it? Would the unfairness of the distribution matter to you? Or would you be more interested in how that $100,000 might change your life? I think most of us would take that deal. It’s too much money to pass up on. Equality be damned.

Well, that’s the deal we are all making. And when you cross the threshold and the deal no longer makes sense (you become one of the billionaires), you rationalize your change of heart. The reason you became a billionaire isn’t because you got lucky — it’s because you worked hard (ignoring the fact that most of your non-billionaire friends worked just as hard or harder). There are all kinds of mental gymnastics here that would make Simone Biles blush. And there’s a good chance that any of us would fall prey to them.

I know for a fact that I got lucky and that thousands of other writers out there worked just as hard or harder than me and have just as much or more talent. I was reading about and obsessed with human psychology, biases, game theory, and evolutionary psychology long before I won the lottery, so I had some defenses against the illusion of meritocracy. Yet another way that i got lucky.

But make no mistake, enough people believe in a meritocracy — or want the rules tilted in their favor — to keep the system rigged in a way that will only increase income inequality. This problem will grow and grow. We tolerate it because the crumbs falling from the table way above us are big enough to live on. But that doesn’t make it any less of a crumby deal.