Are you Smarter than a Pirate?

The Pirate Game:

If you get the theoretical right answer intuitively, that is to say, without googling it up, I’d advise you against a career in pirating–you’d be walking the plank rather quickly. Real pirates knew something about iterative nature of reality, and actually had one of the most egalitarian distribution of plunder in history (wiki it up). They also knew that if you kill surrendered enemies mercilessly even if it was more convenient to just kill them, your future enemies will have no incentive to surrender and fight you to the death. Instead of life on the high seas, might I suggest a career in politics?

 

Rational Irrationality and Human Systems

Why is it that geeky game-theory doesn’t seem to reflect reality? The first idea is that people aren’t so rational after all. We know that people are frequently irrational (other people–important caveat!). People aren’t randomly irrational though; people are irrational when it’s rational to be irrational. Rational irrationality is the idea that it’s often useful (instrumentally rational) to be epistemically irrational. This comes up when the cost of being wrong is low while you’re motivated to believe in something, like, “I’m a good person.” If you’re a hardcore rationalist, you might think being irrational is always bad, but that’s not even close to true in the real world. There’s almost no illusions about who is better at chess–the hierarchy is clear and well understood. In games like poker and Magic, due to variance, there is a massive Dunning-Kruger effect in play, where bad players often think they are good, precisely because they are bad players–they are incapable of assessing their own ineptitude. While bad poker players who think they are good are punished rather swiftly, not so much with Magic players. In society, there are many positive reasons to be irrational. We encourage people to be irrationally self-confident. Not to go as far as idiocracy, but objectivity is associated with clinical depression when it comes to self-assessment. Overconfidence is seldom punished (mostly we don’t have opportunities to fist fight bears anymore), and in fact it’s encouraged, so what does it matter that it might not be objective? Being right is indeed very overrated. Don’t believe in objectivity; believe in yourself. 

There are many statements that are epistemically dubious like “my country is the best in the world” or “Islam is the one true religion,” but have low costs for being wrong. Obviously given the number of countries and religions out there, and you only really knowing one, it’s rather unlikely that you struck the correct one through chance and/or objective judgment, but then again, these aren’t costly mistakes either. What does this mean? Where cost is low, people believe what they want to–what’s pleasing to believe–and hence they form tribes, and become more and more dogmatic in their beliefs and lower their standards for truth in that particular sphere. Religion and politics fits this bill perfectly. This is why we treat the merits of arguments from politicians with similar rigor as we give to rap battle lyrics; it’s rational to be irrational about low impact, high motivation beliefs, and we should expect this. While ideas like futarchy are riddled with technical problems, it’s a good idea to impose a cost on incorrect opinions if getting it right matters. On the other hand, if the cost of getting it wrong is truly low, then we really should care less. 

A good thing to keep in mind is that politics is an arena where we should expect rational irrationality to be extremely high. You might argue that unlike religion, it has a real world cost–like the very costly War in Iraq. It’s less costly on an individual basis, because A, you share the costs of poor policy with your fellow citizens, and B, you have almost no impact on this outside of dutifully voting and having a less than state lottery chance of making a difference. The problem, of course, is that it has a huge societal cost, and therein lies the problem. It’s in everyone’s interest to impose a cost on high impact problems, even if at the individual level, the impact is low, because wrong opinions matter. 

 

The Real World is Complex

So, the simple answer to the pirate question is that the first pirate would offer 96, 0, 1, 0, 1, 0, 1, 0, 1, 0 and this proposal would pass. If you work through backwards induction, and start with the scenario of only 2 pirates remaining, the answer reveals itself. Pirate 9 proposes 100, 0, and overpowers Pirate 10, winning the tiebreaker. Knowing this, when there is Pirate 8, 9, and 10, 8 should propose a division of 99, 0, 1 to secure Pirate 10’s vote. Since 1 gold is better than none (if 10 votes to kill), pirate 10 should accept, being rational. Knowing this, Pirate 7 should offer Pirate 9 1 gold to pass the vote and 9 can’t say no, because he knows 8 doesn’t need to offer 9 any coins, and so on. 

In the real world, this wouldn’t pass. Experiments on variants of the Dictator game suggest that people act in “irrational ways” in the real world. Quite simply, most people reject grossly uneven distributions out of spite or contempt when they feel that the proposal is unfair. In fact, social animals like monkeys will also reject unfair pay. In a weird way, it seems like social animals have a built-in mechanism to reject tyranny, even if it isn’t immediately rational to do so (our EV is less on a one-time basis). Depending on your perspective, you can view this type of theorycrafting as musings of a sophistry that even monkeys can demonstrate to be useless, or as evidence of how irrational we are as human beings. The assumption with the pirate game is that you can’t trust the other pirates (obv right, they’re fucking pirates) so you can’t collude to try and form a coalition to overthrow the less fair pirates. Now we can go on with a closer to real world scenario like iterative prisoner’s dilemma, which has a slightly more complex equilibria, but the general idea is that theory often fails to reflect real world scenarios, either because the empirical world is a messy place full of unintended consequences that we don’t fully grasp, or because people are in fact, quite irrational, designed for optimality in a world where the majority of our history lies–around 50,000 to 100,000 years ago.

A Tangent about Dictatorships and Democracy

If you live in a democracy, collectively,  you have the power to metaphorically make the captain walk the plank–which is presumably what gives you any chance at political gold. This model also illustrates why democracies are better for citizens than dictators. In a dictatorship, the electorate, that is, the people that matter, is small–the inner circle of people with guns. To hold power, the dictator can offer a distribution like 9994, 2, 2, 2, and a long list of zeroes, and as long as that offer is better than other counter-offers from potentially mutinous inner circle groups, they can retain control of power. This is why dictatorships are invariably poor, often at war, and why dictators are ok with that, and why leaders of wealthy nations are also ok with that–it makes for easy plundering and manipulation of a nation’s resources. This is also the exact political structure of corporations and board members. The smaller the number of people you need to support you, the more corrupt your system will be since it will be inexpensive to simply pay out supporters with a bribe.

The genius of Democracy is in expanding the electorate, which has the effect of making the cost to bribe increase to the point where it’s untenable. Actually, there is almost nothing genius about the idea–it’s mostly an unintended consequence of a bad theory, but this illustrates the point that empirical evidence often trumps theory where our understanding of the variables is weak. If you observe the world, democracies, in fact, prosper far more than do dictatorships. You can further subdivide it into places that have oil like Saudi Arabia, or Venezuela (relatively stable because dictators don’t need to rely on citizen support for wealth), and places that don’t, like North Korea (unstable) which also hasn’t done well since like the 60s or something. While we’re lucky for living in a democracy, and aren’t consistently being offered 1s and 0s to the extent that dictators do, we aren’t playing our cards very well at all.

What Game Theory Can Teach Us

As we’ve shown, game theory optimal doesn’t always do so well at predicting what happens in the real world. We aren’t purely rational agents, and the world is a muddled place where it’s impossible to isolate motivations. At the same time, game theory, with help from CGP Grey, does explain a lot of politics well too, like why first past the post will always veer towards a two-party system. You might think that as rational citizens, you can do better than theoretical pirates, but the thing is, you actually have to do it, not just recognize it and be willing to bite a possible negative EV spot from time to time.

As pirates in the back, our sole source of leverage is in our ability to overthrow the leading pirate (the establishment, the party in power, the po’lice, the bourgeoisie, whatever). Game-theory wise, we should be far more liberal in axing pirates, even if they don’t deserve it. Being spiteful isn’t just throwing irrational tantrum; it’s the only way to preserve your power in the long-term. Libertarians, Green Party supporters everywhere, Bernie supporters, you should keep this in mind. Yes you’ll be a spoiler in the “most important election cycle yet” but this logic will remain the same every election cycle, and you will still be the sucker until you take a stand. You want political power, the only way to do this is to make more pirates walk the plank. That is, your share of the social plunder is effectively only protected by your ability to threaten to mutiny and kill the captain, so the only way to change the motivational calculus of the pirates ahead of you is to make the threat to kill the captain more prescient.

Here’s a game scenario. Every tournament poker player knows that you need a better hand to call off than to ship due to the absence of fold equity when calling. So good players ship light on the button, and call tighter in the blinds, opting to wait until they can be the guy shipping. What if you played infinite tournament poker with the same grinders though? Calling marginally costs both you and the shipper, so isn’t there a case to be the guy that makes -EV calls to spite the guys who ship light, thereby discouraging them from shipping light in future games? Imagine if you could ship light, be +EV, and your competitors had to have a stronger range?

For locals, TransLink, BC’s transit system, had a plebiscite for Metro Vancouver area people, asking whether or not we’re willing to pay a 0.5% increase in sales tax to support service expansion and maintenance. They lost quite handily, 62% for no, 38% for yes. I voted in support of the added taxes, albeit with extreme disgust, but now I believe that this was a mistake for the reasons I’ve mentioned. 

 

Sweeping Generalizations

Progressives and Libertarians have a peculiar weak spot, in that they are principled. Conservatism is less principled in the sense that they want to keep changes slow and minimal, but are less guided by a sense of ought to which they stand for something. I don’t mean that conservatives don’t stand for principles; it’s that they are guided more by how things are or were rather than how it ought to be. Now, being less principled might sound like a weakness rather than a strength, but their resulting systems are in many ways, more suited for humans as they are, rather than how they ought to be, or ideally are, which can have unintended consequences. In short, they have less problems proposing theoretically rational pirate solutions that don’t correspond with the real world–and I say this as a liberal.

Warning–sweeping generalization incoming–The kind of inflexible rationality proposed by Descartes, call it principled rationality, lost out to a more Humean approach of just looking at the world and observing. We see that an empirical, scientific approach made people happier, made more sense, and cohered better with how people actually think, and the social sciences this century seems to confirm this worldview.

Take some examples typically associated with conservative orthodoxy–no LGBT rights, no right for women to choose abortion, no atheists, no feminism. Liberals (and libertarians) take a principled stance against this, because obviously, discriminating based on gender, religion, sexual orientation, and so on, is wrong, as is restricting the freedom to choose what happens with your own body. If you look at human societies, though, with very few exceptions, men dominated women, religion is almost universal, and there are taboos everywhere against homosexuality. That is, there were historic reasons why this was something like an evolutionarily stable strategy throughout most of human history. Having religion (even if the details happened to be false), encouraging procreation, and even discriminating against minorities probably had some social utility, call it the price of social cohesion.

The root of conservatism, you can say, is “confusing what is, for what ought to be,” if you have a liberal bent like me. For conservatives they see social anomie as evil; rising rates of divorce as evidence that liberal ideology and excess freedom is degenerate (rather than that women were subjugated and lacked options in the past). Thinkers like Jonathan Haidt talk about the differences in the way that liberals and conservatives think about morality, and it’s interesting, but I prefer to think of it more in historical context. What I appreciate about conservatives is that it’s closer to an optimization based on human psychology through randomness and evolution–in a sense it’s not forced. Liberals often assume that their ideas are evidence based, while that of conservatives are fear/paranoia/irrationality based, but in reality, it’s more historically based, which can in many cases, outperform well-intentioned theorycrafting because it’s a stable strategy that has survived the centuries. What worked, ought to be, because, well, it worked. The problem is, the world is changing, fast. References on what worked have less and less validity in a world where our grandparents share more in common with the Romans than they do with the generation that had Internet since they were born.

For libertarians, individual freedom is above all else, including social cohesion. If you listen to their debates though, it’s clear that they have no plan for global warming or any environmental problems. Simply put, for pure libertarians (think of it like a spectrum), a social contract is vacuous–you as a citizen haven’t signed on to it unless you do so explicitly, making issues like sharing resources and costs a near impossibility. That’s why their answers are so weak–and they veer toward the easy solution–that is to deny global warming altogether. Like the more well known Prisoner’s Dilemma, it’s often in the interest of everyone to have an outside enforcer who ensures that agreements are enforced, like the idea of not polluting, since resources are in fact, shared whether we like it or not.

Liberals are no exception, although being a liberal, it’s harder for me to find concrete examples of this–call it motivated reasoning–but let’s use an example, “tough on crime” bills are consistently opposed to by liberals. This seems reasonable–in that retribution is the least reasonable of the 4 principles of justice, and so we lean towards deterrence, and recidivism–or rather, helping criminals recover and get back to society. This is all well, and in many ways, empirical as well–there’s good evidence that criminals, when given a chance at other better options, take it, as do drug addicts. Except–we aren’t completely rational; certainly we feel extreme discomfort at the thought of criminals “recovering.” We want to see those who hurt us deeply to be suffering, and this is why death penalty will always be tempting.

Principles matter and we should always strive for them, but the how needs to be empirically tested, not theorycrafted. We aren’t even close to being smart enough to move from general principles to how the real world works or doesn’t. Aim towards a goal, but how to get there needs to be approached empirically. If a conservative proposal works for a particular reason, do it. If a libertarian solution works best, do it. If a liberal solution is fit for a particular problem, act on it. Most importantly, be less dogmatic, and encourage small experiments on small scales, often, and analyze the results, and see what happened. That’s how scientists do it. 

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