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Tuesday, April 19, 2011


Marinus Ferreira sent me a long interesting e-mail message criticizing my treatment of the Prisoner's Dilemma in Part Five of my tutorial on The Use and Abuse of Formal Methods in Political Philosophy, originally posted seriatim on my second blog, and now to be found on I should like to attempt a reply, and he has graciously given me permission to reproduce his entire e-mail message as part of that reply. Here it is:

Dear Prof Wolff,

As you posted the link to the archived form of your formal methods tutorial, you made a comment about the prisoner's dilemma in line with your dismissive appraisal of it in the tutorial. Forgive me if I bring up a tiresome topic, but I thought the appraisal was somewhat too
curt. When I was originally reading the tutorial, as you were posting it, I was surprised to see no mention about how prisoner dilemma cases show a tension between utility-maximization and Pareto-optimality. I believe investigating that tension, given as it is between two features of decision-making many people take to be bedrock parts of rationality (though neither you nor I would be in that camp, I'd wager) is sufficient reason to pay some attention to the prisoner's
dilemma. I wrote a comment on the recent post to that effect, except I got somewhat carried away (I blame the rainy weather) and what I wrote became somewhat too large for a comment on a blog post. I posted a slightly longer and dollied-up version of this on my own blog, but
since it is something I came up with in response to what you have said, I thought I would involve you in the discussion.

Contrary to your harsh evaluation, I think there is something to be said for the prisoner's dilemma as an analytic tool. Heaven knows a lot of people make ridiculous claims regarding it (for instance, I was told once that it shows that ethics is impossible), but there are at least two reasons to take it seriously, if only as an analytical device.

The first reason is that there are simply so many theoretically interesting cases which can be modeled as some variation of the PD, that is, where situations arise with the payout matrix I described above. There are traveler's dilemmas, the centipede game, the ultimatum game, etc. I'll leave it up to the reader to investigate these cases, and their link to the PD, on their own. But note that understanding any situation which can be modeled in this way is going to necessitate understanding the implications of the PD (which includes, as you stress, knowing what it doesn't entail).

Secondly, the most important reason to look at the PD (which I was surprised to see get no mention at all in the tutorial) is that it gives a very embarrassing and problematic result for the mass of people who believe that decision theory, etc., provide the gold standard for human reasoning. That is, the PD shows that utility maximization doesn't lead to Pareto-optimal situations (which was a bit of a surprise, since under similar suppositions the free market,
which is driven entirely by utility-maximization, does lead to Pareto-optimal distributions of resources – a bit more on that later in this paragraph). Utility maximization is the procedure whereby at each point you need to make a procedure you take whatever course of action has the best prospects for getting you what you want (after taking into consideration all the likely future effects of your actions), and Pareto-optimality is the idea that one situation is preferable to another if every person involved finds the first one to be at least as good as the latter. In non-wonk terms, the PD demonstrates that if everybody tries at every step to take the action with consequences they'd most prefer, they are quite likely to end up in a situation they find less preferable than one they would have reached had they acted differently. It in fact does even more, in that the situation of the two prisoners if both defect is worse for both of them, whereas it's Pareto-suboptimal if only one person reaches a situation they don't prefer. This is embarrassing and problematic to the decision theorist, because Pareto-optimality is a very low bar indeed. There are a range of terrible situations that are Pareto-optimal – for instance, a fiefdom with its range of landlords and impoverished serfs is a Pareto-optimal distribution of land, since to give any land to a serf you need to take it away from a landlord, which means that changing the distribution of land would always be against the preferences of at least one person. If utility-maximization can't even ensure reaching situations with that low level of goodness, then the decision theorist has reason to worry.

It's this feature of the PD which gives force to the tragedy of the commons (as George Hardin described in the 60s, though not as a PD). Each member of a community who tends sheep and has access to the common pasture always has the incentive to put one more sheep in the field: though this lowers the total productivity of the commons through being overloaded, the individual's gains of having the extra sheep outweigh the marginal loss to each sheep. But if everybody follows this incentive (as utility-maximization demands) then the commons will soon be exhausted and every farmer will be worse off in the end. The lesson to be learn here isn't that co-operation in such situations is impossible (as some people bizarrely claim, showing off a staggering confusion about the structure of human purposive action) but that utility-maximization – the hard-nosed pragmatism which makes the prisoner defect every time – is untenable as a general guide to action. In scenarios with PD pay-offs (and the insights of the
countless writers on this topic indicate just how many there might be) utility-maximization turns out to lead us by the nose to our downfall. And that is what we should learn from the prisoner's dilemma.

Sincerely yours,

Let me say, first of all, that the continuing occurrence of really classy responses like this one to my blog posts is a source of great satisfaction to me. From time to time, I check the comments on one or another of the political blogs I read, and they are just not in the same league with this and many other responses I have received.

My first reply to Marinus is that it had simply never occurred to me to construe the Prisoner's Dilemma as a devastating critique of rational choice theory, but I certainly like the intention. I do not think that is the intention of the great majority of authors who invoke it, at least so far as I can tell, but as Marinus seems to suggest, that is their problem, not ours.

One technical point, which is not at all unimportant, needs to be made. Maximization of expected utility is a rule widely proposed and endorsed for the making of decisions under risk -- that is to say, as I explain in my tutorial, it is intended for situations in which the totality of the possible outcomes of an action is known and also the probability of each [so that the sum of the probabilities is 1.] But Game Theory, which is the locus of the Prisoner's Dilemma, is an analysis of choice under uncertainty -- that is to say, of situations in which the totality of the possible outcomes is known, the participant's ordinal ranking of those outcomes is known, the actions available to oneself and all other participants are known, and the precise outcome associated with each set of possible strategies of the game in the normal form is known, but in which the probabilities of the occurrence of the several outcomes is not known [hence "under uncertainty."]

Now, Marinus' central point, if I understand him correctly, is that if Rational Choice Theory cannot yield a satisfactory answer to the problem of choice in so reduced and elementary a situation as is modeled by the Prisoner's Dilemma, then that fact constitutes a powerful criticism of Rational Choice Theory. But Rational Choice Theory is a theory of choice under risk, not of choice under uncertainty. So despite my sympathy for the intention of the critique, I think it misses its mark.

Marinus is exactly right that Pareto Optimality is a very weak constraint indeed. And I agree the formalization of choice situations is useful in helping us to think through what is involved in them [such as the tragedy of the Commons, etc.]

When one gets into the precise detail of Game Theory, as elaborated by von Neumann, one quickly realizes that his enormously powerful and really elegant Fundamental Theorem applies only to a very, very constrained class of cases. What is perhaps most interesting is that once one moves beyond situations of two players with strictly opposed preference orders [The Prisoner's Dilemma is an instance of a game in which the players do not have strictly opposed preference orders], then, as Thomas Schelling first showed in his brilliant book, The Strategy of Conflict, all manner of informal considerations become essential to an analysis of bargaining situations. In my irreverent critique of the Prisoner's Dilemma, I was trying to make clear some of those essential but difficult to formalize considerations.

1 comment:

Marinus said...

My claim was more modest than that the PD offers a serious challenge for rational choice theory (though I see how especially the last paragraph might invite the reader to think otherwise), it was that one reason to study the PD is that it has this interesting result about the conflict between utility-maximisation and Pareto-optimality (that, and the fact that it has such many analytical uses). If we care about Pareto-optimality and utility-maximisation (and almost everybody in the field does, very much) then we should address the fact that, in a range of significant cases, they conflict.

I do claim that this is a problem for the decision theorist (with cases like the tragedy of the commons showing how large a problem this might be); in fact, I am frequently surprised and somewhat disappointed by the fact that this conflict is so rarely commented on, given that it is a straightforward result of the PD. This, I hope, is sufficient reason to take the PD seriously, which is the conclusion I was intending to argue towards.

That said, there is something to be said in reply to what you have written here. While the difference between decision under uncertainty and under certainty is certainly important, it has no bearing in PD cases. The problem isn't that there are hidden consequences to our action. The issue is that the structure of pay-offs (which is perfectly transparent to those involved) makes it that you have a move to a Pareto-suboptimal outcome. For instance, in the canonical prisoner's dilemma, if you are certain the other prisoner will defect, you will defect too, and if you are certain the other player will not defect, you will defect as well, given that you are a utility-maximiser. You will defect night and day, rain or shine, because it is the dominant strategy. And therein lies the problem. The amount of information available to the agent isn't what is at issue here, it is the structure of the pay-offs.