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The Platonia Dilemma.

I consider myself a reasonably intelligent guy, with rather strong opinions, and a sufficient amount of self-criticism. Note the presence of moderating adjectives in every sub-phrase - reasonably, rather, sufficient. Like a moth to flame, therefore, I am always drawn to writing by those I admire for the same qualities, only more so (without the adjectives). One of these is Kim, a dear ultra-liberal friend from college, still one of my closest (and always will be). Kim is formidably intelligent, with blazingly strong opinions, and fanatical self-criticism. I admire her greatly, because she tends to write things like this:

I've gotten used to hearing Republican claims and assuming that the claimers are just lying scum out for their own advantage, or people who haven't considered the issues thoroughly. I think most are, but some might just be superrational people who see an economic model that could be workable in a platonic world, just as my very liberal view of people acting decently and working hard just because it's the right thing to do may not play so well in the real world...but it requires my adherence anyway. Might make for more interesting discussions with my right-leaning friends, and non-friends. It's interesting to see that I've been long arguing against voodoo economics based on its inapplicability in the real world (actual rich people are the ones best at never letting a dime escape their clutches, so what exactly would "trickle?") and getting very angry when people argue that in the real world, lots of people will refuse to do the right thing environmentally or otherwise, so good people get the short end of the stick. I argue, "so what" be ethical anyway, and deny that in the real world MOST people are evil. Well, I guess the superrational Reaganomics fans think that surely MOST rich people aren't evil, and enough of them would take their ill-gotten capital gains and do good with them. Interesting.

The reference to "super-rational" is from Douglas Hofstadter's book, Metamagical Themas, in relation to the Prisoner's Dilemma[1]. A super-rational (SR) player is defined recursively as one who assumes the other players are also superrational, and chooses to cooperate in order to maximize gain. Unlike the "iterated" PD, where the best strategy is "TIT FOR TAT"[1], Hoftstatder explored the "one-shot" PD, and tried to rationalize a strategy that favors cooperation rather than defection (p.730):

I found that I could not accept the seemingly flawless logical conclusion that says a rational player in a noniterated situation will always defect. In turning this over in my mind and trying to articulate my objections clearly, I found myself inventing variation after variation after variation on the basic situation.

This led Hofstadter to come up with what he called the "Platonia Dilemma", based on the following payoff matrix[2]:


and he then sent out a letter to 20 of his friends and acquaintances, chosen for their rationality and familiarity with the PD concept, including notables such as Martin Gardner and Bob Axelrod, whose own research (summarized in his amazing book, The Evolution of Cooperation) proved the superiority of the TIT FOR TAT strategy in the iterated PD case. The letter read (in part):

Each of you is to give me a single letter: "C" or "D", standing for "cooperate" or "defect". This will be used as your move in a Prisoner's Dilemma with each of the nineteen other players. The payoff matrix I am using is [see above].

Thus if everyone sends in "C", everyone will get $57, while if everyone sends in "D", everyone will get $19. You can't lose! And of course, anyone who sends in "D" will get at least as much as everyone else will. If, for example, 11 people send in "C" and 9 send in "D", then the 11 C-ers will get $3 apiece from each of the other C-ers (making $30) and zero from the D-ers. The D-ers, by contrast, will pick up $5 apiece from each of the C-ers, making $55, and $1 from each of the other D-ers, making $8, for a grand total of $63. No matter what the distribution is, D-ers always do better than C-ers. Of course, the more C-ers there are, the better everyone will do!

By the way, I should make it clear that in making your choice, you should not aim to be the winner, but simply to get as much money for yourself as possible. Thus you should be happier to get $30 (say, as a result of saying "C" along with 10 others, even though the D-ers get more than you) than to get $19 (by saying "D" along with everybody else, so nobody "beats" you).

Hofstadter set this PD up with a clear subtext that cooperation is preferred. Note that the payoff matrix does reward defectors, but only if there are very few. A SR thinker would presumably choose to cooperate to maximize the probability of a large payoff. His expectation was that most would choose to cooperate (p.746):

Any number of ideal rational thinkers faced with the same situation and undergoing similar throes of reasoning agony will neccessarily come up with the ientical answer eventually, so long as reasoning alone is the ultimate justification for their conclusion. Otherwise reasoning would be subjective, not objective as arithmetic is. A conclusion reached by reasoning would [then] be a matter of preference, not necessity. Now some people may believe this of reasoning, but rational thinkers understand that a valid argument must be universally compelling, otherwise it is simply not a valid argument.

If you'll grant this, then you are 90 percent of the way. All you need ask now is, "since we are going to submit the same letter, which one would be more logical? That is, which world is better for the individual rational thinker: one with all C's or one with all D's?" The answer is immediate: "I get $57 if we all cooperate, $19 if we all defect. Clearly I prefer $57, hence cooperating is preferred by this rational thinker. Since I am typical, cooperating must be preferred by all rational thinkers. So, I'll cooperate."

Italics are his emphasis, underlines mine. A clear flaw is the assumption that all players are SR. I have underlined the parts of his argument where this assumption is explicit. Another clear flaw is the assumption that the "throes of reasoning agony" will be correct - it is entirely possible for a rational thinker to simply be wrong. This can be to flaws in logic, omission/ignorance of key facts, or flawed assumptions.[3]

When Hofstadter tallied up the responses, he found (much to his chagrin) that there were 14 defections (each earning $43) and only 6 cooperators (each earning $15). This, despite the fact that he had unconsciously (?) "biased" the sample of participants by selecting his own friends and acquaintances based on his evaluation of their "rationality" - even people like Bob Axelrod and Martin Gardner who are intimately familiar with the PD and game theory (both of whom chose to defect, BTW). Hofstadter writes:

It has disturbed me how vehemently and staunchly my clear-headed friends have been able to defend their decisions to defect. They seem to be able to digest my argument about superrationality, to mull it over, to begrudge some curious kind of validity to it, but ultimately to feel on a gut level that it is wrong, and to reject it. This has led me to consider the notion that my faith in the superrational argument might be similar to a self-fulfilling prophecy or self-supporting claim, something like being absolutely convinced beyond a shadow of a doubt that the Henkin sentence "This sentence is true" actually must be true - when, of course, it is equally defensible to believe it to be false. The sentence is undecidable; its truth value is stable, whichever way you wish it to go (in this way, it is the diametric opposite of the Epimenides sentence "This sentence is false", whose truth value flips faster than the tip of a happy pup's tail). One difference, though, between the Prisoner's Dilemma and oddball self-referential sentence is that whereas your beliefs about such sentences' truth values usually have inconsequential consequences, with the Prisoner's Dilemma, it's quite another matter.

Again, italics are his emphasis, underlines mine. The key to undertanding why seemingly "rational" thinkers could take the same facts and arrive at a different result, is because reason is not logic. The mechanics and machinery of our intellect is ultimately Godelian - no system of analytical statements and rules and formal descriptors can ever fully model it. In fact Hofstadter himself in the same book devotes much time to emphasizing this, that ultimately intellect must be an emergent and statistical property - even creating a wonderful symbolic model called "The Careenium" (a great pun which I won't spoil. Read the book :) to illustrate it.

This is why self-examination is essential. Thought and analysis are ultimately founded upon "gut instinct" as much as pure facts and figures and logic - we cannot escape it. This also is an argument for diversity - because in combining the analyses of two people, who arrive at different conclusions from different facts, we are able to better triangulate the reality which underlies all of existence, towards which we all must grope towards half-blinded when alone.

Self-examination of the kind that Kim engages in so directly and willingly is essential to improving ourselves and the world. And the lessons of the PD are one such route to that goal. Ultimately, though, we do have to apply reason as we understand it, not as we think others do.

[1] Steven Den Beste had a good article on TIT FOR TAT in the iterated PD (which does NOT apply to the one-shot PD, of course).
[2] I assume the reader is familiar with the basic concept of the PD, the "payoff matrix" representation, as well as the terms "cooperate" and "defect" in that context. If not, I highly recommend Hoftstatder's book (Metamagical Themas) or good ol' Google.
[3] this paragraph is self-referential in classic Hoftstatder tradition :) .

permalink | posted by Aziz P. | 2.17.2003 |

Discussion on The Platonia Dilemma: 1 Comments

does fear of getting beat inspire a win or promise defeat?

By Blogger jack sulaiman, at 7:56 AM  

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