Super-Rational

Reason is not logic, but rather a Gödelian process. Gödel showed that provability is a weaker notion than truth, no matter what axiom system is involved.

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Right and wrong.

As Keith noted, the single-shot PD's self-interest matrix is biased towards defection. Note that tit-for-tat is only an optimal strategy for iterated PD, and so it is not really applicable to the single-shot case, since the interaction may never progress to "tat."

I may have read Keith wrongly, but it seems that he explains Hoftstadter's colleagues' defection as a simple function of humans being flawed. Namely, the "right" thing to do was to cooperate, and they were "wrong" to defect. This view is of course founded on the a-priori assumption that cooperation still is the "right" course of action, and any deviation from that course is the result of a flawed analysis. However, as Hofstadter himself points out, there is an analogy to the Henkins statement "this sentence is true." It is equally defensible on the grounds of logic alone to believe the sentence to be "right" or "wrong."

This is why I stated that morality and the PD are incompatible concepts. Morality is a set of values, the PD is a game based on a payoff matrix. The payoff matrix is not a moral matrix, it is usually rigidly defined according to some quantitative metric: a set number of dollars, for example (in the Platonia Dilemma). Of course the qualitative moral implications are related to the quantitative payoff, but that relationship is often quite complex.

For example, to use Kim's Wal-Mart example. You could make a moral argument that supporting that store helps fund social causes that negatively affect society. You could make an equally compelling moral argument that the money you save, partly used to fund social causes that benefit society, have more effect. My yearly donation of $15 to the Sierra Club has a real impact in terms of lobbyist salaries and influencing policy, for example, whereas since there are always people willing to defect and shop at Wal-Mart, the net effect of not shopping there is almost negligible (and Kim ends up having less money in her pocket anyway).

Does that mean that you should shop at Wal-Mart even if you believe in the social causes at risk by that store's methods of doing business? Not at all - see graphic at left (from article in Business Week, free registration required).

What is misleading in the Costco example however is the selective metrics used to make the argument. Yes, profits per employee and per square foot are higher than Wal-Mart, but what if you compare stock prices? COST | WMT

By which metrics do we determine the winner of the payoff matrix, then? Clearly, the "winner" is subjective. Wal-Mart "defects" by paying employees less, Costco cooperates by paying them more, and yet both claim victory. One consumer shops at Wal-Mart and uses a portion of the savings to donate to liberal organizations, another shops at Costco and pays more. Both will claim moral high ground. You could take the argument to an extreme and ask, why do we spend even one dollar on the space program or the NEA when we could be ending world hunger with the same monies?

Overall, these gray areas are inescapable. This is the real reason that Hofstadter's colleagues - including Axelrod himself - were perfectly justified in choosing to defect. Not because they were wrong, but because they were also right. Right and Wrong simply don't map cleanly onto the payoff matrix space.

I like Keith's argument that we need to find a way to rephrase social problems so as to avoid the Prisoner's Dilemma entirely, but I think this is largely an impossible task, aside from ruinously forceful intrusion of the government into personal liberties. And even in that scenario, what the government decides is "right" is not neccessarily so. You can never escape the Henkins paradox when dealing with issues sch as Right and Wrong in dealing with social policy.

It is tempting to try and relate these kinds of issues to simple one-dimensional morality issues like "do not steal" and "share" but in real-life, it is precisely the more complex, gray area situations that we most need to solve which are not so easily characterized. In that sense, Keith's wish is granted, since the PD is simply inapplicable.