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Superrational decision making is a type of rational decision making in which the players cooperate in a one-shot prisoner's dilemma without coordination, punishment, or magical thinking.

The idea is that when playing a symmetric prisoner's dilemma, one assumes that there is a unique solution to the mathematical problem of the optimal strategy, that this solution will be found and played by all superrational players, and that *assuming the players are perfectly correlated*, you maximize your utility.

The result in a one shot prisoner's dilemma is that two superrational players cooperate with each other, as opposed to two Nash-rational (or economically rational) players who defect.

A superrational player playing a Nash-rational economist will defect, and in general, in the absence of other superrational players, will play according to the Nash-rational strategy. It is only when there is a community of superrational players that one finds new types of rational behavior.

I have two closely related questions about the literature on this:

- Douglas Hofstadter expounds this idea at great length in a series of
*Scientific American*articles, reprinted in his collection: "Metamagical Themas", one of which is "Dilemmas for Superrational Thinkers, Leading Up to a Luring Lottery" (*Scientific American*, June 1983). I believe the idea, at least in its mathematically precise form, is original to him, and I credit him whenever I mention it.

Is the mathematically precise definition of superrationality in symmetric multi-player games due to him, or was it somewhere in the literature before?

- Do philosophers take this idea seriously? I have not seen any professional literature which uses this. I am not asking whether philosophers
*should*take the idea seriously, because I think they should. I am asking whether they do and if anyone can point me to specific examples of this that can be found in the literature.

1-1:It is

notinterpretation! This is exactly what Hoftstadter writes, it is exactly what he means, and there is absolutely no confusion here. Hofstandter never talks about "aggregate payoff", the concept never comes up! It is indeed true that the superrational strategy maximizes aggregate payoff in symmetric prisoner's dilemma (since the aggregate payoff divided by the number of players is the average payoff in a symmetric game), but this is not the definition. Hofstadter isn't vague. The reason he is neglected is because he isright, and philosophers prefer political clowns who are wrong. – Ron Maimon – 2012-09-02T13:57:36.013I found a reprint of the articles here, please read them and tell me this is "interpretation". I know what a reinterpretation is, and I know what plagiarism is.

– Ron Maimon – 2012-09-02T14:09:23.313Quote: ... All it means is that all these heavy-duty rational thinkers are going to see that they are in a symmetric situation, so that whatever reason dictates to one, it will dictate to all. From that point on, the process is very simple. Which is better for an individual if it is a universal choice: C or D? That’s all. Actually, it’s not quite all, for I’ve swept one possibility under the rug: maybe throwing a die could be better than making a deterministic choice. Like Chris Morgan, you might think the best thing to do is to choose C with probability p and D with probability 1−p ... – Ron Maimon – 2012-09-02T14:11:53.277

Sorry, these are not superrationality. Superrationality requires at least the analysis of the Luring lottery, to show that the superrational answer for N players is to flip an N-sided dice to and send a postcard if it comes up "1". All the other things are philosophical blah blah blah with no precise counterpart, and no essential modification of economical game-theoretic reasoning required. – Ron Maimon – 2012-08-02T08:18:42.373

3I quoted Hofstadter's definition of superrationality. I don't really see how to distinguish Hofstadter's definition as not "philosophical blah blah". It looks very similar to Schelling and Lewis' definitions. The Luring Lottery is quite similar to Schelling's games involving focal points, with the exception that Hofstadter's proposed focal point could not be observed empirically... although admittedly a contest in Scientific American is not a reliable instrument for doing behavioral economics. – Matt W-D – 2012-08-02T19:53:29.577

The Schelling reference might be relevant. The other ones are philosophical blah blah. Hofstadter's isn't because he can solve the Luring Lottery (it is possible to do Luring Lottery empirically--- simply do a prisoner's dilemma like game with CC payoff of $10 each, DD payoff of $0, and CD payoff of $1000/$1. In this case, I think that it is conceivable to see coin-flipping behavior in humans. The concept of "focal point" is similar, although DD is also a focal point of sorts in prisoner's dilemma, so I need to read Schelling before upvoting or accepting. – Ron Maimon – 2012-08-10T01:11:25.680

1Ok, I looked at the focal point, and it is

completely unrelated, so I should downvote, but I won't because you are sincere in confusing the two concepts. The Schelling fellow does not predict cooperation in one-shot prisoner's dilemma, and his theory is to explain how to coordinate without communication, which is only vaguely related to the Hofstadter idea. Hofstadter's thing is mathematically precise-- I can tell you the superrational strategy in any symmetric game you dream up. – Ron Maimon – 2012-08-10T01:13:55.520@RonMaimon: I made my reply briefer. Can you edit your original post to contain a complete quote from Hofstadter defining superrationality, with a focus on aspects of it you consider essential? I don't see where he lays out a framework for systematically analyzing any arbitrary symmetric game. – Matt W-D – 2012-08-11T21:12:25.093

I can define it for you--- "a superrational strategy in a symmetric game is a mixed strategy (meaning the players can throw dice if they want to) that maximizes the expected payoff for any one of the superrational players, under the assumption that they all play the exact same strategy." This is the precise definition, it is not stated this way in Hofstadter, but it is blindingly obvious given what he writes, so much so that it would be plagiarism to claim this is not what he meant. This definition does not match the focal point, or anything else I have seen. – Ron Maimon – 2012-08-20T07:49:16.613

2That sounds like your own interpretation. I wouldn't call it plagiarism. It neglects the ideas Hofstadter had about rationality, coordination, and aggregate payoff. It speaks to the precision of Hofstadter's concept if you must resort to interpretation in order to provide a definition. Finding an adequate definition in Hofstadter is a matter of scholarship - if you can't find a direct quote then this just boils down to a matter of "he-said, she-said". Perhaps Hofstadter's vagary is part of the reason he's neglected in the mainstream game theory literature. – Matt W-D – 2012-08-20T14:15:40.043