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  #41  
Old 12-17-2005, 10:26 PM
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Default Re: Philosophy questions - Morality & Moral Theories

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I haven't read the other threads on this, but I'll go further than both of you and state that cooperating in the prisoner's dilemma does require either altruism or irrationality.

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I think it's rational self-interest.

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If it's rational self-interest, then both players defect (in the one-shot game), because they both have a dominant strategy.

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I am talking about an iterated prisoner's dilemma...

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There are some other assumptions that have to be made in the finitely repeated prisoner's dilemma (most importantly, common knowledge of rationality), but including all the assumptions leads to a unique equilibrium where players defect on all rounds.

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How do you figure? If both players are rational, a tit-for-tat strategy (or slightly modified), ensures cooperation on all rounds. That is the rational strategy.

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Well, if we make the assumptions:
1) the game is finite
2) both players know that the other player is rational (CKR)
3) both players have perfect recall
4) both players are capable of calculating as many steps as the game has iterations
5) both players have perfect information, i.e., they know how many rounds the game will last, etc.

Then the unique equilibrium is the backward induction one where both players defect on all rounds. E.g., since both players will defect on the last round, they know that the other player will defect on the next to last round, so they'll defect on the next to last round, but the other player knows that ... and so on.

Now, I think this result is fairly absurd, but then one of the assumptions has to go. So which one is it?

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I think #5 is incorrect, they don't know when the game is going to end. However, even if they did, if they were both rational, then they would cooperate every round. This is especially true if they will be playing multiple games with multiple other people, all of whom know how each other have played in previous games. The best strategy is a tit-for-tat, and knowing this, it is best to cooperate. A constant defector may fair a smidgeon better than the tit-for-tat player in one game (since on the first round, the defector will gain more than the cooperator), but when playing multiple games, the defector will end up costing himself a lot -- as everyone else will soon be defecting against him, but cooperating with those that are cooperating -- thus, the cooperators will be gaining more than the defector.

Anyway, even in a single game, the defector will know that the tit-for-tat player will defect on every round after the first if the defector defects on the first round. However, if he cooperates on the first round, then he will gain more on subsequent rounds, and thus will maximize his gain over the course of the game. This is the most rational play that both can make.
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  #42  
Old 12-18-2005, 02:27 PM
atrifix atrifix is offline
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Default Re: Philosophy questions - Morality & Moral Theories

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I think #5 is incorrect, they don't know when the game is going to end.

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IMHO, if we are talking about real-life situations, then all of the assumptions are strictly false, except perhaps #1. I.e., players do not behave rationally, they do not have CKR, perfect information/recall, etc. Some, like perfect recall, may be approximately true, but "approximately true" means "literally false". I think the interesting thing is trying to create a model that can predict behavior, though, and for the model, we'll have to make certain assumptions that are literally false.

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However, even if they did, if they were both rational, then they would cooperate every round. This is especially true if they will be playing multiple games with multiple other people, all of whom know how each other have played in previous games. The best strategy is a tit-for-tat, and knowing this, it is best to cooperate. A constant defector may fair a smidgeon better than the tit-for-tat player in one game (since on the first round, the defector will gain more than the cooperator), but when playing multiple games, the defector will end up costing himself a lot -- as everyone else will soon be defecting against him, but cooperating with those that are cooperating -- thus, the cooperators will be gaining more than the defector.

Anyway, even in a single game, the defector will know that the tit-for-tat player will defect on every round after the first if the defector defects on the first round. However, if he cooperates on the first round, then he will gain more on subsequent rounds, and thus will maximize his gain over the course of the game. This is the most rational play that both can make.

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If our definition of rationality includes not playing dominated strategies, then this is not really correct. I suppose we could have an alternative definition of rationality that doesn't include not playing dominated strategies, but I'm not sure what that would be.

It's true that TFT is strictly dominated by always defecting (ALL D), but more importantly, it's strictly dominated by strategy TFT-1, e.g., TFT until last round, then defect. Now if all the assumptions hold, then no one will play TFT, because they'd do better to play TFT-1. Similarly, both players know that they're rational, they know that TFT won't be played. Since both players realize that TFT-1 is dominated by TFT-2, they both know that they won't play TFT-1...and so on. Hence if all the assumptions hold they'll defect on every round.
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  #43  
Old 12-18-2005, 04:14 PM
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Default Re: Philosophy questions - Morality & Moral Theories

By "rational strategy", I mean one that results in the best outcome for the person (most utility, less jail time, etc.) With your "rational strategy" of ALL-Defect, the person is almost minimizing his utility. That's not rational. Yes, it "beats" the TFT guy, but that's not the goal. The goal is to maximize your own utility/happiness, not "beat the other guy".

Your TFT-1, TFT-2, ... scenario will not be played out by the rational person. Again, the rational person knows that if he defects on the next to last round, the TFT guy will defect on the last round, thus the next-to-last-round defectgor ends up not maximizing his utility, SO he will NOT defect on the next-to-last round. They both might defect on the last round, unless there will be multiple games played with multiple people, and they know you defected on the last round -- there will be retribution to pay -- as no game is really "in a bubble", and previous games will affect subsequent games. Again, maximization strategy is to cooperate -- and use TFT to communicate your strategy.
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  #44  
Old 12-18-2005, 04:46 PM
atrifix atrifix is offline
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Default Re: Philosophy questions - Morality & Moral Theories

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Your TFT-1, TFT-2, ... scenario will not be played out by the rational person. Again, the rational person knows that if he defects on the next to last round, the TFT guy will defect on the last round, thus the next-to-last-round defectgor ends up not maximizing his utility, SO he will NOT defect on the next-to-last round.

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But in this case, the TFT player plays irrationally, which contradicts our assumption that both players are rational. The TFT player does not seek to maximize his utility on the last round, as he could do better by playing TFT-1. Both players are rational, so TFT will not be played. Now, by invoking CKR, we can also see that TFT-1 will not be played, and so on.

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They both might defect on the last round, unless there will be multiple games played with multiple people, and they know you defected on the last round -- there will be retribution to pay -- as no game is really "in a bubble", and previous games will affect subsequent games.

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This is more like a denial of perfect information. If the payoffs, strategies, length of the game, etc. are known beforehand, then both players can employ backward induction.

As long as all the assumptions hold, you won't play against a variety of players (since strategies like TFT are irrational), you'll only play against ALL D, so you can't do any better than ALL D.
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Again, maximization strategy is to cooperate -- and use TFT to communicate your strategy.

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No, the Pareto-optimal strategy is to cooperate. That is, we have a paradox that is similar to the one-shot Prisoner's Dilemma--both players, by acting rationally, end up in a situation that is worse for everyone.
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  #45  
Old 12-18-2005, 05:17 PM
atrifix atrifix is offline
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Default Re: Philosophy questions - Morality & Moral Theories

Another way of framing this: suppose that player A cooperates in round t-1. Player B notes this. Since in the 1-round game defection strictly dominates cooperation, A can only be rational if he believes that B can be induced to cooperate in round t, which would be irrational. Since B is rational and A knows this, A cannot be rational.

Suppose A cooperates in round t-2. He can only be rational if he believes that by cooperating in round t-2 he can induce B to cooperate in either round t-1 or round t. But cooperating in round t is irrational, and cooperating in round t-1 is either irrational, or comes from the belief that cooperation can induce B to cooperate in round t, so cooperating in round t-2 is irrational, and so on.
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  #46  
Old 12-18-2005, 07:36 PM
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Default Re: Philosophy questions - Morality & Moral Theories

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Is your monitor defective and not displaying the word "IMPLEMENT" when I type it?

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Your original post said that utilitarianism was oppressive; it said nothing about implementing it.
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  #47  
Old 12-18-2005, 08:54 PM
tylerdurden tylerdurden is offline
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Default Re: Philosophy questions - Morality & Moral Theories

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Is your monitor defective and not displaying the word "IMPLEMENT" when I type it?

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Your original post said that utilitarianism was oppressive; it said nothing about implementing it.

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Lots of people say things like "slavery is oppressive" without mentioning "implementing" it.
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  #48  
Old 12-19-2005, 01:22 AM
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Default Re: Philosophy questions - Morality & Moral Theories

Again, the goal is not to dominate, it's to maximize utility. It is not rational to have a strategy that does not maximize utility. TFT maximizes utility. If it's one round, then Defecting is the best strategy (well, it's the paradoxical best). Also, the last round of a single game, defecting is best (unless multiple games are going to be played). This has been played out in real world multi-game iterative scenarios... TFT won. I guarantee you that if we have a multi-game contest, and I play TFT, and you play All-D, then I will end up with more utility than you (as long as there is at least one other TFT (or non All-D) player. Which, there should be, because if they also play TFT, we will both maximize utility. The only way I don't win, is if everyone else is irrational.
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  #49  
Old 12-19-2005, 01:57 AM
atrifix atrifix is offline
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Default Re: Philosophy questions - Morality & Moral Theories

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Again, the goal is not to dominate, it's to maximize utility. It is not rational to have a strategy that does not maximize utility.

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Yes, but our goal is to maximize utility given certain constraints. It can be rational not to play Pareto-optimal strategies, as it is in the one-shot game.
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TFT maximizes utility. If it's one round, then Defecting is the best strategy (well, it's the paradoxical best). Also, the last round of a single game, defecting is best (unless multiple games are going to be played).

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But if you agree with this, then surely you can see that if both players know this, they will also defect in the next to last round? If both players are rational (and know the other is rational), they will both defect in the last round, because they do strictly better. This is true regardless of what happens in the next to last round. Thus the outcome of the next to last round doesn't matter in terms of the last round, because both players will defect at that point. So the players would do strictly better to defect in the next to last round.
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This has been played out in real world multi-game iterative scenarios... TFT won.I guarantee you that if we have a multi-game contest, and I play TFT, and you play All-D, then I will end up with more utility than you (as long as there is at least one other TFT (or non All-D) player. Which, there should be, because if they also play TFT, we will both maximize utility. The only way I don't win, is if everyone else is irrational.

[/ QUOTE ]It's true that TFT won Axelrod's tournaments (I think 7/8), but that doesn't prove that it's rational. First of all, Axelrod's tournament didn't have a definite number of rounds known in advance, so assumption #5 was not applicable. More importantly, consider the one-shot game. If we run tournaments, two players who always cooperate will do strictly better than two players who always defect. But if we agree that defecting is the rational strategy, then the players who cooperate cannot be rational, despite the fact that they beat the other two players. Or, consider this (analagous to Newcomb's problem): a player plays completely at random. His opponent cooperates if and only if an accurate predictor of his actions would have predicted that he would cooperate on that round. Cooperating thus does strictly better than defecting, but do we want to say that random play is rational?
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  #50  
Old 12-19-2005, 05:53 AM
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Default Re: Philosophy questions - Morality & Moral Theories

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Is your monitor defective and not displaying the word "IMPLEMENT" when I type it?

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Your original post said that utilitarianism was oppressive; it said nothing about implementing it.

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Lots of people say things like "slavery is oppressive" without mentioning "implementing" it.

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The OP was clearly talking about utilitarianism as a moral theory, and your response did nothing to indicate that you were changing that context to emphasize how the theory is put into practice socially, legally, or otherwise. When people talk about disagreeing with slavery, the discussion is understood to be about the practice of slavery, not some abstract philosophical theory.
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