I’m not sure to what extent we actually disagree vs to what extent I’ve communicated poorly.
I’m not saying the math is wrong. The math seems counter-intuitive, but (as the whole point of the post says), I don’t disagree with the math. I’m not an expert in this kind of math, whenever I think about it it makes my head hurt, I’m too lazy to put much effort into it, and I don’t really expect people to lie about it.
I disagree with the claim that the math can be linked to real-world questions.
If you are considering playing a Prisoner’s Dilemma, and given the choice between these two opponents:
Alice says ‘I will Cooperate if I know you’ll Cooperate, otherwise I’ll Defect’
Bob says ‘I will Defect if I know you’ll Defect, otherwise I’ll Cooperate’
Then as an empirical matter I think it’s pretty clear you should choose Bob as your opponent.
And if two people like Bob play a Prisoners’ Dilemma, I think they’re much more likely to Cooperate than two people like Alice.
I don’t think the math is wrong, but I think that the attempt to extend from the math to “two people who both say ‘I’ll cooperate if I know you’ll cooperate’ will therefore cooperate” is invalid.
I’m pretty sure Neutral-FairBot is just inconsistent.
Not entirely my field, but I think what’s going on is that it could be defined in two different ways, with if-statements in different orders—either this (#1):
If (Proof Exists of Opponent Cooperating)
Then (Cooperate)
Else(
If(Proof Exists of Opponent Defecting)
Then(Defect)
Else(Whatever)
)
or this (#2):
If (Proof Exists of Opponent Defecting)
Then (Defect)
Else(
If(Proof Exists of Opponent Cooperating)
Then(Cooperate)
Else(Whatever)
)
and I think (though open to correction) the mathematical answer is that #1 will cooperate with itself and #2 will defect against itself (which, again, is counterintuitive, and even if the math works out that way I deny that the math has any useful application to the real-world problem of what a person who says “I’ll Defect if I know you’ll Defect and Cooperate if I know you’ll Cooperate” will do).
foreach proof in <some search algorithm over possible proofs> { switch examine(proof) { case PROOF_OF_DEFECTION: Defect case PROOF_OF_COOPERATION: Cooperate: default: continue } }
I’m not sure to what extent we actually disagree vs to what extent I’ve communicated poorly.
I’m not saying the math is wrong. The math seems counter-intuitive, but (as the whole point of the post says), I don’t disagree with the math. I’m not an expert in this kind of math, whenever I think about it it makes my head hurt, I’m too lazy to put much effort into it, and I don’t really expect people to lie about it.
I disagree with the claim that the math can be linked to real-world questions.
If you are considering playing a Prisoner’s Dilemma, and given the choice between these two opponents:
Alice says ‘I will Cooperate if I know you’ll Cooperate, otherwise I’ll Defect’
Bob says ‘I will Defect if I know you’ll Defect, otherwise I’ll Cooperate’
Then as an empirical matter I think it’s pretty clear you should choose Bob as your opponent.
And if two people like Bob play a Prisoners’ Dilemma, I think they’re much more likely to Cooperate than two people like Alice.
I don’t think the math is wrong, but I think that the attempt to extend from the math to “two people who both say ‘I’ll cooperate if I know you’ll cooperate’ will therefore cooperate” is invalid.
Not entirely my field, but I think what’s going on is that it could be defined in two different ways, with if-statements in different orders—either this (#1):
or this (#2):
and I think (though open to correction) the mathematical answer is that #1 will cooperate with itself and #2 will defect against itself (which, again, is counterintuitive, and even if the math works out that way I deny that the math has any useful application to the real-world problem of what a person who says “I’ll Defect if I know you’ll Defect and Cooperate if I know you’ll Cooperate” will do).
Third option:
(Kindly ignore the terrible pseudocode.)