As I understand it, Hofstadter’s advocacy of cooperation was limited to games with some sense of source-code sharing. Basically, both agents were able to assume their co-players had an identical method of deciding on the optimal move, and that that method was optimal. That assumption allows a rather bizarre little proof that cooperation is the result said method arrives at.
And think about it, how could a mathematician actually advocate cooperation in pure, zero knowledge vanilla PD? That just doesn’t make any sense as a model of an intelligent human being’s opinions.
Agreed. But here is what I think Hofstadter was saying: The assumption that is used can be weaker than the assumption that the two players have an identical method. Rather, it just needs to be that they are both “smart”. And this is almost as strong a result as the true zero knowledge scenario, because most agents will do their best to be smart.
Why is he saying that “smart” agents will cooperate? Because they know that the other agent is the same as them in that respect. (In being smart, and also in knowing what being smart means.)
Now, there are some obvious holes in this, but it does hold a certain grain of truth, and is a fairly powerful result in any case. (TDT is, in a sense, a generalization of exactly this idea.)
Have you seen this explored in mathematical language? Cause it’s all so weird that there’s no way I can agree with Hofstadter to that extent. As yet, I don’t know really know what “smart” means.
Yeah, I agree, it is weird. And I think that Hofstadter is wrong: With such a vague definition of being “smart”, his conjecture fails to hold. (This is what you were saying: It’s rather vague and undefined.)
That said, TDT is an attempt to put a similar idea on firmer ground. In that sense, the TDT paper is the exploration in mathematical language of this idea that you are asking for. It isn’t Hofstadterian superrationality, but it is inspired by it, and TDT puts these amorphous concepts that Hofstadter never bothered solidifying into a concrete form.
What ygert said. So-called superrationality has a grain of truth but there are obvious holes in it (at least as originally described by Hofstadter).
And think about it, how could a mathematician actually advocate cooperation in pure, zero knowledge vanilla PD? That just doesn’t make any sense as a model of an intelligent human being’s opinions.
Sadly, even intelligent human beings have been known to believe incorrect things for bad reasons.
More to the point, I’m not accusing Hofstadter of advocating cooperation in a zero knowledge PD. I’m accusing him of advocating cooperation in a one-shot PD where both players are known to be rational. In this scenario, too, both players defect.
Hofstadter can deny this only by playing games(!) with the word “rational”. He first defines it to mean that a rational player gets the same answer as another rational player, so he can eliminate (C, D) & (D, C), and then and only then does he decide that it also means players don’t choose a dominated strategy, which eliminates (D, D). But this is silly; the avoids-dominated-strategies definition renders the gets-the-same-answer-as-another-rational-player definition superfluous (in this specific case). Suppose it had never occurred to us to use the former definition of “rational”, and we simply applied the latter definition. We’d immediately notice that neither player cooperates, because cooperation is strictly dominated according to the true PD payoff matrix, and we’d immediately eliminate all outcomes but (D, D). Hofstadter dodges this conclusion by using a gimmick to avoid consistently applying the requirement that rational players don’t leave free utility on the table.
As I understand it, Hofstadter’s advocacy of cooperation was limited to games with some sense of source-code sharing. Basically, both agents were able to assume their co-players had an identical method of deciding on the optimal move, and that that method was optimal. That assumption allows a rather bizarre little proof that cooperation is the result said method arrives at.
And think about it, how could a mathematician actually advocate cooperation in pure, zero knowledge vanilla PD? That just doesn’t make any sense as a model of an intelligent human being’s opinions.
Agreed. But here is what I think Hofstadter was saying: The assumption that is used can be weaker than the assumption that the two players have an identical method. Rather, it just needs to be that they are both “smart”. And this is almost as strong a result as the true zero knowledge scenario, because most agents will do their best to be smart.
Why is he saying that “smart” agents will cooperate? Because they know that the other agent is the same as them in that respect. (In being smart, and also in knowing what being smart means.)
Now, there are some obvious holes in this, but it does hold a certain grain of truth, and is a fairly powerful result in any case. (TDT is, in a sense, a generalization of exactly this idea.)
Have you seen this explored in mathematical language? Cause it’s all so weird that there’s no way I can agree with Hofstadter to that extent. As yet, I don’t know really know what “smart” means.
Yeah, I agree, it is weird. And I think that Hofstadter is wrong: With such a vague definition of being “smart”, his conjecture fails to hold. (This is what you were saying: It’s rather vague and undefined.)
That said, TDT is an attempt to put a similar idea on firmer ground. In that sense, the TDT paper is the exploration in mathematical language of this idea that you are asking for. It isn’t Hofstadterian superrationality, but it is inspired by it, and TDT puts these amorphous concepts that Hofstadter never bothered solidifying into a concrete form.
What ygert said. So-called superrationality has a grain of truth but there are obvious holes in it (at least as originally described by Hofstadter).
Sadly, even intelligent human beings have been known to believe incorrect things for bad reasons.
More to the point, I’m not accusing Hofstadter of advocating cooperation in a zero knowledge PD. I’m accusing him of advocating cooperation in a one-shot PD where both players are known to be rational. In this scenario, too, both players defect.
Hofstadter can deny this only by playing games(!) with the word “rational”. He first defines it to mean that a rational player gets the same answer as another rational player, so he can eliminate (C, D) & (D, C), and then and only then does he decide that it also means players don’t choose a dominated strategy, which eliminates (D, D). But this is silly; the avoids-dominated-strategies definition renders the gets-the-same-answer-as-another-rational-player definition superfluous (in this specific case). Suppose it had never occurred to us to use the former definition of “rational”, and we simply applied the latter definition. We’d immediately notice that neither player cooperates, because cooperation is strictly dominated according to the true PD payoff matrix, and we’d immediately eliminate all outcomes but (D, D). Hofstadter dodges this conclusion by using a gimmick to avoid consistently applying the requirement that rational players don’t leave free utility on the table.