[ExI] Superrationality

[Lee Corbin]

Damien S. writes

>> Interestingly, the major commercial players in markets sometimes
>> behave in the "superrational" manner, working towards and welcome
>> regulation - ie: externally imposed restrictions. The great example of
> 
> I think that would just be rational, not Hofstadter's superrationality.

Yes.

> The latter is when you agree to the thing not in your immediate
> self-interest, with no actual enforcement of that, in the expectation
> that the other person will follow your thinking and do likewise.  It
> sounds nice but I've never really bought it.

I bought it hook, line, and sinker---having had many exactly
similar thoughts myself---back in 1983, when H published
an SA article on it. It took me at least three years to fully
understand and appreciate the flaw.

The flaw in Hofstadter's superrationality is very simple to state.
Unless the other player's behavior is highly correlated with yours
---for reasons that must be explained and must make sense---
then to Cooperate is to defy the very definition of the two-player
game.

> Maybe second-order rational, like committing to be irrational for game
> theoretic reasons, but it still makes direct sense without weird
> symmetry operations, which I suspect would only work well when the two
> parties share a history, e.g. I can trust the other to be superrational
> because we have common knowledge of having altered ourselves to be
> superrational, and can thus trust each other even without future
> interaction.  Or, more biologically, because we're clones.

Precisely. I would, for example, cooperate only with a "close duplicate",
since physically speaking what I do is what my close duplicate does to a
high degree of fidelity.

One should write Hofstadter and ask him a very simple question:
"Were you able to travel by time machine back to 1983, would
you play C or D against the DH of 1983?"  Unless he violates
the very meaning of the game, DH of 2008 *must* play D, 
because he knows for certain what DH of 2003 will play.
(In fact, *any* time that a player knows with high probability
what his opponent will play, he must play D.)

On the other extreme, the logician Raymond Smullyan is reputed
to have said (in "The Mind's I", I believe) that he would not 
cooperate even with his mirror image!    :-)

But I have stated the necessary and sufficient conditions above for
superrationality to obtain, and so lacking "close physical duplicates",
superrationality at the present time in human history is impossible.

Lee