[extropy-chat] Superrationality

[Lee Corbin]

Hal writes

> Well, I worked out that the superrational thing to do was, if there were
> N participants, to play a 1 with probability 1/N, else to play a 0 (i.e.
> not enter).  I'm not 100% sure this is actually correct, now, but it is
> at least a plausible superrational strategy, perhaps a Schelling point.

I also participated in the Luring Lottery in 1983. However instead 
of 1/N, I calculated that the optimal strategy is one over the square
root of N. (The total prize will be divided among the votes received, 
and, supposing that there are 1,000,000 entrants, if one thousand of
us send in approximately one vote, then he gets the mil, and my
expectation is $1,000, which I believe to be maximal.)

Like Hal, I used a table of random numbers (and didn't "win"). But I
went ahead anyway and sent in a postcard: on your entry you were
permitted to state the number of votes you were entering, and so
I wrote "I am submitting ____ votes.", and then filled in, in red
pen, the numeral 0.

Hofstadter mentioned in his article that six people had for some
mysterious reason sent in "0 votes". I later wrote and ask him who
they were (because to me, we were the ones who for sure understood
the whole thing). Unfortunately he had not kept the information.

As to superrationality, several years later I defected away from
the superrational camp. My reasoning: if you know the other person
is going to cooperate, then according to the table, you must defect.
Likewise, if you know that the person is going to defect, then you
must defect. (Failure to do so simply means that you aren't reading the
payoff table, or don't know what it means.) Only in the case that you
don't know what the person will do---and, most importantly, there is
reason to believe that his behavior is correlated with yours---can
you logically cooperate.

Would you cooperate with a gorilla?  How about with a known ruthless
gangster? The only person that I'd cooperate with---strict mathematical
analysis here only---is a mirror image of myself, my mirror image or my
duplicate. Only in those cases, almost surely, is there any chance that
his action is positively correlated with mine.

> I actually think it would be interesting to see if Hofstadter still
> believes in superrationality.  I guess I could have asked him when I had
> the luck to meet him Saturday, but I didn't think of it.  Probably it
> would have been hard for me to ask without seeming rude, since I would
> really be asking him whether he still holds to an idea which has been
> overwhelmingly rejected by almost everyone who has heard of it for
> over twenty years.

The question you should have asked, rudeness aside, is, if he had a time-
machine and could go back to 1983, would he cooperate or defect against
the 1983 Doug?  Case closed.

Lee

P.S. Fooey: it needs stating to some people that real-life situations
are *far* removed from mathematical theory, and that in fact I'd
cooperate with any human being I thought had a heart, and I advise
others to do likewise, because the other person's good is a factor too
(not shown, of course, in the payoff table).