[extropy-chat] Superrationality

[Lee Corbin]

Hal writes

> Lee Corbin writes:
> > I have one question. Suppose that today Hofstadter suddenly a time machine,
> > and decides to visit the year 1983. He then finds himself in a sealed room,
> > with his 1983 version in an adjacent sealed room. All each know is that
> > they're in a one-shot PD with each other, and each knows the year from which
> > the other comes.
> >
> > Our Doug, (Doug 2006) consults the payoff matrix.  It says
> >
> >      (5,5) | (0,10)
> >      (10,0)| (1,1)
> >
> > It is clear what the 1983 Doug will do. What move should our
> > Doug play in order to maximize his payoff?
> 
> It's funny that you should word the question like that, since there is
> a fundamental ambiguity in the word "his" in this situation.

Well, of course!  I was hoping that the topic of personal identity
wouldn't distract. 

There is a temptation to see the NIPD outside the context of game theory.
But NIPD arose and fundamentally is simply a question in game theory. You
were to translate the above into "what should an instance do", i.e.,
what is the best that a player can attain in a particular 2-person game?

To be clearer to all, let me say a few words about the fundamentals.
Two person games can usually be analyzed by means of a payoff table.
The object is for a player playing rows, say, to select as his "strategy"
whatever row affords him the greatest payoff as made explicit in the
ith row and jth column of the matrix. The most difficult case arises
when a "mixed strategy" is called for. Considerations *outside* the
payoff table---such as that one may be playing against one's husband
who is known to have a terrible temper---are supposed to be completely
irrelevant.

But in extremely simple situations such as the above matrix WHEN YOU
HAPPEN TO KNOW WHAT COLUMN WILL BE SELECTED BY THE OTHER PLAYER, it
amounts simply to finding a row which "dominates" all your other rows.
This is the object of the game.

> I can't speak for Hofstadter, of course, but ignoring these complications
> I strongly suspect he would cooperate in this situation.  We know he
> found the reasoning compelling enough in 1983 to make quite an issue
> of it.  If he still feels that way, he will play the same.  If not,
> I imagine that out of solidarity and sympathy for his earlier self...

Oh yes, I'm sure that he'd cooperate.  But I didn't ask that.  I asked
what he *should* do as a player in the game. 

The NIPD is notoriously challenging.  But, as I contend, only in the
case where a player does *not* know which column the adversary will
select. The game becomes trivial in the case that a player happens
to know what his opponent will do.

It is obvious that if a player happens to know which column his
adversary is going to select, then his best move is to defect.
I can't make it any simpler than that.

Therefore, you have yet to find an argument that suggests that in
the case when a player's opponent's move is known to a player, 
the player in question should Cooperate.

I think that you should admit that Doug2006---if he is to honestly
participate as a player in the NIPD---should Defect against Doug1983.
Yes, he may indeed have side incentives (for instance, people's well
known reluctance to admit that they have been wrong), but they're
irrelevant to the role of player within the game.

It's really easy to see just how the discussion between Doug2006
and Doug1983 would go after an unbiased and open-minded Doug2006 
Defects, and so of course wins against Doug1983.

Doug 1983: "I can't believe that you Defected. WHY!?"

Doug 2006: "I was reading the Extropian list, and it became clear
           that as I *KNEW* what you were going to do, honesty
           compelled me as a player in the game, to Defect! Just
           look at the payoff table: it was clearly better for
           the player whose role I was assuming---as well you know
           ---to Defect. Honestly, I could not do otherwise."

But alas yes, people are seldom so honest or so objective that they
can put ideological considerations or pride behind them.

Lee