There is no "infinity" to be considered here.
We are given a single equation
P = (2/3)P
with the unique solution P=0.
P = (2/3)P
P-(2/3)P = 0
P(1-2/3) = 0
P(1/3) = 0
P=0
QED
As a general rule, you shouldn't even mention infinity except in very select circumstances. Especially not when the solution is so simple!
Of course 0 would be the 'winning' strategy if you dismissed enough non-zero answers. But then you're just cooking the books in a desperate attempt to make the canonical game theory solution seem viable, or interesting.
In other words, you'd be denying reality in order to convince people that the theoretical model has some relationship with the empirical reality. You'd be an economist.
The purpose of this game, admittedly, is to test just how complacent / obedient the Overcoming Bias / Less Wrong community has become.
Think about your assumptions:
First you've got "common rationality". But that's really a smokescreen to hide the fact that you're using a utility function and simply, dearly, hoping that everybody else is using the same one as you!
Your second assumption is that "you gain nothing by defecting alone".
There's no meaningful sense in which you're "winning" if everybody guesses zero and you do too. The...
I was an avid visitor of Overcoming Bias, but yes I am new to Less Wrong. I had assumed that the general feel of this place would be similar to Overcoming Bias - much of which was very dogmatic, although there were a few notable voices of dissent (several of whom were censored and even banned).
Obviously. But there wouldn't be a point to my lecturing them, now would there? No, conchis made t... (read more)