You will pick 100. I know that, so I'll pick 66. You know that I know that, so you'll pick 44 instead. But I know that you know that I know that, so I'll pick 29 instead. But you know that I know that you know that I know that, so you'll pick 20 instead. But I know-
This continues to infinity until both of our guesses approach 0.
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!
That's an interesting variation. Next time we might try this with the stipulation that the five highest answers (if there are at least five submissions greater than 0; otherwise all the positive answers) will get tossed out.
I still doubt that 0 would win that one, though.
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.
You do see that zero is the only Nash equilibrium, right? If everyone plays zero, you gain nothing by defecting alone, because 1/N is still better than nothing (and your guess will always be greater than 2/3 of the average).
So you're arguing that it's not rational, under the assumption of common rationality, to play the unique Nash equilibrium?
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 only purpose of it, the only reward you receive for guessing 0 and 'winning', is the satisfaction that you dutifully followed instructions and submitted the 'correct' answer according to game theory and the arguments put forth by upper echelons of the Less Wrong community.
In fact, there is much to gain by guessing a non-zero number. First of all, it costs nothing to play. Right away, all of your game theory and rationalization is tossed right out the window. It is of no cost to submit an answer of 100, or even to submit several answers of 100. Your theory of games can't account for this - if people get multiple guesses, submitted from different accounts, you'll be pretty silly with your submission of 0 as an answer.
"But that would be cheating." Well, no. See, the game is a cheat. It's to test "Aumann's agreement theorem" among this community here. It's to test whether or not you will follow instructions and run with the herd, buying into garbage about a 'common rationality' and 'unique solutions', 'utility functions' and such.
You see, for me at least, there's great value in defecting. You of course will try to scare people into believing they're defecting alone, but here you're presupposing the results of the experiment - that everybody else is dutifully following instructions. So anyway, I would be greatly pleased if the result turned out to be a non-zero number. It would restore my faith in this community, actually. And to that end, I would submit a high number...
If I were to play.
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I think that you are profoundly mistaken about the attitudes and dispositions of the vast majority here. You appear to be new, so that's understandable. As you look around, though, you'll find a wide array of opinions on the limits of causal decision theory, the aptness of utility functions for describing or prescribing human action, and other topics you assume must be dogma for a community calling itself 'rationalist'. You might even experience the uncomfortable realization that other people already agree with some of the brilliant revelations about rationality that you've derived.
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 the canonical argument and I responded. And if you weren't so uncomfortable with my dissent you might have left a real response, instead of this patronizing and sarcastic analysis.