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Will a majority of respondents to this poll correctly guess the majority response to this poll?

@fool this is interesting because there are two Nash equilibria: everyone guesses 'yes' and everyone flips a coin, but only flipping the coin is stable.

@mithrandir @fool Guessing yes is stable; if everyone flips a coin, guessing “yes” gives you about ½ a chance of being right (the same as flipping a coin), but if, say, 10% say yes and 90% flip a coin, saying “yes” will almost certainly be the right option.

@wizzwizz4 @fool Oh this is true, I messed up the analysis. Everyone flipping a coin is actually only semistable in the "always choose no" direction, unstable in the "always choose yes" direction.

Interesting, then, that the game theoretical solution doesn't match the experimental outcome.
@wizzwizz4 @fool Also, I'm starting to think that 'no' is *always* the incorrect answer, because the poll is specifically asking if the majority of respondents will pick the *majority* answer, now the correct answer, which is tautologically true.

@mithrandir @fool These analyses assume everyone performs the same strategy. Whilst this is a better assumption for coöperative than competitive games, it's still not very good; better to use an acausal decision theory that can model agents modelling (and hence predicting) other agents, and the like.

@wizzwizz4 @fool no they don't. It just happens that all the nash equilibria have all players picking the same strategy(because the game is very simply and symmetrical). You could do the whole analysis for N players by solving a differential equation on an N-dimensional disc, but that's overkill and you'll get the same answer.

A nash equilibrium is a state where nobody could get better results by unilaterally changing their strategy an infinitesimal amount. Whether or not players try to predict each others actions, with perfect play they will almost certainly end up at a Nash equilibrium, because otherwise they would unilaterally change their strategy to get to a better outcome. If there's some reason why they wouldn't do that, probably the game is improperly posed.

@mithrandir @fool They're assuming that people are using the “think the problem through” strategy.

@wizzwizz4 @fool I don't know what you mean here, yes the entire field of game theory is interested in perfect play. Imperfect play is extremely hard to model mathematically because you would have to take into account the psychology of the players. I am not a psychologist, and game theory is hard enough without it.

@fool
I gave the wrong answer only for fun 😃
I let you guess what I answered!

@fool my logic was to take the easiest way: the first option displayed or quickest to click.

Hope to be right when the poll ends.

@Minionslayer If you didn't bring your own, you'll have to wait until the results are official.

@fool I've just expressed my ever-present optimism: NO.

@fool I appreciate that a 108 people joined me in voting no out of spite

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