2 ms·
> two Bayesian agents with a common prior can ensure that they agree to within ±ε about the value of a [0,1]-valued random variable, with probability at least 1
by throwawayjava 8y ago
> two Bayesian agents with a common prior can ensure that they agree to within ±ε about the value of a [0,1]-valued random variable, with probability at least 1-δ over their shared prior, by exchanging only O(1/(δε2)) bits of information—completely independent of how much knowledge the agents have. My conclusion was that, if Aumann’s Nobel-prizewinning theorem fails to demonstrate the irrationality of real-life disagreements, then it’s not for reasons of computational or communication efficiency
Under the gracious assumption that your agents are implementing a reasonable protocol for information exchange :)
- AstralStorm 8y agoYou have to extend the Bayesian thought experiment to include agents not behaving rationally and cases of bounded information. And then go to multivariate models. Combined, these give robust decision making methods. However, none of the above concerns actual hypothesis making which is biased from the get go. Bayesian statistics cannot answer the question of how to build hypotheses, only maybe how to value them. Sometimes. If we solve the question of how to make hypotheses reliably, then we might have some angle of attack on the strong AI problem. Related problem is deciding ways to falsify statements - inverse Bayesian reasoning. That is, given posterior probability, figure out potential priors.