The complexity of agreement

A celebrated 1976 theorem of Aumann asserts that honest, rational Bayesian agents with common priors will never "agree to disagree": if their opinions about any topic are common knowledge, then those opinions must be equal. Economists have written numerous papers examining the assumptions behind this theorem. But two key questions went unaddressed: first, can the agents reach agreement after a conversation of reasonable length? Second, can the computations needed for that conversation be performed efficiently? This paper answers both questions in the affirmative, thereby strengthening Aumann's original conclusion. We first show that, for two agents with a common prior to agree within about the expectation of a [0, 1] variable with high probability over their prior, it suffices for them to exchange order 1/2 bits. This bound is completely independent of the number of bits n of relevant knowledge that the agents have. We then extend the bound to three or more agents; and...

• Type: Conference
• Year: 2005
• Where: STOC
• Authors: Scott Aaronson
• Keywords: Algorithms, Celebrated 1976 Theorem, Limited Computational Resources, Order 1/2 Messages, STOC 2005