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Summary: The Complexity of Agreement
Scott Aaronson
ABSTRACT
A celebrated 1976 theorem of Aumann asserts that Bayesian
agents with common priors can never "agree to disagree":
if their opinions about any topic are common knowledge,
then those opinions must be equal. But two key questions
went unaddressed: first, can the agents reach agreement af-
ter a conversation of reasonable length? Second, can the
computations needed for that conversation be performed ef-
ficiently? This paper answers both questions in the affirma-
tive, thereby strengthening Aumann's original conclusion.
We 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 ex-
change O
1/2
¡
bits. This bound is completely indepen-
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