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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 a#rma
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 su#ces for them to ex
change O 1/# 2
bits. This bound is completely indepen
dent of the number of bits n of relevant knowledge that the
agents have. We also extend the bound to three or more
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