Abstract
Given a finite state space and common priors, common knowledge of the identity of an agent with the minimal (or maximal) expectation of a random variable implies ‘consensus’, i.e., common knowledge of common expectations. This ‘extremist’ statistic induces consensus when repeatedly announced, and yet, with n agents, requires at most log2 n bits to broadcast.
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Hanson, R.D. Consensus By Identifying Extremists. Theory and Decision 44, 293–301 (1998). https://doi.org/10.1023/A:1004918905650
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DOI: https://doi.org/10.1023/A:1004918905650