David A. Meyer and Thad A. Brown,
``Statistical mechanics of voting'',
Physical Review Letters 81 (1998) 1718-1721,
cond-mat/9806359.

Decision procedures aggregating the preferences of multiple agents can produce cycles and hence outcomes which have been described heuristically as `chaotic'. We make this description precise by constructing an explicit dynamical system from the agents' preferences and a voting rule. The dynamics form a one dimensional statistical mechanics model; this suggests the use of the topological entropy to quantify the complexity of the system. We formulate natural political/social questions about the expected complexity of a voting rule and degree of diversity among agents in terms of random matrix models--ensembles of statistical mechanics models--and compute quantitative answers in some representative cases.

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