Statistical mechanics of voting
Abstract
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 cohesion/diversity among agents in terms of random matrix models---ensembles of statistical mechanics models---and compute quantitative answers in some representative cases.
Cite
@article{arxiv.cond-mat/9806359,
title = {Statistical mechanics of voting},
author = {David A. Meyer and Thad A. Brown},
journal= {arXiv preprint arXiv:cond-mat/9806359},
year = {2009}
}
Comments
9 pages, plain TeX, 2 PostScript figures included with epsf.tex (ignore the under/overfull \vbox error messages)