  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.
