Statistical mechanics of voting

TL;DR

This paper models voting dynamics as a one-dimensional statistical mechanics system, using topological entropy to quantify complexity and analyzing how social factors influence voting outcomes through random matrix models.

Contribution

It introduces a novel dynamical system framework for voting preferences and applies statistical mechanics and entropy concepts to analyze voting complexity and social cohesion.

Findings

Topological entropy quantifies voting system complexity.

Random matrix models predict diversity and cohesion effects.

Explicit calculations in representative cases demonstrate the approach.

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.