Statistical mechanics of voting
Authors:
Preprint
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.Keywords
All Related Versions
- Version 1, 1998-06-30, ArXiv
- Published version: Physical Review Letters, 81 (8), 1718.
This publication has 16 references indexed in Scilit:
- Intransitivities in multidimensional spatial voting: period three implies chaosSocial Choice and Welfare, 1994
- Unifying Impossibility Theorems: A Topological ApproachAdvances in Applied Mathematics, 1993
- Simulation of global and local intransitivities in a simple voting game under majority ruleSystems Research and Behavioral Science, 1991
- The ultimate of chaos resulting from weighted voting systemsAdvances in Applied Mathematics, 1984
- Cyclic sets in multidimensional voting modelsJournal of Economic Theory, 1979
- Probabilities of election outcomes for large electoratesJournal of Economic Theory, 1978
- Intransitivities in multidimensional voting models and some implications for agenda controlJournal of Economic Theory, 1976
- A proof of May's theorem p(m, 4) = 2p(m, 3)Systems Research and Behavioral Science, 1973
- Some mathematical remarks on the paradox of votingSystems Research and Behavioral Science, 1971
- On the density of Eigenvalues of a random matrixNuclear Physics, 1960