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Probabilistic voting models with varying speeds of Correlation decay

Part of: Limit theorems Equilibrium statistical mechanics Mathematical economics

Published online by Cambridge University Press:  17 February 2025

Gabor Toth Open the ORCID record for Gabor Toth [Opens in a new window]
Gabor Toth*
Affiliation:
IIMAS-UNAM
*
*Postal address: Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Circuito Escolar S/N, Ciudad Universitaria, Alcaldía Coyoacán, C.P. 04510, Mexico City. Email address: [email protected]
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Abstract

We model voting behaviour in the multi-group setting of a two-tier voting system using sequences of de Finetti measures. Our model is defined by using the de Finetti representation of a probability measure (i.e. as a mixture of conditionally independent probability measures) describing voting behaviour. The de Finetti measure describes the interaction between voters and possible outside influences on them. We assume that for each population size there is a (potentially) different de Finetti measure, and as the population grows, the sequence of de Finetti measures converges weakly to the Dirac measure at the origin, representing a tendency toward weakening social cohesion as the population grows large. The resulting model covers a wide variety of behaviours, ranging from independent voting in the limit under fast convergence, a critical convergence speed with its own pattern of behaviour, to a subcritical convergence speed which yields a model in line with empirical evidence of real-world voting data, contrary to previous probabilistic models used in the study of voting. These models can be used, e.g., to study the problem of optimal voting weights in two-tier voting systems.

Keywords

Spin modelsde Finetti representationlimit theoremsphase transitions

MSC classification

Primary: 60F05: Central limit and other weak theorems 91B12: Voting theory
Secondary: 82B20: Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
Type
Original Article
Information
Advances in Applied Probability , Volume 57 , Issue 1 , March 2025 , pp. 35 - 64
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust.

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