Probabilistic Voting Models with Varying Speeds of Correlation Decay

TL;DR

This paper introduces a probabilistic voting model using de Finetti measures to capture varying social cohesion and correlation decay in multi-group voting systems, aligning with real-world data.

Contribution

It presents a novel framework modeling voting behavior with sequences of de Finetti measures that converge at different speeds, capturing diverse social dynamics.

Findings

Model covers independent, critical, and subcritical voting behaviors.

Aligns with empirical voting data.

Provides insights into optimal voting weights.

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 behaviour, 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.