Block size dependence of coarse graining in discrete opinion dynamics model: Application to the US presidential elections

TL;DR

This paper models the US electoral college as a coarse graining process in opinion dynamics, analyzing how system size and state number influence minority wins, and compares results with real election data.

Contribution

It introduces a two-step coarse graining approach to study opinion dynamics and electoral outcomes, revealing scaling behaviors relevant to US elections.

Findings

Probability of minority win aligns with real data estimates.

System size and number of states significantly affect election outcomes.

Two-step coarse graining provides insights into opinion spread and information aggregation.

Abstract

The electoral college of voting system for the US presidential election is analogous to a coarse graining procedure commonly used to study phase transitions in physical systems. In a recent paper, opinion dynamics models manifesting a phase transition, were shown to be able to explain the cases when a candidate winning more number of popular votes could still lose the general election on the basis of the electoral college system. We explore the dependence of such possibilities on various factors like the number of states and total population (i.e., system sizes) and get an interesting scaling behavior. In comparison with the real data, it is shown that the probability of the minority win, calculated within the model assumptions, is indeed near the highest possible value. In addition, we also implement a two step coarse graining procedure, relevant for both opinion dynamics and information theory.