On the Power-Law Tails of Vote Distributions in Proportional Elections

TL;DR

This paper investigates the distribution of preferences in proportional elections, revealing a transition from lognormal to power-law tails in vote distributions for large candidate lists, using a quenched approximation of a known model.

Contribution

It demonstrates the emergence of power-law tails in vote distributions under certain conditions, extending the understanding of electoral preference patterns.

Findings

Lognormal distribution holds for small lists.

Power-law tails emerge with large candidate lists.

Analysis applies to the original model with modifications.

Abstract

In proportional elections with open lists the excess of preferences received by candidates with respect to the list average is known to follow a universal lognormal distribution. We show that lognormality is broken provided preferences are conditioned to lists with many candidates. In this limit power-law tails emerge. We study the large-list limit in the framework of a quenched approximation of the word-of-mouth model introduced by Fortunato and Castellano (Phys.Rev.Lett.99(13):138701,2007), where the activism of the agents is mitigated and the noise of the agent-agent interactions is averaged out. Then we argue that our analysis applies mutatis mutandis to the original model as well.