How a minority can win: Undemocratic outcomes in a simple model of voter turnout

TL;DR

This paper models how voter turnout decisions based on local perceptions can lead to minority candidates winning elections, highlighting conditions that favor undemocratic outcomes.

Contribution

It introduces a simple network-based model of voter abstention influenced by local perceptions, revealing how minority wins can occur under certain conditions.

Findings

Certain network structures favor minority victories.

Voter complacency and dejectedness influence election outcomes.

Undemocratic results are more likely when local preferences misrepresent the electorate.

Abstract

The outcome of an election depends not only on which candidate is more popular, but also on how many of their voters actually turn out to vote. Here we consider a simple model in which voters abstain from voting if they think their vote would not matter. Specifically, they do not vote if they feel sure their preferred candidate will win anyway (a condition we call complacency), or if they feel sure their candidate will lose anyway (a condition we call dejectedness). The voters reach these decisions based on a myopic assessment of their local network, which they take as a proxy for the entire electorate: voters know which candidate their neighbors prefer and they assume -- perhaps incorrectly -- that those neighbors will turn out to vote, so they themselves cast a vote if and only if it would produce a tie or a win for their preferred candidate in their local neighborhood. We explore various network structures and distributions of voter preferences and find that certain structures and parameter regimes favor undemocratic outcomes where a minority faction wins, especially when the locally preferred candidate is not representative of the electorate as a whole.