ODEs and Mandatory Voting

TL;DR

This paper uses differential equations to model the strategic adjustments of political candidates in response to voter abstention, exploring the impact of mandatory voting on electoral dynamics through a web-based simulation.

Contribution

It introduces a novel application of ODEs to political science, specifically modeling candidate behavior under different voting scenarios, including abstention effects.

Findings

Abstentions significantly influence candidate positioning dynamics.

Discontinuous jumps in optimal positions can occur due to abstention effects.

The model provides a new educational tool for undergraduate students.

Abstract

This paper presents mathematics relevant to the question whether voting should be mandatory. Assuming a static distribution of voters' political beliefs, we model how politicians might adjust their positions to raise their share of the vote. Various scenarios can be explored using our web-based app (see text for the link). Abstentions are found to have great impact on the dynamics of candidates, and in particular to introduce the possibility of discontinuous jumps in optimal candidate positions. This is a paper intended for undergraduate students. It is an unusual application of ODEs. We hope that it might help engage some students who may find it harder to connect with the more customary applications from the natural sciences.