Understanding Distance Measures Among Elections

TL;DR

This paper analyzes six different distance measures among elections, evaluating their computational complexity and expressiveness to provide a more solid mathematical foundation for empirical election data analysis.

Contribution

It introduces and compares six election distance measures, highlighting the map of elections distance as the most balanced in complexity and expressiveness.

Findings

The map of elections distance offers a good balance between complexity and expressiveness.

Among six distances, the map of elections distance is most suitable for empirical analysis.

The swap distance, while precise, is challenging to compute.

Abstract

Motivated by putting empirical work based on (synthetic) election data on a more solid mathematical basis, we analyze six distances among elections, including, e.g., the challenging-to-compute but very precise swap distance and the distance used to form the so-called map of elections. Among the six, the latter seems to strike the best balance between its computational complexity and expressiveness.