Expected Frequency Matrices of Elections: Computation, Geometry, and Preference Learning

TL;DR

This paper introduces a framework for analyzing election distributions through frequency matrices, providing explicit formulas and algorithms, and applying these to learn real-world preferences.

Contribution

It offers explicit formulas and algorithms for computing frequency matrices of election distributions and develops a unified framework for preference learning.

Findings

Explicit formulas and algorithms for frequency matrices

Robustness analysis of the distribution skeleton map

A unified framework for preference learning

Abstract

We use the ``map of elections'' approach of Szufa et al. (AAMAS-2020) to analyze several well-known vote distributions. For each of them, we give an explicit formula or an efficient algorithm for computing its frequency matrix, which captures the probability that a given candidate appears in a given position in a sampled vote. We use these matrices to draw the ``skeleton map'' of distributions, evaluate its robustness, and analyze its properties. Finally, we develop a general and unified framework for learning the distribution of real-world preferences using the frequency matrices of established vote distributions.