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

Niclas Boehmer, Robert Bredereck, Edith Elkind, Piotr Faliszewski, Stanisław Szufa

Keywords: Mallows model, visualizing experimental results, vote distributions, single-peaked elections

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. We further develop a general and unified framework for learning the distribution of real-world preferences using the frequency matrices of established vote distributions.

TL;DR: We show how to compute frequency matrices of elections, which simplifies a "map of elections" and helps with preference learning.