Abductive and Contrastive Explanations for Scoring Rules in Voting

TL;DR

This paper applies formal explainability techniques, specifically abductive and contrastive explanations, to voting rules viewed as classifiers, revealing insights into election outcomes and their relation to classical social choice problems.

Contribution

It introduces a novel application of abductive and contrastive explanations to voting rules, with algorithms for scoring rules and analysis of explanation sizes for the Borda rule.

Findings

Algorithms for abductive and contrastive explanations are developed.

Lower bounds on explanation sizes for the Borda rule are established.

Simulations reveal correlations between profile properties and explanation sizes.

Abstract

We view voting rules as classifiers that assign a winner (a class) to a profile of voters' preferences (an instance). We propose to apply techniques from formal explainability, most notably abductive and contrastive explanations, to identify minimal subsets of a preference profile that either imply the current winner or explain why a different candidate was not elected. Formal explanations turn out to have strong connections with classical problems studied in computational social choice such as bribery, possible and necessary winner identification, and preference learning. We design algorithms for computing abductive and contrastive explanations for scoring rules. For the Borda rule, we find a lower bound on the size of the smallest abductive explanations, and we conduct simulations to identify correlations between properties of preference profiles and the size of their smallest abductive explanations.