Voting Theory and Machine Learning

Abstract

This thesis proposes a novel Hierarchical Transformer (HT) architecture for neural voting rule learning. Based on a differentiable axiomatic loss function, the proposed model integrates a Voter Preference Encoder, a Collective Decision Encoder, and two pluggable modules for Pairwise Comparison and Multi-Round, to simulate complex collective decision-making processes. Experimental results indicate that after training the HT model to learn the classical voting rules - Plurality, Borda, and Copeland - it achieves high prediction accuracy when predicting their outcomes and approximates their axiomatic satisfaction, particularly under the Anonymity axiom. More importantly, the model can discover a new voting rule whose axiomatic satisfaction is significantly different from that of classical rules and exhibits particularly high Independence satisfaction. To enhance interpretability, this thesis introduces surrogate decision trees to analyze the discovered rule. In the single-winner setting, the surrogate decision tree reveals a transparent and human-understandable decision pattern: the new voting rule mainly focuses on the positional features of the front-positioned candidates, which directly corresponds to the high Independence satisfaction observed in the experiment. In addition, the absence of label ambiguity in this setting reduces noise, allowing the decision trees to provide more consistent and reliable interpretations. In contrast, in the multi-winner setting, greater label ambiguity introduces noise and limits interpretability. Although the structure of the new rule is complex, the decision tree still reveals some decision patterns. This work provides a classical voting rule learning and new rule discovery framework for computational social choice and AI alignment that combines human decision-structure simulation, axiom satisfaction, and interpretability.