Computing Voting Rules with Improvement Feedback

TL;DR

This paper investigates how different types of feedback, specifically improvement feedback, affect the ability to compute voting rules, revealing both possibilities and limitations in preference aggregation.

Contribution

It characterizes which positional scoring rules are computable with improvement feedback and highlights differences from pairwise feedback in learning and impossibility results.

Findings

Plurality is learnable with improvement feedback.

Many other positional scoring rules face strong impossibility results.

Improvement feedback cannot compute any Condorcet-consistent rule.

Abstract

Aggregating preferences under incomplete or constrained feedback is a fundamental problem in social choice and related domains. While prior work has established strong impossibility results for pairwise comparisons, this paper extends the inquiry to improvement feedback, where voters express incremental adjustments rather than complete preferences. We provide a complete characterization of the positional scoring rules that can be computed given improvement feedback. Interestingly, while plurality is learnable under improvement feedback--unlike with pairwise feedback--strong impossibility results persist for many other positional scoring rules. Furthermore, we show that improvement feedback, unlike pairwise feedback, does not suffice for the computation of any Condorcet-consistent rule. We complement our theoretical findings with experimental results, providing further insights into the practical implications of improvement feedback for preference aggregation.