Regret-free truth-telling voting rules

TL;DR

This paper investigates voting rules that incentivize agents to truthfully report preferences without regret, analyzing various rule classes and establishing conditions for regret-free truth-telling.

Contribution

It characterizes when different voting rules, including maxmin, scoring, and Condorcet methods, are regret-free truth-telling, providing necessary and sufficient conditions.

Findings

Strategy-proofness is equivalent to regret-free truth-telling among tops-only rules.

Certain maxmin and scoring rules can be regret-free under specific conditions.

Condorcet consistent rules generally are not regret-free truth-telling.

Abstract

We study the ability of different classes of voting rules to induce agents to report their preferences truthfully, if agents want to avoid regret. First, we show that regret-free truth-telling is equivalent to strategy-proofness among tops-only rules. Then, we focus on three important families of (non-tops-only) voting methods: maxmin, scoring, and Condorcet consistent ones. We prove positive and negative results for both neutral and anonymous versions of maxmin and scoring rules. In several instances we provide necessary and sufficient conditions. We also show that Condorcet consistent rules that satisfy a mild monotonicity requirement are not regret-free truth-telling. Successive elimination rules fail to be regret-free truth-telling despite not satisfying the monotonicity condition. Lastly, we provide two characterizations for the case of three alternatives and two agents.