  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.
