Dynamically consistent voting rules

Many preference aggregation problems are not, by nature, one-shot. In these settings, voter preferences need to be repeatedly aggregated as a function of the underlying pool of options that are being voted over. For example, imagine that a firm votes an offer to a candidate. If the offer is declined, then the pool of options shrinks, votes are aggregated once more, and a subsequent offer is made. The primitive of the analysis for a voting problem such as this is a family of voting rules parameterized by the collection of option sets, e.g. pools of candidates in the example. This paper studies sequential voting on the domain of single-peaked preferences. We provide an axiomatic characterization of sequential voting rules which satisfy strategy-proofness and a property we coarsely refer to as “dynamic-consistency”. Informally, this means that the rule is internally consistent across voting rounds. We provide two candidate definitions of dynamic consistency that aim to capture the idea of internal consistency and alternately characterize strategy-proof families of voting rules which satisfy these criteria. As an intermediate step we revisit the static problem and provide a new characterization (distinct from the generalized median) of static strategy-proof voting rules.