Dynamically Consistent Voting Rules ∗ Madhav

This paper studies families of social choice functions (SCF’s), i.e. a collection of social choice functions {ΦA}, where the family is indexed by the option set of choices. These (sets of) functions arise in sequential choice problems where at each stage a set of options is given to a population of voters and a choice rule must aggregate stated preferences to generate an aggregate choice. In such settings, the aggregate decision-making process should reflect some form of consistency across choice problems. We characterize the class of (sequences of) SCF’s that satisfy two properties: (i) strategy-proofness and (ii) a notion of dynamic consistency inspired by Sen’s α from choice theory. When the aggregate choice is anonymous, this class turns out to be exactly the set of q-rules, i.e. rules in which the selected alternative is the most preferred alternative of the voter at the q-thN-tile of the population (whereN is the set of voters). This nests median voter schemes when no phantom voters are admitted in the decision rule. Without anonymity we obtain a class that we call “vote-by-committee” rules, the name due to some similarities with a class of SCF’s axiomatized in Barberá et al. (1991).