Dynamically consistent voting rules

This paper studies preference aggregation in a dynamic choice context. Voters face menus of options in stages and the source of dynamics is that menus possibly get smaller across each stage. We call the family of stage voting rules “dynamic voting rules” and provide an axiomatic characterization, on the domain of single-peaked preferences, of dynamic voting rules that are strategy-proof and satisfy a second property, inspired from choice theory, which we call dynamic consistency.