Reaching consensus: solidarity and strategic properties in binary social choice

We study solidarity and strategic properties in binary social choice. We consider both the standard setting with strict preferences and the “full” preference domain which allows for indifference. Two solidarity properties drive our investigation: “Welfare dominance under preference replacement”, which says that when the preferences of one agent change, the other agents all weakly gain or all weakly lose; and “population monotonicity”, which requires the same conclusion when one agent leaves. We identify the families of rules satisfying these properties on each preference domain. Additionally requiring efficiency characterizes the “consensus” rules in each case. We also relate welfare dominance to other properties. Two results highlight the role of indifference: Welfare dominance implies “anonymity” when preferences are strict, but not otherwise; “group strategy-proofness” implies welfare dominance when indifference is allowed, but not otherwise. Finally, we introduce a “duality” operator which structures the space of rules and extends our results to a model in which rules may select neither alternative. Only in this case are our solidarity properties consistent with “neutrality”.