Group Identification with (Incomplete) Preferences

We consider the problem of identifying members of a group based on individual opinions. Since agents do not have preferences in the model, properties of rules that concern preferences (e.g., strategy-proofness and efficiency) have not been studied in the literature. We fill this gap by working with a class of incomplete preferences derived directly from opinions. Our main result characterizes a new family of group identification rules, called voting-by-equitable-committees rules, using two well-known properties: strategy-proofness and equal treatment of equals. Our family contains as a special case the consent rules [Samet and Schmeidler, Journal of Economic Theory 110, (2003)], which are anonymous and embody various degrees of liberalism and democracy; and it also includes dictatorial and oligarchic rules that value agents' opinions differently. In the presence of strategy-proofness, efficiency turns out to be equivalent to non-degeneracy (i.e., any agent may potentially be included or excluded from the group). This implies that a rule satisfies strategy-proofness, efficiency, and equal treatment of equals if, and only if, it is a non-degenerate voting-by-equitable-committees rule