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The aim of this paper is to study the notion of Generalized Binary Constitution (GBC), a distribution of power due to Ferejohn and Fishburn (1979), which generalizes some classical notions such as simple games and voting games. The GBC helps us to define a preference aggregation rule (PAR) and we characterize GBC's whose collective preferences are either complete, asymmetric, transitive or acyclic when individual preferences are weak orders or linear orders. Since the procedure of aggregation of preferences which satisfies IIA is equivalent to the preference aggregation rule of a GBC, we give relations between our results and some Arrovian results. We also characterize core-stable GBC's and therefore deduce classical results and in particular Nakamura's theorem for simple games.

Preference aggregation, collective choice and generalized binary constitutions