Abstract
The theory of nonbinary social choice deals with cases where choice over two-element sets may not be possible. In this paper we extend the two main approaches to this problem, initiated respectively by Fishburn (1974) and by Grether and Plott (1982). The difference between the two approaches lies essentially in the structure of the family of feasible sets of alternatives. Nonbinary versions of Arrow's General Possibility Theorem and of Gibbard's oligarchy result are established using weak feasibility conditions. The method of proof relies on deeper (fixed agenda) impossibility theorems.
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