Social choice theory without Pareto: The pivotal voter approach

This paper extends the pivotal voter approach pioneered by Barberá [Barberá, S., 1980. Pivotal voters: A new proof of Arrow’s Theorem. Economics Letters 6, 13–6; Barberá, S., 1983. Strategy-proofness and pivotal voters: A direct proof of the Gibbard-Satterthwaite Theorem. International Economic Review 24, 413–7] to all social welfare functions satisfying independence of irrelevant alternatives. Arrow’s Theorem, Wilson’s Theorem, and the Muller–Satterthwaite Theorem are all immediate corollaries of the main result. It is further shown that a vanishingly small fraction of pairs of alternatives can be affected in the group preference ordering by multiple individuals, which generalizes each of the above theorems.