Arrow's Theorem with a fixed feasible alternative


Arrow's Theorem, in its social choice function formulation, assumes that all nonempty finite subsets of the universal set of alternatives is potentially a feasible set. We demonstrate that the axioms in Arrow's Theorem, with weak Pareto strengthened to strong Pareto, are consistent if it is assumed that there is a prespecified alternative which is in every feasible set. We further show that if the collection of feasible sets consists of all subsets of alternatives containing a prespecified list of alternatives and if there are at least three additional alternatives not on this list, replacing nondictatorship by anonymity results in an impossibility theorem



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Allan Gibbard
University of Michigan, Ann Arbor

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A Note on Introducing a 'Zero-Line' of Welfare as an Escape-Route from Arrow's Theorem.Christian List - 2001 - Pacific Economic Review (Special Section in Honour of Amartya Sen) 6 (2):223-238.

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