The proximity condition
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Duddy, Conal; Piggins, Ashley (2011). The proximity condition. Social Choice and Welfare 39 (2), 353-369
We investigate the social choice implications of what we call &quot;the proximity condition&quot;. Loosely speaking, this condition says that whenever a profile moves &quot;closer&quot; to some individual's point of view, then the social choice cannot move &quot;further away&quot; from this individual's point of view. We apply this idea in two settings: merging functions and preference aggregation. The precise formulation of the proximity condition depends on the setting. First, restricting attention to merging functions that are interval scale invariant, we prove that the only functions that satisfy proximity are dictatorships. Second, we prove that the only social welfare functions that satisfy proximity and a version of the Pareto criterion are dictatorships. We conclude that either proximity is not an attractive normative requirement after all, or we must give up some other social choice condition. Another possibility is that our normative intuition about proximity needs to be codified using different axioms.