Sen’s theorem: geometric proof, new interpretations
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Sen’s classic social choice result supposedly demonstrates a conflict between Pareto and minimal forms of liberalism. By providing the first direct mathematical proof of this seminal result, we underscore a significantly different interpretation: rather than conflicts among rights, Sen’s result occurs because the liberalism assumption negates the requirement that voters have transitive preferences. This explanation enriches interpretations of Sen’s conclusion by introducing radically new kinds of societal conflicts, by suggesting ways to sidestep these difficulties, and by providing insight into other approaches that have been used to avoid the difficulties.
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