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The impossibility of unbiased judgment aggregation
Authors:Franz Dietrich  Christian List
Institution:(1) Department of Quantitative Economics, University of Maastricht, P.O. Box 616, 6200, MD, Maastricht, The Netherlands;(2) Department of Government, London School of Economics, London, WC2A 2AE, UK;
Abstract:Standard impossibility theorems on judgment aggregation over logically connected propositions either use a controversial systematicity condition or apply only to agendas of propositions with rich logical connections. Are there any serious impossibilities without these restrictions? We prove an impossibility theorem without requiring systematicity that applies to most standard agendas: Every judgment aggregation function (with rational inputs and outputs) satisfying a condition called unbiasedness is dictatorial (or effectively dictatorial if we remove one of the agenda conditions). Our agenda conditions are tight. When applied illustratively to (strict) preference aggregation represented in our model, the result implies that every unbiased social welfare function with universal domain is effectively dictatorial.
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