Measures of inequality as an aggregation of individual preferences about income distribution: The arrowian case |
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| Institution: | 1. GREQE, Marseille 13002, France;2. Université de Rennes I, Rennes 35000, France;1. College of Mathematics and Statistics, Shaanxi Normal University, Xi''an 710119, China;2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;4. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan;1. Department of Economics, Yale University, New Haven, CT 06520, USA;2. Department of Economics, Princeton University, Princeton, NJ 08544, USA;1. International Monetary Fund, United States;2. Institute of Informatics, Warsaw University, Poland;3. Faculty of Economics & Christ''s College, University of Cambridge, United Kingdom;1. Purdue University, United States;2. Georgia State University, United States;3. University of Pennsylvania, United States |
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| Abstract: | An inequality preorder is a preorder on a simplex which satisfies symmetry and strict Schur-convexity (the mathematical equivalent of the principle of transfers of Pigou and Dalton). It is shown that we cannot aggregate individual inequality preorders to a collective one if we are interested in Arrow's aggregation rules. The proof uses an interesting result of Kalai, Muller and Satterthwaite (Public Choice 34 (1979), 87–97). Moreover, we prove further results for the aggregation of individual inequality indices when we allow cardinality and interpersonal comparibility of utility. |
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