Continuity,completeness, betweenness and cone-monotonicity |
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| Institution: | 1. Department of Economics, Johns Hopkins University, United States;2. Warwick Business School, University of Warwick, United Kingdom;3. Tel Aviv University, Emeritus, Israel;1. BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, Spain;2. Departamento de Fundamentos del Análisis Económico I, Universidad del País Vasco, Avenida Lehendakari Aguirre, 83, E-48015 Bilbao, Spain;3. IKERBASQUE, Basque Foundation of Science, 48011, Bilbao Spain;1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, PR China;2. College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610000, PR China;1. IPAG Business School, France;2. PSE-Université de Paris I, France;3. Université de Paris I, France;4. Paris School of Economics, France;5. Ghent University, Belgium;1. Kent Business School; University of Kent; Kent CT2 7FS, UK;2. Department of Economics; University of Pretoria; Hatfield 0028, South Africa |
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| Abstract: | A non-trivial, transitive and reflexive binary relation on the set of lotteries satisfying independence that also satisfies any two of the following three axioms satisfies the third: completeness, Archimedean and mixture continuity (Dubra, 2011). This paper generalizes Dubra’s result in two ways: First, by replacing independence with a weaker betweenness axiom. Second, by replacing independence with a weaker cone-monotonicity axiom. The latter is related to betweenness and, in the case in which outcomes correspond to real numbers, is implied by monotonicity with respect to first-order stochastic dominance. |
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