Abstract
Convexity of preferences is a canonical assumption in economic theory. In this paper we study a generalized definition of convex preferences that relies on the notion of a convex space, that is an abstraction of the standard notion of convexity in a linear space. We introduce also betweenness relations that characterize convex spaces. First we consider a ternary betweenness relation that gives rise to an interval space structure and then we propose a more general definition of betweenness.
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References
Adaricheva, K.: Algebraic convex geometries revisited. arXiv:1406.3721
M. Cardin, Sugeno integral on property-based preference domains. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K., Krawczak, M. (eds.) Advances in Fuzzy Logic and Technology 2017, EUSFLAT 2017. Advances in Intelligent Systems and Computing, vol. 641 (2018)
Chateauneuf, A., Tallon, J.-M.: Diversification, convex preferences, and non-empty core in the Choquet expected utility model. Econ. Theory 19, 509–523 (2002)
Coppel, W.A.: Foundations of Convex Geometry. Cambridge University Press, Cambridge (1998)
Gordon, S.: Unanimity in attribute-based preference domains. Soc. Choice Welf. 44, 13–29 (2015)
Hedlíková, J.: Ternary spaces, media and Chebyshev sets. Czechoslovak Math. J. 33, 373–389 (1983)
Kubis, W.: Abstract convex structures in topology and set theory. Ph.D. thesis, University of Silesia, Katowice, Poland (1999)
Llinares, J.V.: Abstract convexity, some relations and applications. Optimization 51(6), 797–818 (2002)
Nehring, K., Puppe, C.: The structure of strategy-proof social choice—part I: general characterization and possibility results on median spaces. J. Econ. Theory 135(1), 269–305 (2007)
Nehring, K., Puppe, C.: Abstract Arrowian aggregation. J. Econ. Theory 145, 467–494 (2010)
Rautenbach, D., Schäfer, P.M.: Strict betweennesses induced by posets as well as by graphs. Order 28, 89–97 (2011)
Richter, M., Rubinstein, A.: “Convex preferences”: a new definition. mimeo (2018)
van de Vel, M.L.J.: Theory of Convex Structures North-Holland Mathematical Library, vol. 50. Elsevier, Amsterdam (1993)
Vannucci, S.: Weakly unimodal domains, anti-exchange properties, and coalitional strategy-proofness of aggregation rules. Math. Soc. Sci 84, 50–67 (2016)
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Cardin, M. (2020). Preferences in Abstract Convex Structures. In: Bosi, G., Campión, M., Candeal, J., Indurain, E. (eds) Mathematical Topics on Representations of Ordered Structures and Utility Theory. Studies in Systems, Decision and Control, vol 263. Springer, Cham. https://doi.org/10.1007/978-3-030-34226-5_9
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DOI: https://doi.org/10.1007/978-3-030-34226-5_9
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