Crespo, Juan A. and Sanchez-Gabites, J.J
(2016):
*Solving the Social Choice problem under equality constraints.*

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## Abstract

Suppose that a number of equally qualified agents want to choose collectively an element from a set of alternatives defined by equality constraints. Each agent may well prefer a different element, and the social choice problem consists in deciding whether it is possible to design a rule to aggregate all the agents’ preferences into a social choice in an egalitarian way. In this paper we obtain criteria that solve this problem in terms of conditions that are explicitly computable from the constraints. As a theoretical consequence, we show that the only way to avoid running into a social choice paradox consists in designing (if possible) the set of alternatives satisfying certain optimality condition on the constraints, that is, in the natural way from the point of view of economics.

Item Type: | MPRA Paper |
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Original Title: | Solving the Social Choice problem under equality constraints |

Language: | English |

Keywords: | Social choice, optimization, rational design. |

Subjects: | C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C60 - General D - Microeconomics > D6 - Welfare Economics > D63 - Equity, Justice, Inequality, and Other Normative Criteria and Measurement D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice ; Clubs ; Committees ; Associations |

Item ID: | 72757 |

Depositing User: | Dr Juan A. Crespo |

Date Deposited: | 31 Jul 2016 04:46 |

Last Modified: | 29 Sep 2019 17:28 |

References: | K. J. Arrow. Social choice and individual values. Yale University Press, 1951. G. Aumann. Beitr¨age zur Theorie der Zerlegungsr¨aume. Math. Ann., 1:249–294, 1936. N. Baigent. Topological Theories of social choice, In Handbook of social choice and Welfare: volume 2, (K. J. Arrow, A. K. Sen and K. Suzumura, editors), Chapter 18. Elsevier, 2011. J. C. Candeal and E. Indurain. The Moebius strip and a social choice paradox. Economics Letters,45: 407–412, 1994. G. Chichilnisky. On fixed point theorems and social choice paradoxes. Economics Letters, 3:347–351, 1979. G. Chichilnisky. Social choice and the topology of spaces of preferences. Advances in Mathematics,37: 165–176, 1980. G. Chichilnisky and G. Heal. Necessary and sufficient conditions for a resolution of the social choice paradox. Journal of Economic Theory, 31:68–87, 1983. A. de la Fuente. Mathematical Methods and Models for Economists. Cambridge University Press,2000. B. Eckmann. Ra¨ume mit Mittelbildungen. Comment. Math. Helv., 28: 329–340, 1954. B. Eckmann. Social choice and topology. A case of pure and applied mathematics. Expo. Math.,22: 385–393, 2004. B. Eckmann, T. Ganea and P. Hilton. Generalized means. Studies in mathematical analysis andrelated topics, 82–92. Stanford University Press, 1962. C. H. Edwards. Advanced calculus of several variables. Academic Press, 2015. A. Hatcher. Algebraic Topology. Cambridge University Press, 2002. P. Hilton. A new look at means on topological spaces. Internat. J. Math. Math. Sci. 20(4):617–620, 1997. S. Hu. Theory of retracts. Wayne State University Press, 1965. L. Lauwers. Topological social choice. Mathematical Social Sciences, 40:1–39, 2000. Y. Matsumoto. An introduction to Morse theory. Translations of Mathematical Monographs,1997. J. Milnor. Morse theory. Annals of Mathematical Studies. Princeton University Press, 1963. J. Milnor. Topology from the differentiable viewpoint. Princeton University Press, 1997. C. P. Simon and L. Blume. Mathematics for economists. W. W. Norton & Company, 1994. E. H. Spanier. Algebraic topology. McGraw–Hill Book Co., 1966. S. Weinberger. On the topological social choice model. Journal of Economic Theory, 115(2):377-384, 2007. J. H. C. Whitehead. On C1-Complexes. Ann. of Math., 41(2): 809–824, 1940. H. Whitney. Geometric integration theory. Princeton University Press, 1957. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/72757 |