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Aggregation of preferences from algebraic models on groups

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Abstract

In this paper we introduce the algebraic Chichilnisky social choice model which deals with anonymous and unanimous homomorphisms defined on groups. The main properties of this algebraic model furnish a good tool to obtain an alternative proof for the Chichilnisky-Heal resolution of the topological social choice paradox.

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References

  • Baigent N (1987) Preference proximity and anonymous social choice. Quart J Economics 102: 162–169

    Google Scholar 

  • Candeal JC, Induráin E, Uriarte JR (1992) Some issues related to the topological aggregation of preferences. Soc Choice Welf 9: 213–227

    Google Scholar 

  • Chichilnisky G (1979) On fixed point theorems and social choice paradoxes. Economics Lett 3: 347–351

    Google Scholar 

  • Chichilnisky G (1980) Social choice and the topology of spaces of preferences. Adv Math 37: 165–176

    Google Scholar 

  • Chichilnisky G (1982) Social aggregation rules and continuity. Quart J Economics 87: 337–352

    Google Scholar 

  • Chichilnisky G (1985) Von Neumann-Morgenstern utilities and cardinal preferences. Math Oper Res 10: 633–641

    Google Scholar 

  • Chichilnisky G (1991a) Actions of symmetry groups in social choice. (Working Paper). Columbia University, New York

    Google Scholar 

  • Chichilnisky G (1991b) Social choice and the closed convergence topology. Soc Choice Welf 8: 307–317

    Google Scholar 

  • Chichilnisky G, Heal G (1983) Necessary and sufficient conditions for a resolution of the social choice paradox. J Economic Theo 31: 68–87

    Google Scholar 

  • Debreu G (1972) Smooth preferences. Econometrica 40: 603–615

    Google Scholar 

  • Efimov BA, Koshevoy GA (1994) A topological approach to social choice with infinite populations. Math Soc Sci 27: 145–157

    Google Scholar 

  • Fomenko A, Fuchs DB, Gutenmacher VL (1986) Homotopic topology. Akadémiai Kiadó. Budapest

    Google Scholar 

  • Hungerford TW (1974) Algebra. Holt, Rinehart, and Winston, New York

    Google Scholar 

  • Kaplansky I (1971) Infinite abelian groups. (Revised Edition, second printing). The University of Michigan Press, Ann Arbor

    Google Scholar 

  • Keesling J (1972) The group of homeomorphisms of a solenoid. Transactions of the American Mathematical Society 172: 119–131

    Google Scholar 

  • Kelly JS (1976) Algebraic results on collective choice rules. J Math Economics 3: 285–293

    Google Scholar 

  • Lauwers L (1993) Topological aggregation, the case of an infinite population. (Working Paper). Monitoraat E.T.E.W., K.U. Leuven, Belgium

    Google Scholar 

  • Le Breton M, Trannoy A, Uriarte JR (1985) Topological aggregation of inequality preorders. Social Choice Welf 2: 119–129

    CAS  PubMed  Google Scholar 

  • Rokhlin VA, Fuchs DB (1981) Premier cours de topologie. Chapitres géométriques. Éditions Mir, Moscow. (This is the French translation. The Russian original was published in 1977 by Mir Publishers, Moscow. English translation: “The beginner's course in topology”, Springer, 1984)

    Google Scholar 

  • Rubinstein A, Fishburn PC (1986) Algebraic aggregation theory. J Economic Theo 38: 63–77

    Google Scholar 

  • Spanier EH (1966) Algebraic topology. Mc Graw Hill, New York

    Google Scholar 

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Candeal, J.C., Induráin, E. Aggregation of preferences from algebraic models on groups. Soc Choice Welfare 12, 165–173 (1995). https://doi.org/10.1007/BF00179831

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