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Tytuł artykułu

Strong sequences and their consequences in social choice

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EN
Abstrakty
EN
One of the most famous theorems in social choice theory – Arrow impossibility theorem – was published in 1951. Since Arrowian paper most researchers tried to find different versions of this theorem not only for finite but also for infinite sets of alternative and individuals, where one can treat this situation as anticipation for future social behaviour. The aim of this paper is to find some results concerning social voting for infinite sets using one of the combinatorial methods of set theory – strong sequences method. This method was introduced by Efimov in 1965 for proving wellknown theorems in dyadic spaces, (i.e. continuous images of the Cantor cube).
Rocznik
Strony
49--58
Opis fizyczny
Bibliogr. 13 poz.
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autor
  • Faculty of Mathematics and Natural Sciences, College of Sciences Cardinal Stefan Wyszyński University, Warsaw, Poland
Bibliografia
  • 1. Arrow K.J.: Social Choice and Individual Values. Wiley, New York 1951.
  • 2. Efimov B.A.: Diaditcheskie bikompakty. Trudy Mosk. Matem. O-va 14 (1965), 211–247 (in Russian).
  • 3. Ferejohn J., Page T.: On the foundation of intertemporal choice. J. Agric. Economics 60 (1978), 269–275.
  • 4. Fishburn P.C.: Arrow’s impossibility theorem concise proof and infinite voters. J. Econom. Theory 2 (1970), 103–106.
  • 5. Hansson B.: The existence of group preference functions. Public Choice 38 (1976), 89–98.
  • 6. Jureczko J.: On inequalities among some cardinal invariants. Math. Aeterna 6, no. 1 (2016), 87–98.
  • 7. Kirman A.P., Sondermann D.: Arrow’s theorem, many agents, and invisible dictators. J. Econom. Theory 5 (1972), 267–277.
  • 8. Kurepa D.: The Cartesian multiplication and the cellularity number. Publ. Inst. Math. 2 (1962), 121–139.
  • 9. Marczewski E. (Szpilrajn E.): Remarque sur les produits cartesiens d’espaces topologiques. C.R. (Doklady) Acad. Sci. URSS 31 (1941), 525–527.
  • 10. Mas-Colell A., Sonnenschein H.: General possibility theorems for group decisions. Rev. Econ. Stud. 39 (1972), 185–192.
  • 11. Sen A.: Social choice a re-examination. Econometrica 45, no. 1 (1977), 53–89.
  • 12. Shanin N.A.: On the product of topological spaces. Trudy Mat. Inst. Steklov. 24 (1948), 3–112.
  • 13. Turzański M.: Strong sequences and the weight of regular spaces. Comment. Math. Univ. Carolin. 33, no. 3 (1992), 557-561.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-8d0af471-085e-4ab4-a7e5-1127e26958f7
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