Chichilnisky, Graciela and Heal, Geoffrey (1979): Necessary and sufficient conditions for a resolution of the social choice paradox. Published in: Journal of Economic Theory , Vol. 31, No. No. 1 (October 1983): pp. 68-87.
Download (4034Kb) | Preview
We present a restriction on the domain of individual preferences that is both necessary and sufficient for the existence of a social choice rule that is continuous, anonymous, and respects unanimity. The restriction is that the space of preferences be contractible. Contractibility admits a straightforward intuitive explanation, and is a generalisation of conditions such as single peakedness, value restrictedness and limited agreement, which were earlier shown to be sufficient for majority voting to be an acceptable rule. The only restriction on the number of individuals, is that it be finite and at least 2.
|Item Type:||MPRA Paper|
|Original Title:||Necessary and sufficient conditions for a resolution of the social choice paradox|
|Keywords:||social choice; preferences; mathematical modeling|
|Subjects:||O - Economic Development, Technological Change, and Growth > O2 - Development Planning and Policy > O25 - Industrial Policy
O - Economic Development, Technological Change, and Growth > O2 - Development Planning and Policy > O24 - Trade Policy; Factor Movement Policy; Foreign Exchange Policy
O - Economic Development, Technological Change, and Growth > O2 - Development Planning and Policy > O22 - Project Analysis
|Depositing User:||Graciela Chichilnisky|
|Date Deposited:||28. Apr 2008 02:56|
|Last Modified:||12. Feb 2013 08:09|
C. BISSAGA AND A. PELCZYNSKI, "Selected Topics in Infinite Dimensional Topology," Polska Akadcmia Nauk, Instyut Matema Tyczny, Warsaw, 1975.
D. BLACK, On the rationale of group decision making, J. Pol. Econ. 56 (1948), 23 24.
D. BROWN, Aggregation of preferences, Quart. J. Econ. 80 (1975), 456-469.
G. CHICHILNISKY, Manifolds of preferences and equilibria, Report No. 27, Project on Efficiency of Decision Making in Economic Systems, Harvard University, 1976.
G. CHICHILNISKY, The topological equivalence of the Pareto condition and the existence of a dictator, J. Math. Econ. 9 (1982), 223 233.
G. CHICHILNISKY, Social aggregregation rules and continuity, Quart. J. Econ. 87 (1982).
G. CHICHILNISKY, "Single Peakedness and the Contractibility of Spaces of Preferences," working paper, University of Essex, 1980.
G. CHICHILNISKY, Social choice and the topology of spaces of preferences, Adv. in Math. 37, No. 2 (1980), 165- 176. , G. CHICHILNISKY, The structural instability of decisive majority rules, J. Math. Econ. 9 (1982),207-221.
G. CHICHILNISKY, "Intensity of Preferences and von Neumann-Morgenstern Utilities," Mathematics of Operations Research, in press.
G. CHICHILNISKY AND - G. M. HEAL, Community preferences and social choice, Essex Economic Papers No. 165; J. Math. Econ., 1983.
G. CHICHILNISKY AND G. M. HEAL, "Social Choice with Infinite Populations: Construction of a Social Choice Rule and Impossibility Results," Columbia University Economics Discussion Paper, 1979.
J. CHIPMAN, Homothetic preferences and aggregation, J. Econ. Theory 8 (1974), 26 38.
P. COUGHLIN AND K. P. LIN, Continuity properties of majority rule with intermediate preferences, Mathematical Social Sciences I (1981), 289 -296.
G. DEBREU, Smooth preferences, Econometrica 40 (1972), 603-615.
P. C. FISHBURN, Arrow impossibility theorem: Concise proof and infinite voters, J. Econ. theory 2 (1970), 103-106.
G. M. HEAL, Contractibility and public decision making, in "Social Choice and Welfare" (P. K. Patlanaik and M. Salles, Eds.), North Holland, Amsterdam, 1983.
A. P. KIRMAN AND D. SONDERMAN, Arrow's theorem: Many agents and invisible dictators, J. Econ. theory 5 (1972), 267-277.
G. H. KRAMER, On a class of equilibrium conditions for majority rule, Econometrica (1972).
N. H. KUIPER, "Varietes hilbertiennes, aspects geotnetriqucs," Seminaire do Mathematiques Superieures, Le Presses de I'Universite de Montreal, Montreal, 1971.
W. LEDERMAN, "Introduction to Group Theory," Oliver & Boyd, Edinburgh, 1973.
C. F. MAUNDER, "Algebraic Topology, " Van Nostrand-Reinhold, London, 1970.
A. K. SEN AND P. K. PATTANAIK, Necessary and sufficient conditions for rational choice under majority decision, J. Econ. Theory 1 (1969), 178--202.
E. SPANIER, "Algebraic Topology," McGraw--Hill Series in Higher Mathematics, McGraw Hill, New York, 1966.