Abstract
Elementary geometry is used to understand, extend and resolve basic informational difficulties in choice theory. This includes axiomatic conclusions such as Arrow’s Theorem, Chichilnisky’s dictator, and the Gibbard-Satterthwaite result. In this manner new results about positional voting methods are outlined, and difficulties with axiomatic approach are discussed. A topological result about “dictatorial” behavior is offered.
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References
Arrow KJ (1963) Social choice of individual values, 2nd edn. Wiley, New York
Baigent NJ, Gaertner W (1993) Never choose the uniquely largest: a characterization, preprint.
Chichilnisky G (1982) The topological equivalence of the Pareto condition and the existence of a dictator. J Math Econ 30: 223–233
Chichilnisky G, Heal G (1983) Necessary and sufficient conditions for a resolution of the social choice paradox. J Econ Theory 31: 68–87
Chichilnisky G, Heal G (1997) The geometry of implementation: a necessary and sufficient condition for straightforwardness. Soc Choice Welfare 14: 259–294
Fishburn P (1970) Arrow’s impossibility theorem: Concise proof and infinite voters. J Econ Theory 2: 103–106
Gibbard AF (1973) Manipulation of voting schemes; a general result. Econometrica 41: 587–601
Haunsperger D (1992) Dictionaries of paradoxes for statistical tests on k samples. J Am Stat Assoc 87: 149–155
Hansson B (1976) The existence of group preferences. Public Choice 28: 89–98
Rasmussen H (1997) Strategy-proofness of continuous aggregation maps. Soc Choice Welfare 14: 249–257
Saari DG (1984) A method for constructing message systems for smooth performance functions. J Econ Theory 33: 249–274
Saari DG (1987) Chaos and the theory of elections. In: Kumshanski A, Sigmunol K (eds) Dynamical Systems: Lecture notes in Economics and Mathematical Systems, vol. 287, Springer, pp 179–188
Saari DG (1988) Symmetry, voting and social choice. Math Intelligencer 10: 32–42
Saari DG (1989) A dictionary for voting paradoxes. Econ Theory 48: 443–475
Saari DG (1990) The Borda Dictionary. Soc Choice Welfare 7: 279–317
Saari DG (1991a) Erratic behavior in economic models. J Econ Behav Organ 16: 3–35
Saari DG (1991b) Calculus and extensions of Arrow’s Theorem. J Math Econ 20: 271–306
Saari DG (1992a) Symmetry extensions of “neutrality” I: advantage to the Condorcet loser. Soc Choice Welfare 9: 307–336
Saari DG (1992b) Millions of election rankings from a single profile. Soc Choice Welfare 9: 277–306
Saari DG (1993) Symmetry extensions of “neutrality” II: Partial ordering of dictionaries. Soc Choice Welfare 10: 301–3
Saari DG (1994a) Inner consistency or not inner consistency; a reformulation is the answer. In: Barnett W, Moulin H, Salles M, Schfield N (eds) Social Choice and Welfare
Saari DG (1994b) Geometry of voting. Springer-Verlag, Berlin Heidelberg, New York
Satterthwaite MA (1975) Strategyproofness and Arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions. J Econ Theory 10: 187–217
Sen A (1977) Social choice theory: a re-examination. Econometric 45: 53–89
Young P (1974) An axiomatization of Borda’s Theory. J Econ Theory 9: 478–486
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© 1997 Springer-Verlag Berlin · Heidelberg
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Saari, D.G. (1997). Informational geometry of social choice. In: Heal, G.M. (eds) Topological Social Choice. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60891-9_4
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DOI: https://doi.org/10.1007/978-3-642-60891-9_4
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