Abstract
In the present paper we discuss several aspects of Arrow’s (1951, 1963) famous result which has deeply influenced the methodological attitude towards the formalization of social and economic theories. Instead of discussing more or less ad hoc procedures for the aggregation of individual preferences Arrow stated plausible properties which an aggregation procedure should satisfy and showed that for finite societies these properties are in conflict with one another. Loosely speaking we may say that there exists no satisfactory “democratic” aggregation procedure. For most social scientists this result was rather disappointing and the usual attitude was to criticize one (most often the so-called “independence of irrelevant alternatives”) or more of Arrow’s conditions as not appropriately reflecting our intuitive notions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arrow, K.J.: 1951. Social Choice and Individual Values. New York: Wiley.
Blass, A.: 1977. ‘A Model Without Ultrafilters’. Bulletin Acad. Polon. Sci., Sér. Sci. Math. Astron. Phys. 25, 329–331.
Brown, D.M.: 1975. ‘Aggregation of Preferences’. Quarterly Journal of Economics 89, 456–469.
Choquet, G.: 1968. ‘Construction d’ultrafilters’. N. Bulletin Sci. Math. 92, 41–48.
Fishburn, P. C.: 1970. ‘Arrow’s Impossibility Theorem: Concise Proof and Infinite Voters’. Journal of Economic Theory 2, 103–106.
Fishburn, P.C.: 1973. The Theory of Social Choice. Princeton: Princeton University Press.
Gottwald, S.: 1984. ‘Diktatoren. — Thema mit Variationen — Wiss. Zft’. In Ernst — Moritz—Arndt, Naturwissenchafiliche Reihe XXXIII, University of Greifswald, 22–25.
Hansson, B.: 1976. ‘The Existence of Group Preference Function’. Public Choice 28, 89–98.
Huang, H.H., and S. Negrepontis: 1973. ‘Spaces Homeomorphic to (2a)a’. Bulletin of the American Mathematical Society 79, 143–146.
Huang, H.H., and S. Negrepontis: 1974. ‘Spaces Homeomorphic to (2a) a ’. Transactions of the American Mathematical Society 188, 1–30.
Kelly, J.S.: 1978. Arrow’s Impossibility Theorems. New York: Academic Press.
Kirman, A.P. and D. Sondermann: 1972. ‘Arrow’s Theorem, Many Agents, and Invisible Dictators’. Journal of Economic Theory 5, 267–277.
Martin, D.A.: 1975. ‘Borel Determinacy’. Annals of Mathematics 102, 363–371.
Mycielski, J.: 1964. ‘On the Axiom of Determinateness’. Fund. Math. 53, 205–224.
Richter, M.: 1982. Ideale Punkte, Monaden und Nichstandard—Methoden. Braunschweig: Vieweg.
Robinson, A.: 1966. Non-Standard Analysis. Amsterdam: North-Holland.
Skala, H.J., S. Termini, and E. Trillas: 1984. Aspects of Vagueness. Dordrecht: D. Reidel.
Skala, H.J.: 1982. ‘Some Problems of Measure Theory Which are Related to Economic Theory’. Stochastica, 305–320.
Skala, H.J.: 1981. ‘On the Foundations of the Social Ordering Problem’. In Game Theory and Mathematical Economics, Moeschlin and Pallaschke, eds., Amsterdam: North Holland.
Skala, H.J.: 1978. ‘On Many-Valued Logics, Fuzzy Sets, Fuzzy Logics, and Their Applications’. Fuzzy Sets and Systems 1, 129–149.
Sochor, A.: 1976. ‘The Alternative Set Theory’. In Set Theory and Hierarchy Theory, Springer.
Solovay, R.M.: 1970. ‘A Model of Set Theory in Which Every Set of Reals is Lebesgue-Measurable’. Annals of Mathematics 2, 1–56.
Ulam, S.: 1930. ‘Zur Maßtheorie der Allgemeinen Mengenlehre’. Fund. Math., 140–150.
Vopenka, P. and P. Hájek: 1972. The Theory of Semisets. North-Holland.
Vopenka, P.: 1979. Mathematics in the Alternative Set Theory. Leipzig: Teubner.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 D. Reidel Publishing Company
About this chapter
Cite this chapter
Skala, H.J. (1988). What Does Arrow’s Impossibility Theorem Tell Us?. In: Eberlein, G.L., Berghel, H. (eds) Theory and Decision. Theory and Decision Library, vol 50. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3895-3_14
Download citation
DOI: https://doi.org/10.1007/978-94-009-3895-3_14
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8230-3
Online ISBN: 978-94-009-3895-3
eBook Packages: Springer Book Archive