Existence of a Dictatorial Subgroup in Social Choice with Independent Subgroup Utility Scales, an Alternative Proof
Social welfare orderings for different scales of individual utility measurement in distinct population subgroups are studied. In Khmelnitskaya (2000), employing the continuous version of Arrow’s impossibility theorem, it was shown that for combinations of independent subgroups scales every corresponding social welfare ordering depends on the utilities of only one of the subgroups and is determined in accordance with the scale type proper to this dictatorial subgroup. In this article we introduce an alternative completely self-contained proof based on the study of the structure of level surfaces of a social welfare function which provides a real-valued representation of the social welfare ordering.
Unable to display preview. Download preview PDF.
- Arrow, K. J. (1951). Social choice and individual values (2nd ed., 1963). New York: Wiley.Google Scholar
- Bossert, W., & Weymark, J. A. (2004). Utility in social choice. In: Barberá, S., Hammond, P. J., & Seidl, C. (Eds.), Handbook of utility theory (Vol. 2, pp. 1099–1178). Boston: Kluwer Academic Publishers.Google Scholar
- d’Aspremont, C. (1985). Axioms for social welfare orderings. In: Hurwicz, L., Schmeidler, D., & Sonnenschein, H. (Eds.), Social goals and social organizations: Essays in memory of Elisha Pazner (pp. 19–76). Cambridge: Cambridge University Press.Google Scholar
- Debreu, G. (1954). Representation of a preference ordering by a numerical function. In: Thrall, R. M., Coombs, C. H., & Davis, R. L. (Eds.), Decision processes (pp. 159–165). New York: Wiley.Google Scholar
- Khmelnitskaya, A. B. (1996). Social choice problems with different scales of individual welfares measurement for different subgroups of individuals. In: Kleinschmidt, P., Bachem, A., Derigs, U., Fischer, D., Leopold-Wildburger, U., & Möring, R. (Eds.), Operations research proceedings 1995 (pp. 252–257). Berlin: Springer-Verlag.Google Scholar
- Khmelnitskaya, A. B. (1999). Social welfare orderings for different subgroup utility scales. Discussion Paper #, Center for Rationality and Interactive Decision Theory at The Hebrew University of Jerusalem.Google Scholar
- Khmelnitskaya, A. B. (2002). Social welfare functions for different subgroup utility scales. In: Tangian, A., & Gruber, J. (Eds.), Lecture notes in economics and mathematical systems (vol. 510, pp. 515–530). Berlin: Springer-Verlag.Google Scholar
- Phanzagl, J. (1971). Theory of measurement (2nd ed.). Würzburg–Wien: Physica-Verlag.Google Scholar
- Sen, A. K. (1970). Collective choice and social welfare. San Francisco: Holden-Day.Google Scholar
- Yanovskaya, E. B. (1988). Social choice functions for different scales of individual preference measurement (in Russian). Annals of VNIISI (All-Union Research Institute for System Studies, Moscow), 6, 64–76.Google Scholar
- Yanovskaya, E. B. (1989). Group choice rules in problems with comparisons of individual preferences. Automation and Remote Control, 50, 822–830 (translated from the 1989 Russian original that appeared in Avtomatika i Telemekhanika, 6, 129–138).Google Scholar