Lebesgue measure and social choice trade-offs
- 59 Downloads
- 5 Citations
Summary
An Arrovian social choice rule is a social welfare function satisfying independence of irrelevant alternatives and transitivity of social preference. Assume a measurable outcome spaceX with its (Lebesgue) measure normalized to unity. For any Arrovian rule and any fractiont, either some individual dictates over a subset ofX of measuret or more, or at least a fraction 1−t of the pairs of distinct alternatives have their social ordering fixed independently of individual preferences. Also, for any positive integerβ (less than the total number of individuals), there is some subsetH of society consisting of all butβ persons such that the fraction of outcome pairs (x, y) that are social ranked without consulting the preferences of anyone inH, whenever no individual is indifferent betweenx andy, is at least 1−1/4β.
Keywords
Social Welfare Economic Theory Lebesgue Measure Social Choice Individual PreferencePreview
Unable to display preview. Download preview PDF.
References
- Arrow, K. J.: Social choice and individual values, 2nd edn. New York: Wiley (1963)Google Scholar
- Campbell, D. E.: Equity, efficiency, and social choice. Oxford: The Clarendon Press (1992)Google Scholar
- Campbell, D. E., Kelly, J. S.:t or 1−t. There is the Trade-off. Econometrica61, 1355–1366 (1993)Google Scholar
- Dugundji, J.: Topology. Boston. Allyn and Bacon (1966)Google Scholar
- Hahn, H., Rosenthal, A.: Set functions. Albuquerque. The University of New Mexico Press (1948)Google Scholar
- Kelly, J. S.: The free triple assumption. Soc. Choice Welfare11, 97–102 (1994)Google Scholar
- Royden, H. L.: Real analysis. New York: Macmillan (1968)Google Scholar
- Wilson, R. B.: Social choice without the pareto principle. J. Econ. Theory5, 14–20 (1972)Google Scholar