Stochastic Dominance Relations for Integer Variables
The objective of this paper is to derive some integer-majorization results for variable-sum comparisons. We use an axiomatic framework to establish equivalence between several intuitively reasonable conditions. © 2011 Elsevier Inc. All rights reserved.
KeywordsStochastic dominance Generalized Lorenz curve Grids Integers Measures Majorization
JEL classificationD63 D81
For comments and suggestions, we are grateful to two referees, an associate editor of this journal, Vincenzo Denicolò and participants of the JET Symposium on “Inequality and Risk”, Paris, June 25–26, 2010. Chakravarty thanks the Bocconi University, Milan, Italy, for support. Financial support from the Italian Ministero dell’Istruzione, dell’Università e della Ricerca (Prin 2007) is gratefully acknowledged by Claudio Zoli.
- Aboudi, R., & Thon, D. (1995). The duality approach to stochastic dominance with standardized random variables. Mimeo.Google Scholar
- Atkinson, A. B. (1998). Social exclusion, poverty and unemployment (pp. 1–20). CASE/4, Centre for Analysis of Social Exclusion, London School of Economics.Google Scholar
- Hardy, G. H., Littlewood, J. E., & Pólya, G. (1934). Inequalities. Cambridge: Cambridge University Press.Google Scholar
- Levy, H. (2006). Stochastic dominance. Investment decision making under uncertainty (2nd ed.). New York: Springer.Google Scholar
- Marshall, A. W., & Olkin, I. (1979). Inequalities: Theory of majorization and its applications. New York: Academic Press.Google Scholar
- Rothschild, M., & Stiglitz, J. E. (1970). Increasing risk: I. A definition. Journal of Economic Theory, 3, 225–243.Google Scholar
- Shaked, M., & Shanthikumar, G. (2006). Stochastic orders. New York: Springer.Google Scholar