Abstract
This article considers, in the context of the fixed-population constant-sum comparison of income distributions, a number of intransitive binary relations smaller than Lorenz dominance. We determine their transitive closure, and we study how they relate to each other and to other relations that have appeared in the literature. Among other results, we provide alternative characterizations of Lorenz dominance.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aboudi R, Thon D (2006) Refinements of Muirhead’s Lemma and income inequality. Math Soc Sci 51: 201–216
Aboudi R, Thon D (2008) Second degree Pareto dominance. Soc Choice Welf 30: 475–493
Chateauneuf A, Moyes P (2004) Lorenz non-consistent welfare and inequality measurement. J Econ Inequal 2: 61–87
Chateauneuf A, Moyes P (2006) Measuring inequality without the Pigou–Dalton condition. In: McGillivray M (eds) Inequality, poverty and well-being. Palgrave MacMillan, Basingstoke, Hampshire,, pp 22–65
Chateauneuf A, Cohen M, Meilijson I (2004) Four notions of mean-preserving increases in risk, risk attitudes and applications to the rank-dependent expected utility model. J Math Econ 40: 547–571
Dalton H. (1920) The measurement of the inequality of income. Econ J 30: 348–361
Diamond P, Stiglitz J (1974) Increases in risk and risk aversion. J Econ Theory 8: 337–360
Ebert U (2009) Taking empirical studies seriously: the principle of concentration and the measurement of welfare and inequality. Soc Choice Welf 32: 555–574
Fei J (1981) Equity oriented fiscal programs. Econometrica 49(4): 869–881
Fishburn P (1973) The theory of social choice. Princeton University Press, Princeton
Hemming R, Keen M (1983) Single-crossing conditions in comparisons of tax progressivity. J Public Econ 20: 373–380
Jakobsson U (1976) On the measurement of the degree of progression. J Public Econ 5: 161–168
Kolm S (1999) The rational foundations of income inequality measurement. In: Silber J (eds) Handbook of income inequality measurement. Kluwer, Boston, pp 19–100
Lambert P (2001) The distribution and redistribution of income, 3rd edn. Manchester University Press, Manchester
Le Breton M, Moyes P, Trannoy A (1996) Inequality reducing properties of composite taxation. J Econ Theory 69: 71–103
Marshall A, Olkin I (1979) Inequalities: majorization theory and its applications. Academic Press, New York
Moyes P (1994) Inequality reducing and inequality preserving transformations of income: symmetric and individualistic transformations. J Econ Theory 63: 271–298
Muirhead R (1903) Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters. Proc Edinb Math Soc 21: 144–157
Preston I (2007) Inequality and income gaps. In: Lambert P (eds) Equity, vol 15. Research on income inequality. Elsevier, Oxford, pp 33–56
Thistle P (1989) Uniform progressivity, residual progression and single-crossing. J Public Econ 37: 121–126
Thon D (1987) Redistributive properties of progressive taxation. Math Soc Sci 14: 185–191
Thon D, Wallace S (2004) Dalton transfers, inequality and altruism. Soc Choice Welf 22: 447–456
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Aboudi, R., Thon, D. Characterizations of egalitarian binary relations as transitive closures with a special reference to Lorenz dominance and to single-crossing conditions. Soc Choice Welf 35, 575–593 (2010). https://doi.org/10.1007/s00355-010-0452-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00355-010-0452-y