Abstract
If Rawls’s A Theory of Justice has achieved fame among economists, this is due to his Difference Principle, which says that inequalities of resources should be to the benefit of the less fortunate, or more operationally, that allocations of resources should be ranked by the maximin criterion. We extend the Rawlsian maximin in two ways: first, by resorting to the more general min-of-means formula of decision theory, second, by addressing the case where the resources accruing to each individual are uncertain to society. For the latter purpose, we resort to the ex ante versus ex post distinction of welfare economics. The paper axiomatically characterizes the ex ante and ex post forms of the Rawlsian maximin and compares them in terms of egalitarian criteria. It finally recommends and axiomatizes a compromise egalitarian theory that mixes the two forms.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Adler, M.D., Sanchirico, C.W.: Inequality and uncertainty: theory and legal applications. Univ. Pa. Law Rev. 155(2), 279–377 (2006)
Alexander, S.: Social evaluation through notional choice. Quart. J. Econ. 88, 597–624 (1974)
Alon, S., Gayer, G.: Utilitarian preferences with multiple priors. Econometrica 84, 1181–1201 (2016)
Anand, S., Peter, F., Sen, A.: Public Health, Ethics, and Equity. Oxford University Press, Oxford (2006)
Arrow, K.: Some ordinalist-utilitarian notes on Rawls’ Theory of Justice. J. Philos. 70, 245–263 (1973)
Atkinson, A.: Public Economics in Action. Clarendon Press, Oxford (1995)
Barberà, S., Jackson, M.: Maximin, leximin, and the protective criterion: characterizations and comparisons. J. Econ. Theory 46(1), 34–44 (1988)
Ben-Porath, E., Gilboa, I., Schmeidler, D.: On the measurement of inequality under uncertainty. J. Econ. Theory 75, 194–204 (1997)
Boadway, R., Jacquet, L.: Optimal marginal and average income taxation under maximin. J. Econ. Theory 143, 425–441 (2008)
Bosmans, K., Ooghe, E.: A characterization of maximin. Econ. Theory Bull. 1(2), 151–156 (2013)
Bossert, W., Weymark, J.A.: Utility in social choice. In: Barberà, S., Hammond, P.J., Seidl, C. (eds.) Handbook of Utility Theory II, Ch. 20, pp. 1099–1178. Kluwer, Dordrecht (2004)
Ceron, F., Vergopoulos, V.: Aggregation of Bayesian preferences: unanimity vs monotonicity. Soc. Choice Welfare 52(3), 419–451 (2019)
Crès, H., Gilboa, I., Vieille, N.: Aggregation of multiple prior opinions. J. Econ. Theory 146, 2563–2582 (2011)
d’Aspremont, C., Gevers, L.: Equity and the informational basis of collective choice. Rev. Econ. Stud. 44(2), 199–209 (1977)
d’Aspremont, C., Gevers, L.: Social welfare and interpersonal comparability. In: Arrow, K., Sen, A., Suzumura, K. (eds.) Handbook of Social Choice and Welfare, Ch. 10, vol. 1, pp. 459–541. Elsevier, Amsterdam (2002)
Deschamps, R., Gevers, L.: Leximin and utilitarian rules: a joint characterization. J. Econ. Theory 17(2), 143–163 (1978)
Diamond, P.: Cardinal welfare, individualistic ethics, and interpersonal comparison of utility: Comment. J. Polit. Econ. 75, 765–766 (1967)
Fleurbaey, M.: Assessing risky social situations. J. Polit. Econ. 118(4), 649–680 (2010)
Fleurbaey, M.: Welfare economics, risk and uncertainty. Can. J. Econ. 51, 5–40 (2018)
Fleurbaey, M., Maniquet, F.: Utilitarianism versus fairness in welfare economics. In: Fleurbaey, M., Salles, M. (eds.) Justice, Political Liberalism and Utilitarianism: Themes from Harsanyi and Rawls, Ch. 11, pp. 263–280. Cambridge University Press, Cambridge (2009)
Fleurbaey, M., Maniquet, F.: A Theory of Fairness and Social Welfare. Cambridge University Press, Cambridge (2011)
Fleurbaey, M., Tungodden, B.: The tyranny of non-aggregation versus the tyranny of aggregation in social choices: a real dilemma. Econ. Theory 44(3), 399–414 (2010)
Gajdos, T., Kandil, F.: The ignorant observer. Soc. Choice Welfare 31(2), 193 (2008)
Gajdos, T., Maurin, E.: Unequal uncertainties and uncertain unequalities: an axiomatic approach. J. Econ. Theory 116, 93–118 (2004)
Gibbard, A.: Disparate goods and Rawls’s difference principle: a social choice theoretic treatment. Theor. Decis. 11, 267–288 (1979)
Gilboa, I.: Theory of Decision under Uncertainty, vol. 45. Cambridge University Press, Cambridge (2009)
Gilboa, I., Schmeidler, D.: Maxmin expected utility with non-unique prior. J. Math. Econ. 18, 141–153 (1989)
Hammond, P.: Equity, Arrow’s condition, and Rawl’s difference principle. Econometrica 44(4), 793–804 (1976)
Hammond, P.: Utilitarianism, uncertainty and information. In: Sen and Williams (1982), Ch. 4, pp. 85–102 (1982)
Harsanyi, J.: Cardinal utility in welfare economics and in the theory of risk-taking. J. Polit. Econ. 61, 434–435 (1953)
Harsanyi, J.: Cardinal welfare, individualistic ethics, and interpersonal comparison of utility. J. Polit. Econ. 61, 309–321 (1955). (also in Harsanyi (1976), ch. II, pp. 6-23)
Harsanyi, J.: Can the maximin principle serve as a basis for morality? A critique of John Rawls’s theory. Am. Polit. Sci. Rev. 59, 594–606 (1975). (Also in Harsanyi (1976), ch. IV, p. 37-63)
Harsanyi, J.: Essays on Ethics, Social Behavior, and Scientific Explanation. D. Reidel, Dordrecht (1976)
Hayashi, T., Lombardi, M.: Fair social decision under uncertainty and belief disagreements. Econ. Theory 67, 775–816 (2019)
Lombardi, M., Miyagishima, K., Veneziani, R.: Liberal egalitarianism and the Harm Principle. Econ. J. 126(597), 2173–2196 (2016)
Mariotti, M., Veneziani, R.: ‘Non-interference’ implies equality. Soc. Choice Welfare 32(1), 123–128 (2009)
Maskin, E.: Decision-making under ignorance with implications for social choice. Theor. Decis. 11(3), 319–337 (1979)
Milnor, J.: Games against nature. In: Thrall, R., Coombs, C., Davis, R. (eds.) Decision Processes, Ch. 4, pp. 49–60. Wiley, New York (1954)
Mongin, P.: Consistent Bayesian aggregation. J. Econ. Theory 66, 313–351 (1995)
Mongin, P.: Spurious unanimity and the Pareto principle. Tech. rep., THEMA, Université de Cergy-Pontoise, published as Mongin (2016) (1997)
Mongin, P.: The paradox of the Bayesian experts and state-dependent utility theory. J. Math. Econom. 29, 331–361 (1998)
Mongin, P.: Spurious unanimity and the Pareto principle. Econ. Philos. 32, 511–532 (2016). (earlier circulated as Mongin (1997))
Mongin, P., Pivato, M.: Ranking multidimensional alternatives and uncertain prospects. J. Econ. Theory 157, 146–171 (2015)
Mongin, P., Pivato, M.: Social evaluation under risk and uncertainty. In: Adler, M., Fleurbaey, M. (eds.) The Oxford Handbook of Well-Being and Public Policy, Ch. 24, pp. 711–745. Oxford UP, Oxford (2016)
Mongin, P., Pivato, M.: Social preference under twofold uncertainty. Econ. Theory 70(3), 633–663 (2020)
Moulin, H.: Axioms of Cooperative Decision Making. Cambridge University Press, Cambridge (1988)
Musgrave, R.: Maximin, uncertainty, and the leisure trade-off. Quart. J. Econ. 88, 625–632 (1974)
Phelps, E.: Taxation of wage income for economic justice. Quart. J. Econ. 87, 331–354 (1973)
Qu, X.: Separate aggregation of beliefs and values under ambiguity. Econ. Theory 63(2), 503–519 (2017)
Rawls, J.: A Theory of Justice. Harvard University Press, Cambridge, Mass., 2nd revised edition (1989). References are to the Oxford University Paperback edition of 1973 (1971)
Rawls, J.: Some reasons for the maximin criterion. Am. Econ. Rev. Pap. Proc. 64, 141–146 (1974a). (also in Rawls (1999), ch. 11)
Rawls, J.: Reply to Alexander and Musgrave. Quart. J. Econ. 88, 633–655 (1974b)
Rawls, J.: Social unity and primary goods. In: Sen and Williams (1982), Ch. 8, pp. 159–185, also in Rawls (1999), ch. 17 (1982)
Rawls, J.: Collected Papers (edited by Samuel Freeman). Harvard University Press, Cambridge (1999)
Rawls, J.: Justice as Fairness: A Restatement. Harvard Unversity Press, Cambridge (2001)
Roemer, J.E.: Theories of Distributive Justice. Harvard UP, Cambridge (1996)
Segal, U., Sobel, J.: Min, max, and sum. J. Econ. Theory 106(1), 126–150 (2002)
Sen, A.: Collective Choice and Social Welfare. North Holland, Amsterdam (1970)
Sen, A.: Rawls versus Bentham. Theor. Decis. 4, 301–309 (1974)
Sen, A.: Inequality Reexamined. Harvard University Press, Cambridge (1992)
Sen, A., Williams, B. (eds.): Utilitarianism and Beyond. Cambridge University Press, Cambridge (1982)
Strasnick, S.: Social choice and the derivation of Rawls’s difference principle. J. Philos. 73(4), 85–99 (1976)
Tungodden, B.: Egalitarianism: is leximin the only option? Econ. Philos. 16(2), 229–245 (2000)
Tungodden, B.: The value of equality. Econ. Philos. 19(1), 1–44 (2003)
Vallentyne, P.: Equality, efficiency, and the priority of the worse-off. Econ. Philos. 16(1), 1–19 (2000)
van Parijs, P.: Difference principles. In: Freeman, S. (ed.) The Cambridge Companion to Rawls, pp. 200–240. Cambridge University Press, Cambridge (2003)
Wakker, P.: Additive Representations of Preferences. Kluwer, Dordrecht (1989)
Weymark, J.A.: Generalized Gini inequality indices. Math. Soc. Sci. 1(4), 409–430 (1981)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The authors gratefully acknowledge Marc Fleurbaey’s and Itzhak Gilboa’s comments on this paper.
M. Pivato: Supported by Labex MME-DII (ANR11-LBX-0023-01) and CHOp (ANR-17-CE26-0003).
Rights and permissions
About this article
Cite this article
Mongin, P., Pivato, M. Rawls’s difference principle and maximin rule of allocation: a new analysis. Econ Theory 71, 1499–1525 (2021). https://doi.org/10.1007/s00199-021-01344-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00199-021-01344-x