JOURNAL OF ECONOMIC THEORY 46, 3444 (1988) Maximin, Leximin, and the Protective Criterion: Characterizations and Comparisons* SALVADOR BARBARA Deportumenf d’Economiu i Histckia Econdmica, Universirat Autdnoma de Barcelona, Spain AND MATTHEW JACKSON Kellogg School of Management, Norrhnesrern University, Evanston, Illinois 60208 Received January 24, 1986; revised August 26, 1987 In this paper we characterize maximin, leximin, and the protective criterion. In particular, we provide a new proof for a classical characterization of maximin. we provide a new characterization of leximin. and we define and characterize a new variant of maximin: the protective criterion, The decision criteria are considered and compared in both a game agains nature framework and a social welfare framework. Journal of Economic Lirerarure Classification Numbers: 024. 025, 026. ( ’ 1988 Academic Press, Inc INTRODUCTION The object of this paper is to define, to compare, and to characterize three variants of the maximin criterion. More specifically, we ( 1) provide a new proof for a classical characterization of maximin, (2) characterize leximin by a new set of axioms, and (3) define and characterize a new variant of maximin, to be called the protective criterion. * This research was conducted while Barbera was visiting the Graduate School of Business at Stanford University. He wishes to acknowledge their hospitality as well as financial support from the Comision Conjunta Hispano-Norteamericana para la Cooperation Cultural y Educativa. Jackson acknowledges the support of a National Science Foundation Graduate Fellowship and the Graduate School of Business at Stanford University. We thank Bhaskar Dutta, John Roberts, Hugo Sonnenschein, and Alain Trannoy for helpful discussions and comments. The insightful comments of two referees and the associate editor of Journal oj Economic Theor! led to a reevaluation of our results and their interpretations. 34 0022-0531/88 $3.00 CopyrIght SC_) 1988 by Academic Press. Inc All rights of reproducflon m any form reserved.