Ordinal aggregation and quantiles

Consider the problem of aggregating a pro…le of interpersonally comparable utilities into a social utility. We require that the units of measurement of utility used for agents is the same as the units of measurement for society (ordinal covariance) and a mild Pareto condition (monotonicity). We provide several representations of such social aggregation operators: a canonical representation, a Choquet expectation representation, a minimax representation, and a quantile representation (with respect to a possibly non-additive set function on the agents). We also isolate an additional condition that gives us a quantile representation with respect to a probability measure, in both the …nite and in…nite agents case. Keywords: Ordinal, quantile, axiom, Choquet integral, probability, Rawlsian, social welfare. JEL classi…cation: D31, D63, D71, D81. Assistant Professor of Economics, Division of the Humanities and Social Sciences, California Institute of Technology. Mail Code 228-77. Phone: (626) 395-3559. Email: [email protected]. I would like to thank Federico Echenique for helpful conversations. I am also very grateful to two anonymous referees, as well as the associate editor. All errors are my own.