An ordinal characterization of the linear opinion pool

Given a collection of individual ordinal probabilities on a …nite state space, we discuss an ordinal condition that is necessary and su¢ cient for an ordinal probability to be represented as a weighted average of probability representations of the individual probabilities. We also give necessary and su¢ cient conditions for when such an ordinal probability can be represented as an unweighted average of probability representations. Keywords: Opinion pool, linear opinion pool, ordinal probability, probability aggregation, utilitarian. JEL classi…cation: D71, D81. Assistant Professor of Economics, Division of the Humanities and Social Sciences, 228-77, California Institute of Technology, Pasadena, CA 91125. Phone: (626) 395-3559. Email: [email protected]. Many thanks are due to an anonymous referee, who provided detailed comments and corrections which greatly improved this paper.