Journal Article On a Theorem of Scarf Get access Gerard Debreu Gerard Debreu New Haven, Conn., and Berkeley, Calif. Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 30, Issue 3, October 1963, Pages 177–180, https://doi.org/10.2307/2296318 Published: 01 October 1963

Cardinal Utility for Even-chance Mixtures of Pairs of Sure Prospects Get access Gerard Debreu Gerard Debreu New Haven, Conn. Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 26, Issue 3, June 1959, Pages 174–177, https://doi.org/10.2307/2295745 Published: 01 June 1959

[Changes in the mathematical form of theoretic models of an economy during the past four decades and the growth of mathematical economics in that period are considered in relation to each other and to the development of the Econometric Society. The fit of the mathematical form to the economic content of theoretic models, their separation in a completed axiomatic theory and their interplay in its elaboration are examined. Consequences of the axiomatization of economic theory are analyzed.]

Given a set of economic agents and a set of coalitions, a non-empty family of subsets of the first set closed under the formation of countable unions and complements, an allocation is a countably additive function from the set of coalitions to the closed positive orthant of the commodity space. To describe preferences in this context, one can either introduce a positive, finite real measure defined on the set of coalitions and specify, for each agent, a relation of preference or difference on the closed positive orthant of the commodity space, or specify, for each coalition, a relation of preference or indifference on the set of allocations. This article studies the extent to which these two approaches are equivalent.