Journal Article Transitivity Get access Peter C. Fishburn Peter C. Fishburn Pennsylvania State University Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 46, Issue 1, January 1979, Pages 163–173, https://doi.org/10.2307/2297179 Published: 01 January 1979 Article history Received: 01 February 1977 Accepted: 01 April 1978 Published: 01 January 1979

Journal Article A Probabilistic Model of Social Choice: Comment Get access Peter C. Fishburn Peter C. Fishburn The Pennsylvania State University Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 42, Issue 2, April 1975, Pages 297–301, https://doi.org/10.2307/2296538 Published: 01 April 1975

Journal Article Axioms for Lexicographic Preferences Get access Peter C. Fishburn Peter C. Fishburn Pennsylvania State University Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 42, Issue 3, July 1975, Pages 415–419, https://doi.org/10.2307/2296854 Published: 01 July 1975

Journal Article On Collective Rationality and a Generalized Impossibility Theorem Get access Peter C. Fishburn Peter C. Fishburn The Pennsylvania State University Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 41, Issue 4, October 1974, Pages 445–457, https://doi.org/10.2307/2296696 Published: 01 October 1974

Journal Article Unbounded Utility Functions in Expected Utility Theory Get access Peter C. Fishburn Peter C. Fishburn Pennsylvania State University Search for other works by this author on: Oxford Academic Google Scholar The Quarterly Journal of Economics, Volume 90, Issue 1, February 1976, Pages 163–168, https://doi.org/10.2307/1886093 Published: 01 February 1976

I. Subset choice conditions, 320. — II. Methods for computing C, 323. — III. Two examples, 325. — IV. Discussion, 326.

This paper considers a generalized mean value m(p) defined implicitly for a probability measure p on the reals as the unique y for which J +(x, y) dp(x) = 0, where 0 is skewsymmetric and strictly increasing in its first argument. Conditions on m that are necessary and sufficient for the implicit characterization are given and its relationship to certainty equivalence is discussed.

[A choice function, which maps each set of alternatives in a domain of feasible sets into a non-empty subset of itself (called the choice set), is said to be representable by a weak order if some weak order on the alternatives has maximum elements within each feasible set, all of which are in the choice set of that feasible set. A Partial Congruence Axiom ("every non-empty finite collection of feasible sets has an alternative which is in the choice set of every feasible set in the collection which contains that alternative") is shown to be necessary and sufficient for weak order representability when all choice sets are finite. A stronger form of partial congruence is proved to be necessary and sufficient for weak order representability when the number of feasible sets is countable, regardless of the cardinalities of the choice sets. The general case of arbitrary cardinalities for the domain and the choice sets is presently unsettled.]

[Arrow's impossibility theorem can be viewed as requiring that each subset of two social alternatives be a potential feasible subset or environment, with transitive and complete social choices over these subsets for each profile of individual preference orders. The feasibility assumption for every two-alternative subset is relaxed with consequent changes in the social ordering condition. An Arrow-type impossibility result still obtains when the set of social alternatives is the union of two disjoint sets, each of which has two or more elements, and when \{x, y\} is feasible whenever x is from one set and y is from the other. Variants of the basic theorem are included, one of which requires that strict binary social choices be acyclic.]

[Transitivity-like properties for binary social choices on a triple of alternatives are shown to follow from simple conditions that apply within each voter preference profile, coupled with structural profile restrictions such as those used in single-peakedness. These results are compared to results obtained under the simple majority rule. The special intraprofile conditions used in the main theorem are related to interprofile conditions such as independence, neutrality, and monotonicity.]