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 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 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 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
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.
Axioms for an individual's preferences over time, taken from the present perspective, usually assume that the individual will live, or expects to live, throughout a given horizon span. This paper offers an axiomatization that explicitly recognizes the uncertainty of an individual's lifetime. It divides a horizon span into n periods and assumes that if death is not immediate then it will occur at the end of one of the periods. The theory is based on an unconditional preference relation over potential future consumption streams that accounts for uncertain lifetime, along with a conditional preference order that is based on the hypothesis that death will occur at the end of period i. There is a conditional order for each i from 1 to n. The utility representation involves an order-preserving utility function for each of the n conditional orders such that one potential consumption stream is unconditionally preferred to another if, and only if, the sum of the conditional utilities for the first stream exceeds the sum of the conditional utilities for the second. It is argued that the theory seems fairly reasonable only if probability of survival does not depend significantly on past consumption.
[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.]
[A one-way expected utility representation has the expected utility of one probability measure greater than the expected utility of another probability measure whenever the first is preferred to the second. It requires preferences to be acyclic but not necessarily transitive, and does not require indifference to be transitive. Preference axioms which are sufficient for one-way expected utility for sets of simple probability measures have been presented before (see [8]). This paper uses additional axioms to extend the one-way representation to sets of discrete and more general probability measures.]