Utility theory is the systematic study of preference structures and ways to represent preferences quantitatively. The objects on which preferences are defined could be potential outcomes of a decision, decision alternatives, individual or family consumption bundles in a fixed time period, time streams of net profits, investment portfolios, the entrees on a restaurant menu, or just about anything else. The preferences themselves are usually those of an individual, but are sometimes attributed to groups or organizations.
Let A denote the set of objects on which preferences are defined and let ⩾ be a binary relation on A, that is, a set of ordered pairs (x, y) of objects in A. When (x, y) is a member of ⩾, it is customary to write x ⩾ y and to say that x is at least as preferred as y. If x ⩾ y and not(y ⩾ x), then xis (strictly) preferred to y; if x ⩾ y and y ⩾ x then x and y are equally preferred, or are indifferent; if neither x ⩾ y nor y ⩾ x then x and y are preferentially incomparable...
- Eatwell, J., Milgate, M., and Newman, P., eds. (1990). The New Palgrave: Utility and Probability, Macmillan, London.Google Scholar
- Fishburn, P.C. (1970). Utility Theory for Decision Making, Wiley, New York.Google Scholar
- Fishburn, P.C. (1988). Nonlinear Preference and Utility Theory, The Johns Hopkins University Press, Baltimore.Google Scholar
- Fishburn, P.C. (1991). Nontransitive Preferences in Decision Theory, Jl. Risk & Uncertainty 4, 113–134.Google Scholar
- Keeney, R.L. and Raiffa, H. (1976). Decisions with Multiple Objectives: Preferences and Value Trade-offs, Wiley, New York.Google Scholar
- Luce, R. D. and Suppes, P. (1965). Preference, Utility and Subjective Probability, In Handbook of Mathematical Psychology, III, R. D. Luce, R. R. Bush and E. Galanter, eds. Wiley, New York, 249–410.Google Scholar
- Page, A.N., ed. (1968). Utility Theory: A Book of Readings, Wiley, New York.Google Scholar
- Raiffa, H. (1968). Decision Analysis: Introductory Lectures on Choice under Uncertainty, Addison-Wesley, Reading, Massachusetts.Google Scholar
- Savage, L.J. (1954). The Foundations of Statistics, Wiley, New York.Google Scholar
- Wakker, P.P. (1989). Additive Representations of Preferences, Kluwer, Dordrecht, The Netherlands.Google Scholar