Utility theory

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...