# Utility theory

**DOI:**https://doi.org/10.1007/1-4020-0611-X_1096

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*...

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