Chapter 39 Utility and subjective probability

Utility and subjective probability involve the systematic study of people's preferences and beliefs, including quantitative representations of preference and belief that facilitate analyses of problems in decision making and choice behavior. Its history spans more than 250 years and is mainly because of people in economics, mathematics, statistics, and psychology. Utility theory is primarily concerned with properties of a binary relation on a set X , where X could be a set of commodity bundles, decision alternatives, monetary gambles, n -tuples of pure strategies, and so forth, and x > y is interpreted as x is preferred to y . The formal development of utility and subjective probability is based on the notion of a binary relation. Special types of binary relations are identified by conjunctions of properties that are equivalence, linear order, weak order, and partial order.