In expected utility theory

Expected utility hypothesis

In economics, game theory, and decision theory the expected utility hypothesis is a theory of utility in which "betting preferences" of people with regard to uncertain outcomes are represented by a function of the payouts , the probabilities of occurrence, risk aversion, and the different utility...

, a lottery is a discrete distribution of probability

Probability

Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

 on a set of states of nature. The elements of a lottery

Lottery

A lottery is a form of gambling which involves the drawing of lots for a prize.Lottery is outlawed by some governments, while others endorse it to the extent of organizing a national or state lottery. It is common to find some degree of regulation of lottery by governments...

 correspond to the probability that a certain outcome arises from a given state of nature

State of nature

State of nature is a term in political philosophy used in social contract theories to describe the hypothetical condition that preceded governments...

. In economics

Economics

Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...

 individuals are assumed to rank lotteries according to a rational system of preferences

Rational choice theory

Rational choice theory, also known as choice theory or rational action theory, is a framework for understanding and often formally modeling social and economic behavior. It is the main theoretical paradigm in the currently-dominant school of microeconomics...

, unless one follows a behavioral economics approach.

Preference under risk and uncertainty

People have preferences over a set of lotteries and outcomes.