# Rational choice theory

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Rational decision making entails choosing an action given one's preferences, the actions one could take, and expectations about the outcomes of those actions. Actions are often expressed as a set, for example a set of j exhaustive and exclusive actions:

For example, if a person is to vote for either Roger or Sara or to abstain, their set of possible voting actions is:

Individuals can also have similar sets of possible outcomes.

Rational choice theory makes two assumptions about individuals' preferences for actions:

• Completeness – all actions can be ranked in an order of preference (indifference between two or more is possible).
• Transitivity – if action a1 is preferred to a2, and action a2 is preferred to a3, then a1 is preferred to a3.

Together these assumptions form the result that given a set of exhaustive and exclusive actions to choose from, an individual can rank them in terms of his preferences, and that his preferences are consistent.

An individual's preferences can also take forms:

• Strict preference occurs when an individual prefers a1 to a2, but not a2 to a1.
• In some models, a weak preference can be held in which an individual has a preference for at least aj, similar to the mathematical operator ≤.
• Indifference occurs when an individual does not prefer a1 to a2, or a2 to a1.

In more complex models, other assumptions are often incorporated, such as the assumption of independence axiom. Also, with dynamic models that include decision-making over time, time inconsistency may affect an individual's preferences.

### Other assumptions

Often, some possibly unrealistic assumptions are made about the real world outside of academia in order to get tractable and testable predictions. These can include:

• An individual has full or perfect information about exactly what will occur due to any choice made. More complex models rely on probability to describe outcomes.
• An individual has the cognitive ability and time to weigh every choice against every other choice. Studies about the limitations of this assumption are included in theories of bounded rationality.

Even more realistic theories of human action include such components as Amos Tversky and Daniel Kahneman's prospect theory, which reflects the empirical finding as that, contrary to rational choice theory, individuals attach extra value to items that they already own compared to similar items owned by others. To rational choice theory, the amount that an individual is willing to pay for an item (such as a drinking mug) should equal the amount he or she is willing to be paid in order to part with it. In experiments, the former price is typically significantly higher than the latter. Behavioral economics has added a large number of other amendments to our picture of human behavior that go against pure economic rationality.

### Utility maximization

Often preferences are described by their utility function or payoff function. This is an ordinal number an individual assigns over the available actions, such as:

The individual's preferences are then expressed as the relation between these ordinal assignments. For example, if an individual prefers the candidate Sara over Roger over abstaining, their preferences would have the relation: