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Preference (or "taste") is a concept, used in the social sciences, particularly economics. It assumes a real or imagined "choice" between alternatives and the possibility of rank ordering of these alternatives, based on happiness, satisfaction, gratification, enjoyment, utility they provide. More generally, it can be seen as a source of motivation. In cognitive sciences, individual preferences enable choice of objectives/goals.

Also, more consumption of a normal good is generally (but not always) assumed to be preferred to less consumption.

Contents 1 Preference in economics 1.1 Rock, Paper, Scissors 2 Notation 3 References 4 See also 5 External links

In microeconomics, preferences of consumers and other entities are modelled with preference relations.

Let S be the set of all "packages" of goods and services (or more generally "possible worlds"). Then ≤ is a preference relation on S if it is a binary relation on S such that a ≤ b if and only if b is at least as preferable as a. It is conventional to say "b is weakly preferred to a", or just "b is preferred to a". If a ≤ b but not b ≤ a, then the consumer strictly prefers b to a, which is written a < b. If a ≤ b and b ≤ a then the consumer is indifferent between a and b.

These assumptions are commonly made:

• The relation is reflexive: a ≤ a
• The relation is transitive: a ≤ b and b ≤ c then a ≤ c. Together with reflexivity this means it is a preorder
• The relation is complete: for all a and b in S we have a ≤ b or b ≤ a or both (notice that completeness implies reflexivity). This means the consumer is able to form an opinion about the relative merit of any pair of bundles.
• If S is a topological space, then the relation is continuous if for every pair of convergent sequences and with for all n has x ≤ y. This is automatically satisfied if S is finite.

If ≤ is both transitive and complete, then it is a rational preference relation. In some literature, a transitive and complete relation is called a weak order (or total preorder)http://en.wikipedia.org/wiki/Strict_weak_ordering#Total_preorders.

Completeness is more philosophically questionable. In most applications, S is an infinite set and the consumer is not conscious of all preferences. For example, one does not have to make up one's mind about whether one prefers to go on holiday by plane or by train if one does not have enough money to go on holiday anyway (although it can be nice to dream about what one would do if one would win the lottery). However, preference can be interpreted as a hypothetical choice that could be made rather than a conscious state of mind. In this case, completeness amounts to an assumption that the consumer can always make up their mind whether they are indifferent or prefer one option when presented with any pair of options.

Behavioral economics investigates the circumstances when human behavior is consistent and inconsistent with these assumptions.

The indifference relation ~ is an equivalence relation. Thus we have a quotient set S/~ of equivalence classes of S, which forms a partition of S. Each equivalence class is a set of packages that is equally preferred. If there are only two commodities, the equivalence classes can be graphically represented as indifference curves. Based on the preference relation on S we have a preference relation on S/~. As opposed to the former, the latter is antisymmetric and a total order.

It is usually more convenient to describe a preference relation on S with a utility function , such that u(a) ≤ u(b) if and only if a ≤ b. A continuous utility function always exists if ≤ is a continuous rational preference relation on Rⁿ. For any such preference relation, there are many continuous utility functions that represent it. Conversely, every utility function can be used to construct a unique preference relation.

All the above is independent of the prices of the goods and services and independent of the budget of the consumer. These determine the feasible packages (those he or she can afford). In principle the consumer chooses a package within his or her budget such that no other feasible package is preferred over it; the utility is maximized.

However, in practice, it is sometimes the case that a preference relation is not transitive. This can be exemplified by the traditional game, Rock, Paper, Scissors : Rock is preferred to Scissors, Scissors are preferred to Paper, but Paper is preferred to Rock.

Similar examples occur in nature; for example, in the lizard Uta stansburiana, there are three varieties of male which, for the purposes of mating, exhibit a circular arrangement of preference.

The Voting paradox is a one such relation. Suppose the consumer has an apple, and prefers apples to oranges, oranges to bananas, and bananas to apples. Then, the consumer would be prepared to pay, say, one cent to trade their apple for a banana, because they prefer bananas to apples. After that, they would pay one cent more to trade their banana for an orange, and again the orange for an apple, and so on. (See: Intransitivity. Occurences.)

In intransitive cases, it is not possible to model a utility function for the scenarios.

Sometimes symbols like are used as a reminder that equivalence is not necessarily equality.

• Pairwise comparison
• Revealed preference
• Arrow's paradox
• Behavioral finance
• Economic subjectivism
• Envy
• Gibbard-Satterthwaite theorem
• Greed
• Hope
• Lexicographic preferences
• Motivation
• Preferential voting
• Second-order desire
• Sexual desire
• Sexual orientation
• Strict weak ordering
• Time preference theory of interest
• Preference regression (in marketing)
• preferred number

• Stanford Encyclopedia of Philosophy article on 'Preferences'
• Customer preference formation (white paper from ICR)

view	Topics in game theory
Definitions	Normal form game · Extensive form game · Cooperative game · Information set · Preference
Equilibrium concepts	Nash equilibrium · Subgame perfection · Bayesian-Nash · Perfect Bayesian · Trembling hand · Proper equilibrium · Epsilon-equilibrium · Correlated equilibrium · Sequential equilibrium · Quasi-perfect equilibrium · Evolutionarily stable strategy · Risk dominance
Strategies	Dominant strategies · Mixed strategy · Tit for tat · Grim trigger · Collusion
Classes of games	Symmetric game · Perfect information · Dynamic game · Repeated game · Signaling game · Cheap talk · Zero-sum game · Mechanism design · Stochastic game · Nontransitive game
Games	Prisoner's dilemma · Traveler's dilemma · Coordination game · Chicken · Volunteer's dilemma · Dollar auction · Battle of the sexes · Stag hunt · Matching pennies · Ultimatum game · Minority game · Rock, Paper, Scissors · Pirate game · Dictator game · Public goods game · Nash bargaining game · Blotto games  · War of attrition
Theorems	Minimax theorem · Purification theorems · Folk theorem · Revelation principle · Arrow's theorem