# Preference

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Preference

Preference (also called "taste" or "penchant") 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.

Preference in economics

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.

*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.
*The relation is continuous (if S is a topological space, this means that for every pair of convergent sequences $x_n ightarrow x$ and $y_n ightarrow y$ with $x_n leq y_n$ for all n, we have 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 ml|Strict weak ordering|Total_preorders|weak order (or total preorder).

If a consumer has a preference relation that violates transitivity, then an unscrupulous person can milk them as follows. 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 once cent to trade their banana for an orange, and again the orange for an apple, and so on. (See: "Intransitivity. Occurences.")

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 $u : S ightarrow extbf R$, 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 $R^n$. 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.

Notation

Sometimes symbols like $prec, succ, precsim, succsim$ are used as a reminder that equivalence is not necessarily equality.

References

*Kreps, David (1990). "A Course in Microeconomic Theory". New Jersey: Princeton University Press. ISBN 0-691-04264-0
*Mas-Colell, Andreu; Whinston, Michael; & Green, Jerry (1995). "Microeconomic Theory". Oxford: Oxford University Press. ISBN 0-19-507340-1

ee also

*Behavioral economics
*Convex preferences
*Economic subjectivism
*Envy
*Gibbard-Satterthwaite theorem
*Greed
*Hope
*Lexicographic preferences
*Motivation
*Pairwise comparison
*Preference regression (in marketing)
*Preferential voting
*Preferred number
*Revealed preference
*Second-order desire
*Sexual desire
*Sexual orientation
*Strict weak ordering
*Time preference theory of interest
*Nutrition
*Choice

* [http://plato.stanford.edu/entries/preferences/ Stanford Encyclopedia of Philosophy article on 'Preferences']
* [http://www.icrsurvey.com/docs/Customer%20Preference%20Formation_1205.doc Customer preference formation] (white paper from ICR)

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• préférence — [ preferɑ̃s ] n. f. • preferance v. 1458; de préférer 1 ♦ Jugement ou sentiment par lequel on place une personne, une chose au dessus des autres; jugement plus favorable. Les préférences de chacun. « Sur quelque préférence une estime se fonde »… …   Encyclopédie Universelle

• preference — pref·er·ence / pre frəns, fə rəns/ n 1: the right to prior payment of a debt with preference over the creditors of the heirs or legatees Louisiana Civil Code 2: the transfer of an insolvent debtor s interest in property to a creditor for an… …   Law dictionary

• Preference — (fr., spr. Preferangs), Stichspiel, mit Deutscher Karte unter drei, gewöhnlich aber unter vier Personen, so daß der Geber beim Spiele nicht betheiligt ist, gespielt. Der Geber läßt zur rechten Hand abheben, legt die zwei obersten Blätter (Talon)… …   Pierer's Universal-Lexikon

• Preference — Préférence Voir « préférence » sur le Wiktionnaire …   Wikipédia en Français

• preference — Preference. s. f. Choix que l on fait d une personne, d une chose plustost que d une autre. Preference certaine, incontestable. juste preference. demander, avoir, obtenir la preference. disputer, emporter la preference. donner la preference.… …   Dictionnaire de l'Académie française

• Preference — Pref er*ence, n. [Cf. F. pr[ e]f[ e]rence.] 1. The act of Preferring, or the state of being preferred; the setting of one thing before another; precedence; higher estimation; predilection; choice; also, the power or opportunity of choosing; as,… …   The Collaborative International Dictionary of English

• preference — a payment by a debtor made during a specified period (90 days or one year) prior to the filing that favors one creditor over others. Preference payments can usually be recovered and returned to the debtor s estate (Glossary of Common Bankruptcy… …   Glossary of Bankruptcy

• preference — [n1] first choice alternative, choice, cup of tea*, desire, druthers*, election, favorite, flash*, groove, inclination, option, partiality, pick, predilection, prepossession, propensity, say, say so*, selection, top, weakness; concepts 20,529,709 …   New thesaurus

• preference — [pref′ər əns] n. [MFr préférence < ML praeferentia < L praeferens, prp. of praeferre, to PREFER] 1. a preferring or being preferred; greater liking 2. the right, power, or opportunity of prior choice or claim 3. something preferred; one s… …   English World dictionary

• Préférence — (franz., spr. āngß , »Vorzug«), Kartenspiel zwischen drei Personen, das mit der deutschen Karte gespielt wird, und in dem die Mehrheit der Stiche den Gewinn entscheidet. Es hat seinen Namen von dem Vorzug, der darin einer Farbe vor der andern… …   Meyers Großes Konversations-Lexikon