Preference

For other uses, see Preference (disambiguation).

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. Strict weak ordering|Total_preorders|weak order (or total preorder)}}.

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 $u :\; S\; \backslash rightarrow\; \backslash textbf\; R$, 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.

Rock, Paper, Scissors

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.

Notation

Sometimes symbols like $\backslash prec\; \backslash succ\; \backslash precsim\; \backslash succsim\; \backslash sim$ 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

See also

Look up prefer in Wiktionary, the free dictionary.

• 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

External links

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

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