# Preference

**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. More generally, it can be seen as a source of motivation.

For example, happiness is generally preferred to suffering, sadness, or grief. Also, more consumption of a normal good is generally (but not always) assumed to be preferred to less consumption.

## Microeconomics

In microeconomics, a mathematical model for **preferences** of consumers can be as follows. For a discussion on the validity of this model, see also Indifference curve.

Let S be the set of all "packages" of goods and services.
For each consumer there is assumed to be binary relation <=, called a **preference relation**, on S.

a<=b means: b is at least as preferable as a.

Assumed properties:

- The relation is
**reflexive**: a<=a (this is logically true) - The relation is
**transitive**: a<=b and b<=c then a<=c (this is logically true, but in practice consumers may not always be that consistent) - For all a and b in S we have a<=b or b<=a or both:
- a<=b and not b<=a; this is also written a
- the converse
- a<=b and b<=a; this is also written a~b: the consumer prefers a and b equally, he or she is
**indifferent**to the choice.

- a<=b and not b<=a; this is also written a

However, in practice the consumer makes lots of choices, and if a is chosen while b also could have been chosen (say, they cost the same), it is reasonable to assume that apparently b<=a.

The **indifference relation** ~ is easily shown to be 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.

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.

In the case of only two products the equivalence classes can be graphically represented as indifference curves.

For a given preference relation on S we may construct a utility function U on S, with U(a)<=U(b) if and only if a<=b. It is not unique, it is determined up to a strictly monotonically increasing function.

Conversely, from a utility function follows a 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 principal the consumer chooses a package within his or her budget such that no other feasible package is preferred over it; the utility is maximized.