Preference Specification

Synonyms

Preference Definition

Definition

Usually, preference relations are formalized as strict partial orders (SPO), which means that a preference relation ≻ satisfies the following properties:

• irreflexivity: $\forall x\ (x\nsucc x)$,

• transitivity: ∀x, y, z (x ≻ y ∧ y ≻ z → x≻z).

Additionally, an SPO ≻ is a weak order if ∀x, y, z (x ≻ y → x ≻ z ∨ z ≻ y), and a total order if ∀x, y (x ≻ y ∨ y ≻ x ∨ x = y).

The formal properties of orders capture the nature of preferences in an abstract, application-independent way. It is obvious that irreflexivity should hold: preferring an object over itself seems to violate the basic intuitions behind preference. But transitivity is debatable. On one hand, it captures the rationality of preferences [1, 2]. On the other, transitivity is sometimes violated by preference aggregation in voting scenarios [3]. The weak order property implies that the set ordered by the preference relation can be viewed as consisting of disjoint layers each of which...