Preference (COMSOC)

Definition

Preference ( COMSOC)

A preference expresses how a voter compares alternatives. For voter $v_i$, write

$$a{\succ }_{i}b\text{to mean}\text{“voter }{v}_i\text{ prefers }a\text{ to }b\text{”.}$$

The voter’s comparisons form a binary relation over the alternatives. This is relative: preferring $a$ to $b$ does not mean liking $a$ or disliking $b$, nor does it specify how much $a$ is preferred.

From Preferences to Rankings

A preference ranking arranges all alternatives from most to least preferred, without ties. The chain

$$a{\succ }_{i}b{\succ }_{i}c$$

records $a{\succ }_{i}b$, $b{\succ }_{i}c$, and, by transitivity, $a{\succ }_{i}c$. Thus a ranking represents one voter’s preferences as a strict total order; a profile collects one ranking per voter.

More general preference models may allow ties or incomparable alternatives, so preferences need not always form a strict ranking.