Preference (COMSOC)

Definition

Preference ( COMSOC)

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

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

From Preferences to Rankings

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

records , , and, by transitivity, . 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.