Definition
Strict Preference Ranking ( COMSOC)
A strict preference ranking over alternatives
orders every pair of distinct alternatives without ties. It is a relation satisfying Thus it is irreflexive and transitive. “Exactly one direction” combines asymmetry (not both directions) with comparability (at least one direction for distinct alternatives). The statement
expresses a strict preference for over . These are the rankings in
: the preference ranking note uses “ranking” to mean this strict, no-ties case. A strict relation alone need not compare every pair; a strict ranking does.