Kemeny Winner (COMSOC)

Definition

Kemeny Winner ( COMSOC)

A Kemeny winner is an alternative ranked first in at least one Kemeny preference ranking. For a profile $R$ over alternatives $C$,

$$x\text{ is a Kemeny winner}⟺\exists \text{ Kemeny ranking }{\succ }^{\ast }\text{ of }R:\forall y\in C\setminus \{x\},x{\succ }^{\ast }y.$$

It is enough for one optimal ranking to place $x$ first; not every optimal ranking must do so. Different Kemeny rankings may have different first alternatives, yielding several Kemeny winners.