Co-winner (COMSOC)

Definition

Co-winner ( COMSOC)

For a social choice correspondence $\lambda$ and a profile $R$, an alternative $c\in C$ is a co-winner if it belongs to the winner set:

$$c\text{ is a co-winner}⟺c\in \lambda (R).$$

Other alternatives may also win. In contrast, $c$ is the unique winner exactly when $\lambda (R)=\{c\}$. Thus a unique winner is also a co-winner; co-winning does not require an actual tie.