Unanimous Voting Rule (COMSOC)

Definition

Unanimous Voting Rule ( COMSOC)

A voting rule is unanimous if an alternative ranked first by every voter wins. For every non-empty profile $R=({\succ }_1,\dots ,{\succ }_n)$ over $C$,

$$(\forall i\in \{1,\dots ,n\}\forall y\in C\setminus \{x\}:x{\succ }_{i}y)⟹x\in \lambda (R).$$

All voters must agree on the first alternative; their lower rankings may differ. For a single-winner rule $f$, the conclusion is $f(R)=x$. Requiring $\lambda (R)=\{x\}$ is the stronger, unique-winner version for set-valued rules.