Collective Preference Ranking (COMSOC)

Definition

Collective Preference Ranking ( COMSOC)

A collective preference ranking is one ranking of all alternatives intended to represent a group’s preferences. For a profile $R=({\succ }_1,\dots ,{\succ }_n)$ over alternatives $C$, it is a relation

$$\succ \in \mathcal{L}(C),a\succ b\text{ means “the group ranks }a\text{ above }b\text{”,}$$

where $\mathcal{L}(C)$ is the set of complete, strict rankings over $C$. The profile contains one ranking per voter; a collective ranking gives one order for the group. It need not coincide with any voter’s ranking or express unanimous agreement.

A candidate collective ranking is a proposed group order; an aggregation rule determines which proposals are selected. A social welfare function selects one collective ranking for each profile. A winner set alone does not rank all alternatives.

A general collective preference relation need not be a ranking: pairwise aggregation can yield cycles even when every individual ranking is transitive. Under the strict-ranking convention used here, a collective preference ranking must be complete, transitive and without ties.