Social Choice Correspondence (COMSOC)

Definition

Social Choice Correspondence ( COMSOC)

For a non-empty set of alternatives and voters, a social choice correspondence is a voting rule

Here is the set of preference rankings, and is the power set of . Given a profile , the rule returns a non-empty set of winning alternatives. Several winners are allowed; no winner is not.

Unlike a social choice function, it need not select a single winner. Multiple winners do not necessarily form an elected committee; they may be tied alternatives.

Resoluteness

Definition

Resolute Social Choice Correspondence ( COMSOC)

A social choice correspondence is resolute if it selects exactly one winner for every preference profile:

It therefore determines a social choice function by

Resoluteness concerns the whole voting rule: a unique winner on just one profile is not enough.

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