Unanimous Preference Profile (COMSOC)

comsoc

Definition

Unanimous Preference Profile (COMSOC)

In COMSOC, a preference profile is unanimous on the ordered pair if every voter ranks the alternative above the alternative .

Formally, let

be a preference profile over alternatives . For , define

The profile is unanimous on precisely when

If a profile is called unanimous without specifying a pair, this usually means full unanimity: all voters have the same complete preference ranking. Pairwise unanimity is weaker; it only requires agreement about one ordered pair.

Notation

Some lecture notes write the condition as

Here denotes the voters in the profile who rank above , while denotes the whole profile or voter set. Thus the equality means that the supporting set for is the whole profile.

Example

Pairwise unanimity without full unanimity

Let

Every voter ranks above , so the profile is unanimous on :

The profile is not fully unanimous, because the voters do not have the same complete ranking.