Independence of Irrelevant Ballots
IIB is equivalent to the Blank Ballot Criterion. It says that a voter who has no preference between any candidates should not impact which of them wins or loses by voting.
A generalization of this concept is to treat an irrelevant ballot as simply being a ballot with no preference between the candidates in a set of candidates, and the requirement as being that that ballot shouldn't impact who wins or loses among that set of candidates.
In general, Largest remainder methods violate this criterion because an irrelevant voter will change the size of the quota. See the Quota rule#Notes for an example.
Blank Ballot Criterion
Definitions
A blank ballot is a ballot that fails to indicate any preference between any of the candidates. For cardinal methods, this can mean each candidate is given a score of zero or the same positive score (including approval in approval methods).
Statement of Criterion
The addition of one or more blank ballots cannot change the winner.
Complying Methods
- Complies: Approval voting, Cardinal Ratings, Schulze, COWPEA, COWPEA Lottery, Propotional Approval Voting
- Fails: Median Ratings