Independence of Irrelevant Ballots (IIB), also known as the Blank Ballot Criterion, says that a voter who has no preference between any candidates should not impact which of them wins or loses by voting. A blank ballot or irrelevant ballot is a ballot that fails to indicate any preference between any of the candidates. For ranked-ballot methods, this would mean all candidates are equally ranked or left unranked. For score or graded methods, this would mean that each candidate is given the same bottom-level or positive score/grade. For approval voting, every candidate would be approved or every candidate unapproved.
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. There are proportional cardinal methods that pass this criterion with "empty ballots" (where all candidates are given a zero or unapproved) but fail with "full ballots" (where candidates are given the same positive score or approved). For example, Phragmen's voting rules passes with empty ballots but fails with full ballots. Monroe's method fails with both full and empty ballots. In general, it is easier for a method to pass this criterion with empty ballots.