View source for Independence of Irrelevant Ballots

'''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 method|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.

=== Complying Methods ===

* '''Complies''': [[Approval voting]], [[Cardinal Ratings]], [[Schulze method|Schulze]], [[COWPEA]], [[COWPEA|COWPEA Lottery]], [[Proportional_approval_voting|Propotional Approval Voting]]
* '''Fails''': [[Median Ratings]], [[Phragmen's voting rules]], [[Monroe's method]]

[[Category:Voting system criteria]]