In voting systems theory, the independence of clones criterion measures an election method's robustness to strategic nomination. Nicolaus Tideman was the first to formulate this criterion, which states that the winner must not change due to the addition of a non-winning candidate who is similar to a candidate already present. To be more precise, a subset of the candidates, called a set of clones, exists if no voter ranks any candidate outside the set between (or equal to) any candidates that are in the set. If a set of clones contains at least two candidates, the criterion requires that deleting one of the clones must not increase or decrease the winning chance of any candidate not in the set of clones.
In some systems (such as the plurality vote), the addition of a similar candidate divides support between similar candidates, which can cause them both to lose. In some other systems (such as the Borda count), the addition of a similar alternative increases the apparent support for one of the similar candidates, which can cause it to win. In yet other systems (such as ranked pairs), the introduction of similar alternatives does not affect the chances of the dissimilar candidates, as required by the criterion. There are further systems where the effect of the additional similar alternatives depends on the distribution of other votes.
Clone negative and clone positive
Election methods that fail independence of clones can be clone negative (the addition of a similar candidate decreases another candidate's chance of winning) or clone positive (the addition of a similar candidate increases another candidate's chance of winning).
A method can also fail the independence of clones method in a way that's neither clone positive nor negative. This happens if the method changes its decision about the winner when a non-winning candidate is cloned, but the new winner is not the candidate that was cloned. The effect is called crowding.
The Borda count is an example of a clone positive method. Plurality voting is an example of a clone negative method because of vote-splitting. Copeland's method is an example of a method that exhibits crowding.
Compliant methods
Instant-runoff voting and some election methods that comply with the Condorcet criterion such as ranked pairs and the Schulze method also meet independence of clones.
The interpretation of the term "set of clones" for scored voting systems is controversial. If clones are candidates that are considered nearly identical by the voters, range voting and majority judgment satisfy the criterion. If clones also include candidates that are still similar but clearly superior to an existing candidate, that superior clone can win in range voting, even if no inferior clone of that candidate would have won. However, since range voting and majority judgment satisfy the Independence of irrelevant alternatives criterion, the addition of clones never helps or harms candidates who are already present.
Some of the other methods that fail the criterion are the Borda count, minimax, the Kemeny–Young method, Copeland's method, Bucklin voting, the plurality vote, and the two-round system. Variants of Instant-runoff voting that eliminate multiple candidates per round (e.g. the contingent vote) or forbid the voters from ranking all the candidates (e.g. the supplementary vote) also fail the criterion.
Examples
Borda count
Consider an election in which there are two candidates, A and B. Suppose the voters have the following preferences:
Candidate A would receive 66% Borda points (66%×1 + 34%×0) and B would receive 34% (66%×0 + 34%×1). Thus candidate A would win by a 66% landslide.
Now suppose supporters of B nominate an additional candidate, B2, that is very similar to B but considered inferior by all voters. For the 66% who prefer A, B continues to be their second choice. For the 34% who prefer B, A continues to be their least preferred candidate. Now the voters' preferences are as follows:
Candidate A now has 132% Borda points (66%×2 + 34%×0). B has 134% (66%×1 + 34%×2). B2 has 34% (66%×0 + 34%×1). The nomination of B2 changes the winner from A to B, overturning the landslide, even though the additional information about voters' preferences is redundant due to the similarity of B2 to B.