Independence of clones criterion

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In social choice theory, the independence of (irrelevant) clones criterion says that adding a clone, i.e. a new candidate very similar to an already-existing candidate, should not spoil the results.^[1] It can be considered a very weak form of the independence of irrelevant alternatives (IIA) criterion.

A group of candidates are called clones if they are always ranked together, placed side-by-side, by every voter; no voter ranks any of the non-clone candidates between or equal to the clones. In other words, the process of cloning a candidate involves taking an existing candidate C, then replacing them with several candidates C1, C2... who are slotted into the original ballots in the spot where C previously was, with the clones being arranged in any order. 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.

Ranked pairs, the Schulze method, and any system that satisfies independence of irrelevant alternatives such as range voting or majority judgment satisfies the criterion. Instant-runoff voting is generally described as passing, but this may depend on specific details in how the criterion is defined and how tied ranks are handled.^[2]

The Borda count, minimax, Kemeny–Young, Copeland's method, plurality, and the two-round system all fail the independence of clones criterion. Voting methods that limit the number of allowed ranks also fail the criterion, because the addition of clones can leave voters with insufficient space to express their preferences about other candidates. For similar reasons, ballot formats that impose such a limit may cause an otherwise clone-independent method to fail.

This criterion is very weak, as adding a substantially similar (but not quite identical) candidate to a race can still substantially affect the results and cause vote splitting. For example, the center squeeze pathology that affects instant-runoff voting means that several similar (but not identical) candidates competing in the same race will tend to hurt each others' chances of winning.^[3]