Independence of clones criterion

Condorcet methods Positional voting Cardinal voting Quota-remainder methods Approval-based committees Fractional social choice Semi-proportional representation By ballot type Pathological response Strategic voting Paradoxes of majority rule Positive results 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 weak form of the independence of irrelevant alternatives (IIA) criterion that nevertheless is failed by a number of voting rules.

If they are allowed, its clone independence depends on specific details of how the criterion is defined and how tied ranks are handled.

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.

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 other's chances of winning.

Now suppose supporters of B nominate an additional candidate, B2, that is very similar to B but considered inferior by all voters.

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.

In typical elections, game theory suggests this manipulability of Borda can be expected to be a serious problem, particularly when a significant number of voters can be expected to vote their sincere order of preference (as in public elections, where many voters are not strategically sophisticated; cite Michael R. Alvarez of Caltech).

These examples show that Copeland's method violates the Independence of clones criterion.

Assume five candidates A, B, B2, B3 and C and 4 voters with the following preferences: Note, that B, B2 and B3 form a clone set.

Thus, Copeland's method is vulnerable against crowding and fails the independence of clones criterion.

Again, assume five candidates A, B, B2, B3 and C and 2 voters with the following preferences: Note, that B, B2 and B3 form a clone set.

Thus, Copeland's method is vulnerable against Teaming and fails the Independence of clones criterion.

Whenever the voters use an absolute scale that does not depend on the candidates running, range voting satisfies IIA and thus is also clone-independent.

This can be done strategically or just as a natural way of anchoring one's ratings to the candidates that matter in the election.

Assume five candidates A, B1, B2, B3 and C and 13 voters with the following preferences: Note, that B1, B2 and B3 form a clone set.

The preferences would be: The Kemeny–Young method arranges the pairwise comparison counts in the following tally table (with

This example shows that the minimax method violates the Independence of clones criterion.

Since all preferences are strict rankings (no equals are present), all three minimax methods (winning votes, margins and pairwise opposite) elect the same winners.

Thus, the minimax method is vulnerable against spoilers and fails the independence of clones criterion.

STAR voting consists of an automatic runoff between the two candidates with the highest rated scores.