Independence of clones criterion
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In voting systems theory, the independence of clones criterion is a criterion that measures an election method's robustness to strategic nomination. The criterion, first formulated by Nicolaus Tideman[1], states that the addition of a candidate identical to one already present in an election will not cause the winner of the election to change.
In some systems, the introduction of a clone will tend to divide support between the similar candidates, making it less likely either will be elected. In some other systems, the presence of a clone will tend to reduce support for dissimilar candidates, making it more likely that one (or more) of the similar candidates will be elected. In yet other systems, the introduction of clones will not significantly affect the chances that one of the similar candidates will be elected. There are further systems where the effect of the introduction of clones depends on the distribution of other votes.
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[edit] Clone Negative and Clone Positive
Elections methods that fail independence of clones can either be clone negative (the addition of an identical candidate will decrease a candidate’s chance of winning) or clone positive (the addition of an identical candidate will increase a candidate’s chance of winning).
The Borda count is an example of a clone positive method. Plurality is an example of a clone negative method.
An election method that fails the independence of clones criterion in the direction of being clone negative is also sometimes said to fail Clone-Winner, whereas a method that fails it in the direction of being clone positive fails Clone-Loser; the terms were originally used by Douglas Woodall.
[edit] Complying Methods
Instant-runoff voting, approval voting and range voting meet the independence of clones criterion. Many election methods that comply with the Condorcet criterion such as Ranked pairs and Schulze[2] also meet independence of clones.
The Borda count, two-round system, Bucklin voting and plurality fail the independence of clones criterion.
[edit] Examples of failure of the independence of clones criterion
[edit] Plurality
For example in an election there are two candidates A and B. Candidate A receives 100 votes and candidate B receives 75 votes. A clone of candidate A, called "candidate A(clone)" is added to the candidate set. The votes are now A 50, A(clone) 50 and B 75.
| A 100 | A 50 |
| A(clone) not present | A(clone) 50 |
| B 75 | B 75 |
As a result of the presence on the ballot of another candidate identical to candidate A the winner of the election has changed from A to B.
[edit] Borda Count
For example in an election there are two candidates A and B. The following votes are cast:
| 55: A>B | 45: B>A |
A obtains 55 Borda points (55 x 1 + 45 x 0) and B obtains 45 Borda points (55 x 0 + 45 x 1).
| A 55 | B 45 |
Candidate A is the winner.
A candidate identical to candidate B candidate B(clone) is added to the candidate set. The following votes are now cast:
| 55: A>B>B(clone) | 45: B>B(clone)>A |
Candidate A has 110 Borda points (55 x 2 + 45 x 0). Candidate B has 145 Borda points (55 x 1 + 45 x 2). Candidate B(clone) has 45 Borda points (55 x 0 + 45 x 1).
| A 110 | B 145 | B(clone) 45 |
As a result of the addition of candidate B(clone) to the candidate set the winner of the election has changed from A to B.
