Independence of clones criterion
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[edit] Definition
The addition to the candidate set for an election of a candidate identical to one already present will not cause the winner of the election to change.
[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.
[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 also meet independence of clones.
The Borda count, Top-two runoff, Bucklin 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 55 votes and candidate B receives 45 votes. A clone of candidate A candidate A(clone) is added to the candidate set. The votes are now A 30, A(clone) 25 and B 45.
| A 55 | A 30 |
| A(clone) not present | A(clone) 25 |
| B 45 | B 45 |
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.
