Independence of clones criterion

In voting systems theory, the independence of clones criterion measures an election method's robustness to strategic nomination. Nicolaus Tideman first formulated the criterion, which 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.^[1]

In some systems, the introduction of a clone tends to divide support between the similar candidates, worsening all their chances. In some other systems, the presence of a clone tends to reduce support for dissimilar candidates, improving the chances of one (or more) of the similar candidates. In yet other systems, the introduction of clones does not significantly affect the chances of similar candidates. There are further systems where the effect of the introduction of clones depends on the distribution of other votes.

Clone negative and clone positive

Elections methods that fail independence of clones can either be clone negative (the addition of an identical candidate decreases a candidate’s chance of winning) or clone positive (the reverse).

The Borda count is an example of a clone positive method. Plurality is an example of a clone negative method because of vote-splitting.

Complying methods

Instant-runoff voting, approval voting and range voting meet the independence of clones criterion. Some election methods that comply with the Condorcet criterion such as Ranked pairs and Schulze^[2] also meet independence of clones.

The Borda count, Minimax, two-round system, Bucklin voting and plurality fail the independence of clones criterion.

Examples of failure of the independence of clones criterion

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.

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.

References

1. ^ T. Nicolaus Tideman, "Independence of clones as a criterion for voting rules", Social Choice and Welfare Vol. 4, No. 3 (1987), pp. 185–206.
2. ^ M. Schulze, "A New Monotonic and Clone-Independent Single-Winner Election Method", Voting Matters 17 (2003), pp 9–19.

See also

• Strategic nomination