Independence of clones criterion
Encyclopedia
In voting system
s 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.
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.
The Borda count
is an example of a clone positive method. Plurality
is an example of a clone negative method because of vote-splitting.
, 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
also meet independence of clones.
The Borda count
, Minimax
, two-round system
, Bucklin voting
and plurality
fail the independence of clones criterion.
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.
A obtains 55 Borda points (55 x 1 + 45 x 0) and B obtains 45 Borda points (55 x 0 + 45 x 1).
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:
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).
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.
Voting system
A voting system or electoral system is a method by which voters make a choice between options, often in an election or on a policy referendum....
s theory, the independence of clones criterion measures an election method's robustness to strategic nomination. Nicolaus Tideman
Nicolaus Tideman
T. Nicolaus Tideman is a Professor of Economics at Virginia Polytechnic Institute and State University. He received his Bachelor of Arts in economics and mathematics from Reed College in 1965 and his PhD in economics from the University of Chicago in 1969...
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.
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
Borda count
The Borda count is a single-winner election method in which voters rank candidates in order of preference. The Borda count determines the winner of an election by giving each candidate a certain number of points corresponding to the position in which he or she is ranked by each voter. Once all...
is an example of a clone positive method. Plurality
Plurality voting system
The plurality voting system is a single-winner voting system often used to elect executive officers or to elect members of a legislative assembly which is based on single-member constituencies...
is an example of a clone negative method because of vote-splitting.
Complying methods
Instant-runoff votingInstant-runoff voting
Instant-runoff voting , also known as preferential voting, the alternative vote and ranked choice voting, is a voting system used to elect one winner. Voters rank candidates in order of preference, and their ballots are counted as one vote for their first choice candidate. If a candidate secures a...
, approval voting
Approval voting
Approval voting is a single-winner voting system used for elections. Each voter may vote for as many of the candidates as the voter wishes. The winner is the candidate receiving the most votes. Each voter may vote for any combination of candidates and may give each candidate at most one vote.The...
and range voting
Range voting
Range voting is a voting system for one-seat elections under which voters score each candidate, the scores are added up, and the candidate with the highest score wins.A form of range voting was apparently used in...
meet the independence of clones criterion. Some election methods that comply with the Condorcet criterion
Condorcet criterion
The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared with every other candidate, is preferred by more voters. Informally, the Condorcet winner is the person who would win a two-candidate election against each of the other candidates...
such as Ranked pairs
Ranked Pairs
Ranked pairs or the Tideman method is a voting system developed in 1987 by Nicolaus Tideman that selects a single winner using votes that express preferences. RP can also be used to create a sorted list of winners....
and Schulze
Schulze method
The Schulze method is a voting system developed in 1997 by Markus Schulze that selects a single winner using votes that express preferences. The method can also be used to create a sorted list of winners...
also meet independence of clones.
The Borda count
Borda count
The Borda count is a single-winner election method in which voters rank candidates in order of preference. The Borda count determines the winner of an election by giving each candidate a certain number of points corresponding to the position in which he or she is ranked by each voter. Once all...
, Minimax
Minimax Condorcet
In voting systems, the Minimax method is one of several Condorcet methods used for tabulating votes and determining a winner when using preferential voting in a single-winner election...
, two-round system
Two-round system
The two-round system is a voting system used to elect a single winner where the voter casts a single vote for their chosen candidate...
, Bucklin voting
Bucklin voting
Bucklin voting is a class of voting systems that can be used for single-member and multi-member districts. It is named after its original promoter, James W. Bucklin of Grand Junction, Colorado, and is also known as the Grand Junction system...
and plurality
Plurality voting system
The plurality voting system is a single-winner voting system often used to elect executive officers or to elect members of a legislative assembly which is based on single-member constituencies...
fail 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.