Plurality criterion
Encyclopedia
Plurality criterion is a voting system criterion devised by Douglas R. Woodall for ranked voting methods with incomplete ballots. It is stated as follows:
This criterion is trivially satisfied by rank ballot
methods which require voters to strictly rank all the candidates (and so do not allow truncation). The Borda count
is usually defined in this way.
Woodall has called the Plurality criterion "a rather weak property that surely must hold in any real election", and noted that "every reasonable electoral system seems to satisfy it." Most proposed methods do satisfy it, including Plurality voting, IRV, Bucklin voting
, and approval voting
.
Among Condorcet method
s which permit truncation, whether the Plurality criterion is satisfied depends often on the measure of defeat strength. When winning votes is used as the measure of defeat strength in methods such as the Schulze method
, Ranked Pairs
, or Minimax
, Plurality is satisfied. Plurality is failed when margins is used. Minimax
using pairwise opposition also fails Plurality.
When truncation is permitted under Borda count, Plurality is satisfied when no points are scored to truncated candidates, and ranked candidates receive no fewer votes than if the truncated candidates had been ranked. If truncated candidates are instead scored the average number of points that would have been awarded to those candidates had they been strictly ranked, or if Nauru's modified Borda count is used, the Plurality criterion is failed.
- If the number of ballots ranking A as the first preference is greater than the number of ballots on which another candidate B is given any preference, then A's probability of winning must be no less than B's.
This criterion is trivially satisfied by rank ballot
Preferential voting
Preferential voting is a type of ballot structure used in several electoral systems in which voters rank candidates in order of relative preference. For example, the voter may select their first choice as '1', their second preference a '2', and so on...
methods which require voters to strictly rank all the candidates (and so do not allow truncation). 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 usually defined in this way.
Woodall has called the Plurality criterion "a rather weak property that surely must hold in any real election", and noted that "every reasonable electoral system seems to satisfy it." Most proposed methods do satisfy it, including Plurality voting, IRV, 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 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...
.
Among Condorcet method
Condorcet method
A Condorcet method is any single-winner election method that meets the Condorcet criterion, which means the method always selects the Condorcet winner if such a candidate exists. The Condorcet winner is the candidate who would beat each of the other candidates in a run-off election.In modern...
s which permit truncation, whether the Plurality criterion is satisfied depends often on the measure of defeat strength. When winning votes is used as the measure of defeat strength in methods such as the Schulze method
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...
, 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....
, or 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...
, Plurality is satisfied. Plurality is failed when margins is used. 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...
using pairwise opposition also fails Plurality.
When truncation is permitted under Borda count, Plurality is satisfied when no points are scored to truncated candidates, and ranked candidates receive no fewer votes than if the truncated candidates had been ranked. If truncated candidates are instead scored the average number of points that would have been awarded to those candidates had they been strictly ranked, or if Nauru's modified Borda count is used, the Plurality criterion is failed.