Plurality criterion is a

voting system criterion Electoral systems are the rules for conducting elections, a main component of which is the algorithm for determining the winner (or several winners) from the ballots cast. This article discusses methods and results of comparing different electora ...

devised by Douglas R. Woodall for ranked voting methods with incomplete ballots. It is stated as follows: :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 methods which require voters to strictly rank all the candidates (and so do not allow truncation). The

Borda count The Borda count is a family of positional voting rules which gives each candidate, for each ballot, a number of points corresponding to the number of candidates ranked lower. In the original variant, the lowest-ranked candidate gets 0 points, the ...

is usually defined in this way. Woodall has called the Plurality criterion "a rather weak property that surely must hold in any real election" opining that "every reasonable electoral system seems to satisfy it." Most proposed methods do satisfy it, including

Plurality voting Plurality voting refers to electoral systems in which a candidate, or candidates, who poll more than any other counterpart (that is, receive a plurality), are elected. In systems based on single-member districts, it elects just one member per ...

, IRV, Bucklin voting, and

approval voting Approval voting is an electoral system in which voters can select many candidates instead of selecting only one candidate. Description Approval voting ballots show a list of the options of candidates running. Approval voting lets each voter i ...

. Among

Condorcet method A Condorcet method (; ) is an election method that elects the candidate who wins a majority of the vote in every head-to-head election against each of the other candidates, that is, a candidate preferred by more voters than any others, whenever ...

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 The Schulze method () is an electoral 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. The Schulze method is also known a ...

, Ranked Pairs, or

Minimax Minimax (sometimes MinMax, MM or saddle point) is a decision rule used in artificial intelligence, decision theory, game theory, statistics, and philosophy for ''mini''mizing the possible loss for a worst case (''max''imum loss) scenario. When ...

, Plurality is satisfied. Plurality is failed when ''margins'' is used.

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.

References

* D R Woodall,
Properties of Preferential Election Rules
, '' Voting matters'', Issue 3 (1994), pp. 8–15. * D R Woodall,
Monotonicity and Single-Seat Election Rules
, ''Voting matters'', Issue 6 (1996), pp. 9–12. {{voting systems Electoral system criteria