Homogeneity is a common property for

voting system An electoral or voting system is a set of rules used to determine the results of an election. Electoral systems are used in politics to elect governments, while non-political elections may take place in business, nonprofit organizations and inf ...

s. The property is satisfied if, in any election, the result depends only on the proportion of ballots of each possible type. That is, if every ballot is replicated the same number of times, then the result should not change.

Complying methods

Any voting method that counts voter preferences proportionally satisfies homogeneity, including voting methods such as

Plurality voting Plurality voting refers to electoral systems in which the candidates in an electoral district who poll more than any other (that is, receive a plurality) are elected. Under single-winner plurality voting, and in systems based on single-member ...

Two-round system The two-round system (TRS or 2RS), sometimes called ballotage, top-two runoff, or two-round plurality, is a single-winner electoral system which aims to elect a member who has support of the majority of voters. The two-round system involves one ...

Single transferable vote The single transferable vote (STV) or proportional-ranked choice voting (P-RCV) is a multi-winner electoral system in which each voter casts a single vote in the form of a ranked ballot. Voters have the option to rank candidates, and their vot ...

Instant Runoff Voting Instant-runoff voting (IRV; ranked-choice voting (RCV), preferential voting, alternative vote) is a single-winner ranked voting election system where one or more eliminations are used to simulate runoff elections. When no candidate has a ...

Contingent vote The contingent vote is a two-stage electoral system that elects a single representative, in which the winner receives a majority of votes. It uses ranked voting. The voter ranks the candidates in order of preference, and when the votes are f ...

Coombs' method Coombs' method is a ranked voting system. Like instant-runoff (IRV-RCV), Coombs' method is a sequential-loser method, where the last-place finisher according to one method is eliminated in each round. However, unlike in instant-runoff, each rou ...

Approval voting Approval voting is a single-winner rated voting system where voters can approve of all the candidates as they like instead of Plurality voting, choosing one. The method is designed to eliminate vote-splitting while keeping election administration ...

Anti-plurality voting Anti-plurality voting describes an electoral system in which each voter votes ''against'' a single candidate, and the candidate with the fewest votes against wins. Anti-plurality voting is an example of a positional voting method. Example I ...

Borda count The Borda method or order of merit is a positional voting rule that gives each candidate a number of points equal to the number of candidates ranked below them: the lowest-ranked candidate gets 0 points, the second-lowest gets 1 point, and so on ...

Range voting Score voting, sometimes called range voting, is an electoral system for single-seat elections. Voters give each candidate a numerical score, and the candidate with the highest average score is elected. Score voting includes the well-known approva ...

Bucklin voting Bucklin voting is a class of voting methods that can be used for single-member and multi-member districts. As in highest median rules like the majority judgment, the Bucklin winner will be one of the candidates with the highest median ranking ...

Majority Judgment Majority judgment (MJ) is a single-winner voting system proposed in 2010 by Michel Balinski and Rida Laraki. It is a kind of highest median rule, a cardinal voting system that elects the candidate with the highest median rating. Voting proce ...

Condorcet methods 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, whenever there is such a candidate. A candidate with this property, the ...

and others.

Noncomplying methods

A voting method that determines a winner by eliminating candidates not having a ''fixed'' number of votes, rather than a ''proportional'' or a ''percentage'' of votes, may not satisfy the homogeneity criterion. Dodgson's method does not satisfy homogeneity.

Example of Proportional Preference Profiles

The following four voter preference profiles show rankings of candidates by voters that are proportional. Profile 1 Profile 2 Profile 3 Profile 4 A voting method satisfying homogeneity will return the same election results for each of the four preference profiles.

References

{{voting systems Electoral system criteria