The mutual majority criterion is a criterion used to compare voting systems. It is also known as the majority criterion for solid coalitions and the generalized majority criterion. The criterion states that if there is a subset S of the candidates, such that more than half of the voters strictly prefer every member of S to every candidate outside of S, this majority voting sincerely, the winner must come from S. This is similar to but stricter than the majority criterion, where the requirement applies only to the case that S contains a single candidate.
The Schulze method, ranked pairs, instantrunoff voting, Nanson's method, and Bucklin voting pass this criterion.
The plurality vote, approval voting, range voting, the Borda count, and minimax fail this criterion.
Contents

Examples 1

Borda count 1.1

Minimax 1.2

Plurality 1.3

Range voting 1.4

See also 2
Examples
Borda count

Majority criterion#Borda count
The mutual majority criterion implies the majority criterion so the Borda count's failure of the latter is also a failure of the mutual majority criterion. The set solely containing candidate A is a set S as described in the definition.
Minimax
Assume four candidates A, B, C, and D with 100 voters and the following preferences:
19 voters

17 voters

17 voters

16 voters

16 voters

15 voters

1. C

1. D

1. B

1. D

1. A

1. D

2. A

2. C

2. C

2. B

2. B

2. A

3. B

3. A

3. A

3. C

3. C

3. B

4. D

4. B

4. D

4. A

4. D

4. C

The results would be tabulated as follows:
Pairwise election results

X

A

B

C

D

Y

A


[X] 33
[Y] 67

[X] 69
[Y] 31

[X] 48
[Y] 52

B

[X] 67
[Y] 33


[X] 36
[Y] 64

[X] 48
[Y] 52

C

[X] 31
[Y] 69

[X] 64
[Y] 36


[X] 48
[Y] 52

D

[X] 52
[Y] 48

[X] 52
[Y] 48

[X] 52
[Y] 48


Pairwise election results (wontiedlost):

201

201

201

003

worst pairwise defeat (winning votes):

69

67

64

52

worst pairwise defeat (margins):

38

34

28

4

worst pairwise opposition:

69

67

64

52


[X] indicates voters who preferred the candidate listed in the column caption to the candidate listed in the row caption

[Y] indicates voters who preferred the candidate listed in the row caption to the candidate listed in the column caption
Result: Candidates A, B and C each are strictly preferred by more than the half of the voters (52%) over D, so {A, B, C} is a set S as described in the definition and D is a Condorcet loser. Nevertheless, Minimax declares D the winner because its biggest defeat is significantly the smallest compared to the defeats A, B and C caused each other.
Plurality
Assume the Tennessee capital election example.
42% of voters
(close to Memphis)

26% of voters
(close to Nashville)

15% of voters
(close to Chattanooga)

17% of voters
(close to Knoxville)


Memphis

Nashville

Chattanooga

Knoxville


Nashville

Chattanooga

Knoxville

Memphis


Chattanooga

Knoxville

Nashville

Memphis


Knoxville

Chattanooga

Nashville

Memphis

There are 58% of the voters who prefer Nashville, Chattanooga and Knoxville over Memphis, so the three cities build a set S as described in the definition. But since the supporters of the three cities split their votes, Memphis wins under Plurality.
Range voting

Majority criterion#Range voting
Range voting does not satisfy the Majority criterion. The set solely containing candidate A is a set S as described in the definition, but B is the winner. Thus, range voting does not satisfy the mutual majority criterion.
See also
This article was sourced from Creative Commons AttributionShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, EGovernment Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a nonprofit organization.