# Majority

Last updated

A majority is the greater part, or more than half, of the total. It is a subset of a set consisting of more than half of the set's elements.

In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment. A is a subset of B may also be expressed as B includes A; or A is included in B.

In mathematics, a set is a collection of distinct objects, considered as an object in its own right. For example, the numbers 2, 4, and 6 are distinct objects when considered separately, but when they are considered collectively they form a single set of size three, written {2, 4, 6}. The concept of a set is one of the most fundamental in mathematics. Developed at the end of the 19th century, set theory is now a ubiquitous part of mathematics, and can be used as a foundation from which nearly all of mathematics can be derived. In mathematics education, elementary topics from set theory such as Venn diagrams are taught at a young age, while more advanced concepts are taught as part of a university degree.

## Contents

"Majority" can be used to specify the voting requirement, as in a "majority vote". A majority vote is more than half of the votes cast.

A majority can be compared to a plurality, which is a subset larger than any other subset considered. A plurality is not necessarily a majority as the largest subset considered may consist of less than half the set's elements. This can occur when there are three or more possible choices.

A plurality vote or relative majority describes the circumstance when a candidate or proposition polls more votes than any other, but does not receive a majority. For example, if 100 votes were cast, including 45 for Candidate A, 30 for Candidate B and 25 for Candidate C, then Candidate A received a plurality of votes but not a majority. In some votes, the winning candidate or proposition may have only a plurality, depending on the rules of the organization holding the vote.

In British English the term majority is also alternatively used to refer to the winning margin, i.e., the number of votes separating the first-place finisher from the second-place finisher.

Other related terms containing the word "majority" have their own meanings, which may sometimes be inconsistent in usage.

## Explanation

A majority is the greater part, or more than half, of the total. [1] For example, if a group consists of 20 individuals, a majority would be 11 or more individuals. For this group, having 10 or fewer individuals would not constitute a majority.

## Majority vote

In parliamentary procedure, the term "majority" simply means "more than half." [2] As it relates to a vote, a majority vote is more than half of the votes cast. [3] Abstentions or blanks are excluded in calculating a majority vote. [4] Also, the totals do not include votes cast by someone not entitled to vote or improper multiple votes by a single member. [5]

Parliamentary procedure is the body of rules, ethics and customs governing meetings and other operations of clubs, organizations, legislative bodies and other deliberative assemblies.

Abstention is a term in election procedure for when a participant in a vote either does not go to vote or, in parliamentary procedure, is present during the vote, but does not cast a ballot. Abstention must be contrasted with "blank vote", in which a voter casts a ballot willfully made invalid by marking it wrongly or by not marking anything at all. A "blank voter" has voted, although their vote may be considered a spoilt vote, depending on each legislation, while an abstaining voter hasn't voted. Both forms may or may not, depending on the circumstances, be considered to be a protest vote.

Depending on the parliamentary authority used, there may be a difference in the total that is used to calculate a majority vote due to "illegal votes". Illegal votes are votes which are cast for unidentifiable or ineligible candidates or choices. [5] In this definition, "illegal" refers to the choices made on the ballot and does not refer to the persons who cast the votes (i.e. the persons are eligible to vote).

A parliamentary authority is a book of rules on conducting business in deliberative assemblies. A group generally creates its own rules and then adopts such a book to cover meeting procedure not covered in its rules. Different books have been used by organizations and by legislative assemblies.

In Robert's Rules of Order Newly Revised (abbreviated RONR), illegal votes are counted as votes cast, but are not credited to any candidate. [5]

Robert's Rules of Order Newly Revised, commonly referred to as Robert’s Rules of Order, RONR, or simply Robert’s Rules, is the most widely used manual of parliamentary procedure in the United States. It governs the meetings of a diverse range of organizations—including church groups, county commissions, homeowners associations, nonprofit associations, professional societies, school boards, and trade unions—that have adopted it as their parliamentary authority.

In The Standard Code of Parliamentary Procedure (abbreviated TSC), illegal votes are not included in the total and a majority vote is defined as being more than half of all eligible votes cast. [6]

The issue of "illegal votes" does not exist when only two options are possible (e.g. "yes" or "no"), such as when a majority vote is required to adopt a proposal (motion). In this context, a majority vote is more "yes" votes than "no" votes. [7]

A majority vote is not the same as a vote of a "majority of the members present" or a vote of a "majority of the entire membership".

## Examples

For example, assume that votes are cast for three people for an office: Alice, Bob, and Carol.

### Scenario 1

Alice14
Bob4
Carol2
Total20

In Scenario 1, Alice received a majority vote. There were 20 votes cast and Alice received more than half of them.

### Scenario 2

Alice10
Bob6
Carol4
Total20

In Scenario 2, assume all three candidates are eligible. In this case, no one received a majority vote. This example also illustrates that half the votes cast is not a majority vote.

### Scenario 3

Alice10
Bob6
Carol (ineligible)4
Total20

In Scenario 3, assume that Alice and Bob are eligible candidates, but Carol is not. Using Robert's Rules of Order , no one received a majority vote, which is the same as Scenario 2. In this case, the 4 votes for Carol are counted in the total, but are not credited to Carol (which precludes the possibility of an ineligible candidate being credited with receiving a majority vote).

However, using The Standard Code , Alice received a majority vote since only votes for eligible candidates are counted using this book. In this case, there are 16 votes for eligible candidates and Alice received more than half of those 16 votes.

### Comparison to plurality

In all three scenarios, Alice received a plurality, or the most votes among the candidates. [8] However, only in Scenario 1 did Alice receive a majority vote using Robert's Rules of Order.

Other related terms containing the word "majority" have their own meanings, which may sometimes be inconsistent in usage. [9]

A majority may sometimes be called a "simple majority" to contrast with other terms using "majority". [9] A "simple majority" may also mean a "relative majority", or a plurality. [10] These two definitions would conflict when a "simple majority" (i.e. plurality) is not a "majority" (also see the disambiguation page for simple majority).

An "absolute majority" may mean a majority of all electors, not just those who voted. [9] [11] This usage would be equivalent to a "majority of the entire membership". However, the definition for "absolute majority" is not consistent, as it could also mean the same as "majority" or "simple majority". [9] [12] [13] [14] The meanings for "absolute majority" and "simple majority" would have to be determined from the context in which these terms are used.

A "supermajority", or a "qualified majority", is a specified higher threshold than one half. [9] A common use of a supermajority is a "two-thirds vote", which is sometimes referred to as a "two-thirds majority".

In parliamentary systems, an "overall majority" is the difference of legislators between the government and its opposition. [15] In this context, the term "majority" could be also alternatively used to refer to the winning margin, i.e. the number of votes separating the first-place finisher from the second-place finisher. [1] [15]

A "double majority" is a voting system which requires a majority of votes according to two separate criteria. [9]

## Temporary majority

A temporary majority exists when the positions of the members present and voting in a meeting of a deliberative assembly on a subject are not representative of the membership as a whole. Parliamentary procedure contains some provisions designed to protect against a temporary majority violating the rights of absentees. For instance, previous notice is required to rescind, repeal or annul or amend something previously adopted by a majority vote; if previous notice has not been given, a two-thirds vote is required. [16] However, in this and many other cases, previous notice is not required if a majority of the entire membership votes in favor, because that indicates that it is clearly not a temporary majority. Another protection against a decision being made by a temporary majority is the motion to reconsider and enter on the minutes, by which two members can suspend action on a measure until it is called up at a meeting on another day. [17]

## Application in other voting requirements

"Majority" could be specified with respect to the voting body.

### "Majority of the entire membership" and "majority of the fixed membership"

A "majority of the entire membership" means more than half of all the members of a body. [18] A "majority of the fixed membership" means more than half of all the seats of a body. [18] A majority of the entire membership is different from a majority of the fixed membership when there are vacancies. [18]

For example, say a board has 12 seats. If the board has the maximum number of members, or 12 members, a majority of the entire membership and a majority of the fixed membership would be 7 members. However, if there are two vacancies (so that there are only 10 members on the board), then a majority of the entire membership would be 6 members (more than half of 10), but a majority of the fixed membership would still be 7 members. [18]

### "Majority of the members present"

A "majority of the members present" means more than half of the members at the meeting. [18] If 30 members were at a meeting, a majority of the members present would be 16. In any situation which specifies such a requirement for a vote, an abstention would have the same effect as a "no" vote. [4]

A vote of a "majority of the members present" is not the same as a "majority vote". When unqualified, a "majority vote" is taken to mean more than half of the votes cast. [3] If 30 members were at a meeting, but only 20 votes were cast, a majority vote would be 11 votes. [18]

## Erroneous definitions

Erroneous definitions of majority include "50% +1" and "51%". [2]

### "50% + 1"

For example, say a board has 7 members. A majority would be 4 (more than half of 7). If "50% +1" is used, the number calculated would be 3.5+1, and thus majority may be mistaken as 4.5, and by rounding up, 5. [2] This confusion would exist for all odd numbers using the erroneous definition of "50%+1", though this can be fixed by remembering to always round down, in which case both odd and even numbers would work out correctly.

### "51%"

In another example, say a convention has 1000 delegates. Using the erroneous definition of 51% would result in a majority being mistaken as 510 instead of 501.

The same logic applies for 50.1%, 50.01%, 50.001%, etc.

## Related Research Articles

Approval voting is a single-winner electoral system where each voter may select ("approve") any number of candidates. The winner is the most-approved candidate.

Plurality voting is an electoral system in which each voter is allowed to vote for only one candidate, and the candidate who polls the most among their counterparts is elected. In a system based on single-member districts, it may be called first-past-the-post (FPTP), single-choice voting, simple plurality or relative/simple majority. In a system based on multi-member districts, it may be referred to as winner-takes-all or bloc voting. The system is often used to elect members of a legislative assembly or executive officers. It is the most common form of the system, and is used in most elections in the United States, the lower house in India, elections to the House of Commons and English local elections in the United Kingdom and Canada.

The two-round system is a voting method used to elect a single winner, where the voter casts a single vote for their chosen candidate. However, if no candidate receives the required number of votes, then those candidates having less than a certain proportion of the votes, or all but the two candidates receiving the most votes, are eliminated, and a second round of voting is held.

Voting is a method for a group, such as a meeting or an electorate, in order to make a collective decision or express an opinion, usually following discussions, debates or election campaigns. Democracies elect holders of high office by voting. Residents of a place represented by an elected official are called "constituents", and those constituents who cast a ballot for their chosen candidate are called "voters". There are different systems for collecting votes.

A supermajority or supra-majority or a qualified majority, is a requirement for a proposal to gain a specified level of support which is greater than the threshold of more than one-half used for majority.

The majority criterion is a single-winner voting system criterion, used to compare such systems. The criterion states that "if one candidate is ranked first by a majority of voters, then that candidate must win".

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.

A special rule of order is parliamentary procedure term for a rule adopted by the organization that relate to procedure or to the duties of officers within meetings.

The exhaustive ballot is a voting system used to elect a single winner. Under the exhaustive ballot the elector simply casts a single vote for their chosen candidate. However, if no candidate is supported by an overall majority of votes then the candidate with the fewest votes is eliminated and a further round of voting occurs. This process is repeated for as many rounds as necessary until one candidate has a majority.

Deliberative assemblies – bodies that use parliamentary procedure to arrive at decisions – use several methods of voting on motions. The regular methods of voting in such bodies are a voice vote, a rising vote, and a show of hands. Additional forms of voting include a recorded vote and balloting.

Plurality-at-large voting, also known as block vote or multiple non-transferable vote (MNTV), is a non-proportional voting system for electing several representatives from a single multimember electoral district using a series of check boxes and tallying votes similar to a plurality election. Multiple winners are elected simultaneously to serve the district. Block voting is not a system for obtaining proportional representation; instead the usual result is that where the candidates divide into definitive parties the most popular party in the district sees its full slate of candidates elected, resulting in a landslide.

In parliamentary procedure, the motion to postpone indefinitely is a subsidiary motion used to kill a main motion without taking a direct vote on it. This motion does not actually "postpone" it.

An overvote occurs when one votes for more than the maximum number of selections allowed in a contest. The result is a spoiled vote which is not included in the final tally.

Parliamentary procedure is the body of rules, ethics, and customs governing meetings and other operations of clubs, organizations, legislative bodies, and other deliberative assemblies. General principles of parliamentary procedure include rule of the majority with respect for the minority.

In parliamentary procedure, the verb to table has the opposite meaning in different countries:

Preferential block voting is a majoritarian voting system for electing several representatives from a single multimember constituency. Unlike the single transferable vote, preferential block voting is not a method for obtaining proportional representation, and instead produces similar results to plurality block voting, of which it can be seen as the instant-runoff version. Under both systems, a single group of like-minded voters can win every seat, making both forms of block voting nonproportional.

Instant-runoff voting (IRV) or Ranked choice voting (RCV) is a type of ranked preferential voting method used in single-seat elections with more than two candidates. Instead of indicating support for only one candidate, voters in IRV elections can rank the candidates in order of preference. Ballots are initially counted for each voter's top choice. If a candidate has more than half of the vote based on first-choices, that candidate wins. If not, then the candidate with the fewest votes is eliminated. The voters who selected the defeated candidate as a first choice then have their votes added to the totals of their next choice. This process continues until a candidate has more than half of the votes. When the field is reduced to two, it has become an "instant runoff" that allows a comparison of the top two candidates head-to-head.

## References

1. See dictionary definitions of "majority" at Merriam-Webster, dictionary.com Archived 2015-12-21 at the Wayback Machine , Oxford English Dictionary, thefreedictionary.com, and Cambridge English Dictionary.
2. "Frequently Asked Questions about RONR (Question 4)". The Official Robert's Rules of Order Web Site. The Robert's Rules Association. Retrieved 2015-12-29.
3. Robert, Henry M.; et al. (2011). Robert's Rules of Order Newly Revised (11th ed.). Philadelphia, PA: Da Capo Press. p. 400. ISBN   978-0-306-82020-5. The word majority means "more than half"; and when the term majority vote is used without qualification—as in the case of the basic requirement—it means more than half of the votes cast by persons entitled to vote, excluding blanks or abstentions, at a regular or properly called meeting.
4. "Frequently Asked Questions about RONR (Question 6)". The Official Robert's Rules of Order Web Site. The Robert's Rules Association. Retrieved 2015-12-29.
5. Robert 2011 , p. 416
6. The Standard Code of Parliamentary Procedure, 4th edition, 2001, pp. 134, 158-9
7. Robert 2011 , p. 405
8. Robert 2011 , pp. 404–405: "A plurality vote is the largest number of votes to be given any candidate or proposition when three or more choices are possible; the candidate or proposition receiving the largest number of votes has a plurality."
9. Schermers, Henry G.; Blokker, Niels M. (2011). International Institutional Law: Unity Within Diversity (Fifth Revised ed.). Leiden, The Netherlands: Martinus Nijhoff Publishers. pp. 561–563. ISBN   978-90-04-18798-6.
10. See dictionary definition of "simple majority" at dictionary.com.
11. See dictionary definitions of "simple majority", "absolute majority", and "qualified majority" at EUabc.com.
12. See dictionary definition of "absolute majority" at dictionary.com.
13. "With three-cornered contests as common as they now are, we may have occasion to find a convenient single word for what we used to call an absolute majority... In America the word majority itself has that meaning while a poll greater than that of any other candidate, but less than half the votes cast is called a plurality. It might be useful to borrow this distinction..." (Fowler, H.W. 1965 A Dictionary of Modern English Usage)
14. "Overall Majority". Longman Dictionary of Contemporary English. Longmans. Retrieved 2009-04-26.
15. Robert 2011 , p. 306
16. Robert 2011 , p. 332
17. Robert 2011 , p. 403