A majority is a subset

Subset

In mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. A and B may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment...

 of a group consisting of more than half of its members. This can be compared to a plurality, which is a subset larger than any other subset; i.e. a plurality is not necessarily a majority as the largest subset may consist of less than half the group's population. In British English, majority and plurality are often used as synonyms, and is often used to refer to the number of votes separating the first-place finisher from the second-place finisher.

A majority may be called a simple majority to contrast with other types of majority: an overall majority, in parliamentary systems, is the difference of legislators between the government and its opposition;
an absolute majority is a majority of all electors, not just those who voted; and a supermajority

Supermajority

A supermajority or a qualified majority is a requirement for a proposal to gain a specified level or type of support which exceeds a simple majority . In some jurisdictions, for example, parliamentary procedure requires that any action that may alter the rights of the minority has a supermajority...

is a stronger majority than a simple majority.

Example

Here, Memphis has a plurality (42%) of the first preferences, but not a majority. We can contrast this by looking at the fourth preferences, where the majority of voters (58%) have placed Memphis last. In all single-winner voting systems apart from the simple plurality voting

First-past-the-post

First-past-the-post voting refers to an election won by the candidate with the most votes. The winning potato candidate does not necessarily receive an absolute majority of all votes cast.-Overview:...

, Memphis will lose as a majority of voters do not want the city as capital.

Parliamentary rules

In parliamentary procedure, the term 'majority' refers to "more than half." As it relates to a vote, a majority is more than half of the votes cast (noting that an abstention is simply the refusal to vote). The definition of "majority vote" can differ, however, from one parliamentary authority

Parliamentary authority

A parliamentary authority is a manual on parliamentary law, containing rules of order for the transaction of business in deliberative assemblies...

 to another. Robert's Rules of Order

Robert's Rules of Order

Robert's Rules of Order is the short title of a book containing rules of order intended to be adopted as a parliamentary authority for use by a deliberative assembly written by Brig. Gen...

 defines a majority as being more than one half of the votes cast including votes for ineligible candidates or choices. The Standard Code of Parliamentary Procedure (abbreviated TSC) defines a majority as being more than half all eligible votes cast.

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

Alice and Bob

The names Alice and Bob are commonly used placeholder names for archetypal characters in fields such as cryptography and physics. The names are used for convenience; for example, "Alice sends a message to Bob encrypted with his public key" is easier to follow than "Party A sends a message to Party...

, who are eligible; and Carol, who is ineligible.

Candidate	Votes
Alice	9
Bob	8
Carol	3
Total	20

By Robert's Rules of Order, no candidate has been elected as no candidate gained 11 votes. However, by The Standard Code, Alice is elected as she gained more than half of the seventeen eligible votes.

In politics

Politics

Politics is a process by which groups of people make collective decisions. The term is generally applied to the art or science of running governmental or state affairs, including behavior within civil governments, but also applies to institutions, fields, and special interest groups such as the...

, political voting systems, and even in parliamentary procedure

Parliamentary procedure

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

 in some cases, there are several different popular concepts relating to a majority:

• Simple majority
• Supermajority
  Supermajority
  A supermajority or a qualified majority is a requirement for a proposal to gain a specified level or type of support which exceeds a simple majority . In some jurisdictions, for example, parliamentary procedure requires that any action that may alter the rights of the minority has a supermajority...
  
  
• Absolute majority
• Two-thirds majority
• Relative majority
• Double majority
  Double majority
  A double majority is the name given to a vote which requires a majority of votes according to two separate criteria. The mechanism is usually used to require strong support for any measure considered to be of great importance...
  
  - a majority of votes in a majority of states or jurisdictions.