Majority rule

Majority rule is a decision rule that selects alternatives which have a majority, that is, more than half the votes. It is the binary decision rule used most often in influential decision-making bodies, including all 
the legislatures of democratic nations.

Distinction with plurality 
Though plurality (first-past-the post) is often mistaken for majority rule, they are not the same. Plurality makes the option with the most votes the winner, regardless of whether the fifty percent threshold is passed. This is equivalent to majority rule when there are only two alternatives. However, when there are more than two alternatives, it is possible for plurality to choose an alternative that has less than fifty percent of the votes cast in its favor.

Use 

Majority rule is used pervasively in many modern western democracies. It is frequently used in legislatures and other bodies in which alternatives can be considered and amended in a process of deliberation until the final version of a proposal is adopted or rejected by majority rule. It is one of the basic rules prescribed in books like Robert's Rules of Order. The rules in such books and those rules adopted by groups may additionally prescribe the use of a supermajoritarian rule under certain circumstances, such as a two-thirds rule to close debate.

Many referendums are decided by majority rule.

Properties

May's Theorem 

According to Kenneth May, majority rule is the only reasonable decision rule that is "fair", that is, that does not privilege voters by letting some votes count for more or privilege an alternative by requiring fewer votes for its passing. Stated more formally, majority rule is the only binary decision rule that has the following properties:

 Fairness: This can be further separated into two properties:
 Anonymity: The decision rule treats each voter identically. When using majority rule, it makes no difference who casts a vote; indeed the voter's identity need not even be known.
 Neutrality: The decision rule treats each alternative equally. This is unlike supermajoritarian rules, which can allow an alternative that has received fewer votes to win.
 Decisiveness: The decision rule selects a unique winner.
 Monotonicity: The decision rule would always, if a voter were to change a preference, select the alternative that the voter preferred, if that alternative would have won before the change in preference. Similarly, the decision rule would never, if a voter were to change a preference, select a candidate the voter did not prefer, if that alternative would not have won before the change in preference.

Strictly speaking, it has been shown that majority rule meets these criteria only if the number of voters is odd or infinite. If the number of voters is even, there is the chance that there will be a tie, and so the criterion of neutrality is not met. Many deliberative bodies reduce one participant's voting capacity—namely, they allow the chair to vote only to break ties. This substitutes a loss of total anonymity for the loss of neutrality.

Other properties 
In group decision-making it is possible for a voting paradox to form. That is, it is possible that there are alternatives a, b, and c such that a majority prefers a to b, another majority prefers b to c, and yet another majority prefers c to a.
Because majority rule requires an alternative to have only majority support to pass, a majority under majority rule is especially vulnerable to having its decision overturned. (The minimum number of alternatives that can form such a cycle (voting paradox) is 3 if the number of voters is different from 4, because the Nakamura number of the majority rule is 3. For supermajority rules the minimum number is often greater, because the Nakamura number is often greater.)

As Rae argued and Taylor proved in 1969, majority rule is the rule that maximizes the likelihood that the issues a voter votes for will pass and that the issues a voter votes against will fail.

Schmitz and Tröger (2012) consider a collective choice problem with two alternatives and they show that the majority rule maximizes utilitarian welfare among all incentive compatible, anonymous, and neutral voting rules, provided that the voters’ types are independent. Yet, when the votersʼ utilities are stochastically correlated, other dominant-strategy choice rules may perform better than the majority rule. Azrieli and Kim (2014) extend the analysis for the case of independent types to asymmetric environments and by considering both anonymous and non-anonymous rules.

Limitations

Arguments for limitations

Minority rights 

Because a majority can win a vote under majority rule, it has been commonly argued that majority rule can lead to a "[tyranny of the majority]". Supermajoritarian rules, such as the three-fifths supermajority rule required to end a filibuster in the United States Senate, have been proposed as preventative measures of this problem. Other experts argue that this solution is questionable. Supermajority rules do not guarantee that it is a minority that will be protected by the supermajority rule; they only establish that one of two alternatives is the status quo, and privilege it against being overturned by a mere majority. To use the example of the US Senate, if a majority votes against cloture, then the filibuster will continue, even though a minority supports it. Anthony McGann argues that when there are multiple minorities and one is protected (or privileged) by the supermajority rule, there is no guarantee that the protected minority won't be one that is already privileged, and if nothing else it will be the one that has the privilege of being aligned with the status quo.

Another way to safeguard against tyranny of the majority, it is argued, is to guarantee certain rights. Inalienable rights, including who can vote, which cannot be transgressed by a majority, can be decided beforehand as a separate act, by charter or constitution. Thereafter, any decision that unfairly targets a minority's right could be said to be majoritarian, but would not be a legitimate example of a majority decision because it would violate the requirement for equal rights. In response, advocates of unfettered majority rule argue that because the procedure that privileges constitutional rights is generally some sort of supermajoritarian rule, this solution inherits whatever problems this rule would have. They also add the following: First, constitutional rights, being words on paper, cannot by themselves offer protection. Second, under some circumstances, the rights of one person cannot be guaranteed without making an imposition on someone else; as Anthony McGann wrote, "one man's right to property in the antebellum South was another man's slavery". Finally, as Amartya Sen stated when presenting the liberal paradox, a proliferation of rights may make everyone worse off.

Erroneous priorities
The erroneous priorities effect (EPE) states that groups acting upon what they initially consider important are almost always misplacing their effort. When groups do this they have not yet determined which factors are most influential in their potential to achieve desired change.  Only after identifying those factors are they ready to take effective action. EPE was discovered by Kevin Dye after extensive research at the Food and Drug Administration. The discovery of EPE led to the recognition that even with good intentions for participatory democracy, people cannot collectively take effective actions unless they change the paradigm for languaging and voting. EPE is a negative consequence of phenomena such as spreadthink and groupthink. Effective priorities for actions that are dependent on recognizing the influence patterns of global interdependencies, are defeated by the EPE, when priorities are chosen on the basis of aggregating individual stakeholder subjective voting that is largely blind to those interdependencies. Dye's work resulted in the discovery of the 6th law of the science of structured dialogic design, namely: "Learning occurs in a dialogue as the observers search for influence relationships among the members of a set of observations."

Other arguments for limitations 

Some argue that majority rule can lead to poor deliberation practice or even to "an aggressive culture and conflict". Along these lines, some have asserted that majority rule fails to measure the intensity of preferences. For example, the authors of An Anarchist Critique of Democracy argue that "two voters who are casually interested in doing something" can defeat one voter who has "dire opposition" to the proposal of the two.

Voting theorists have often claimed that cycling leads to debilitating instability. Buchanan and Tullock argue that unanimity is the only decision rule that guarantees economic efficiency.

Supermajority rules are often used in binary decisions where a positive decision is weightier than a negative one. Under the standard definition of special majority voting, a positive decision is made if and only if a substantial portion of the votes support that decision—for example, two thirds or three fourths. For example, US jury decisions require the support of at least 10 of 12 jurors, or even unanimous support. This supermajoritarian concept follows directly from the presumption of innocence on which the US legal system is based. Rousseau advocated the use of supermajority voting on important decisions when he said, "The more the deliberations are important and serious, the more the opinion that carries should approach unanimity."

Arguments against limitations

Minority rights 

McGann argues that majority rule helps to protect minority rights, at least in settings in which deliberation occurs. The argument is that cycling ensures that parties that lose to a majority have an interest to remain part of the group's process, because the decision can easily be overturned by another majority. Furthermore, if a minority wishes to overturn a decision, it needs to form a coalition with only enough of the group members to ensure that more than half approves of the new proposal. (Under supermajority rules, a minority might need a coalition consisting of something greater than a majority to overturn a decision.)

To support the view that majority rule protects minority rights better than supermajority rules McGann points to the cloture rule in the US Senate, which was used to prevent the extension of civil liberties to racial minorities. Ben Saunders, while agreeing that majority rule may offer better protection than supermajority rules, argues that majority rule may nonetheless be of little help to the most despised minorities in a group.

Other arguments against limitations 
Some argue that deliberative democracy flourishes under majority rule. They argue that under majority rule, participants always have to convince more than half the group at the very least, while under supermajoritarian rules participants might only need to persuade a minority. Furthermore, proponents argue that cycling gives participants an interest to compromise, rather than strive to pass resolutions that only have the bare minimum required to "win".

Another argument for majority rule is that within this atmosphere of compromise, there will be times when a minority faction will want to support the proposal of another faction in exchange for support of a proposal it believes to be vital. Because it would be in the best interest of such a faction to report the true intensity of its preference, so the argument goes, majority rule differentiates weak and strong preferences. McGann argues that situations such as these give minorities incentive to participate, because there are few permanent losers under majority rule, and so majority rule leads to systemic stability. He points to governments that use majority rule which largely goes unchecked—the governments of the Netherlands, Austria, and Sweden, for example—as empirical evidence of majority rule's stability.

See also
 Appeal to the majority
 Arrow's theorem
 Condorcet's jury theorem
 Majority criterion
 Majority loser criterion
 Mutual majority criterion
 Majoritarianism
 Majoritarian democracy
 No independence before majority rule (NIBMAR)
 Ochlocracy
 Quadratic voting
 Voting paradox
 Voting system criterion
 Voting system

References

Further reading
 
 
 
 

Category:Monotonic electoral systems
Category:Voting theory