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Decision rule that selects alternatives which have a majority

Majority rule is the principle that a group which has more than half of all voters should be allowed to make the decisions for a group. Majority rule is the binary decision rule most often used in decision making bodies, including many legislatures of democratic nations. Where no one party wins a majority of the seats in a legislature, the majority of legislators that wields power is partly composed of members of other parties in support. Where only two candidates are competing for a single seat, one or the other will receive a simple majority of valid votes, unless they tie. But in situations where more than two are competing for a single seat, simple plurality is sometimes considered as close as possible to majority in which case having plurality is enough to be elected, while in some systems such as instant runoff voting special efforts are made to ensure that the winner is in fact the majority choice even where three or more are competing for the same office. However, that does not always happen. Where multiple members are elected in a district as may happen under proportional representation or plurality block voting, no candidate may receive a majority of votes cast. Under block voting, the winners, usually of just one party, often have received only a minority of the votes cast.

One alternative to majority rule is plurality (First past the post voting or FPTP). This is often used in elections with more than two candidates. In this case, the winner is the one with the most votes, whether or not that constitutes a majority.

Parliamentary rules may prescribe the use of a supermajoritarian rule under certain circumstances, such as the 60% filibuster rule to close debate in the US Senate. However such requirement means that 41 percent of the members or more could prevent debate from being closed, an example where the majority will would be blocked by a minority. Switzerland is an example of consensus democracy where generally supermajority rule is applied. A national unity government is a government with a supermajority.

Majority rule is common in liberal democracies. It is used in legislatures and other bodies. Mandatory referendums where the question is yes or no are also decided by majority rule, while optional referendums and popular initiatives correspond to consensus rule (e. g. Switzerland).

In group decision making voting paradoxes can form. It is possible that alternatives a, b, and c exist such that a majority prefers a to b, another majority prefers b to c, and yet another majority prefers c to a. (For each proposition to have majority, the measure must involve more than just voter's first preference.) Because majority rule requires an alternative to have majority support to pass, majority rule is vulnerable to rejecting the majority's decision. (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.)

A super majority rule actually empowers the minority, making it stronger (at least through its veto) than the majority. McGann argued that when only one of multiple minorities is protected by the super majority rule (same as seen in simple plurality elections systems), so the protection is for the status quo, rather than for the faction that supports it. Another possible way to prevent tyranny is to elevate certain rights as inalienable. Thereafter, any decision that targets such a right might be majoritarian, but it would not be legitimate, because it would violate the requirement for equal rights. Constitutional rights cannot by themselves offer protection. Under some circumstances, the legal rights of one person cannot be guaranteed without unjustly imposing on someone else. McGann wrote, "one man's right to property in the antebellum South was another man's slavery." Amartya Sen noted the liberal paradox, stating that a proliferation of rights may make everyone worse off.

The erroneous priorities effect (EPE) states that groups that act upon what they initially consider important almost always misplace their effort. Such groups have not yet determined which factors are most influential. Only after identifying those factors can they take effective action. EPE was articulated by K. M. Dye at the Food and Drug Administration. This discovery led to the recognition that even with good intentions, effective action requires a different paradigm for language and voting. EPE is a negative consequence of phenomena such as spreadthink and groupthink. Effective priorities are dependent on recognizing the influence patterns of global interdependencies and are defeated by EPE when priorities simply aggregate individual stakeholder's subjective voting that does not consider those interdependencies. Dye's work resulted in the discovery of the 6th law of the science of structured dialogic design, namely that "Learning occurs in a dialogue as the observers search for influence relationships among the members of a set of observations." Along these lines, majority rule may fail to measure the preferences intensity. 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. Strict observance of majority rule would allow two voters (a majority) to pass legislation that hurts one voter (the minority). Voting theorists claimed that cycling leads to debilitating instability.

McGann argued that majority rule helps to protect minority rights, at least in deliberative settings. 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 any decision can easily be overturned by another majority. Furthermore, suppose a minority wishes to overturn a decision. In that case, under majority rule it just needs to form a coalition that has more than half of the officials involved and that will give it power. Under supermajority rules, a minority needs its own supermajority to overturn a decision.

Saunders argued that deliberative democracy flourishes under majority rule and that under majority rule, participants always have to convince more than half the group, while under supermajoritarian rules participants might only need to persuade a minority (to prevent a change). Where large changes in seats held by a party may arise from only relatively slight change in votes cast (such as under FPTP), and a simple majority is all that is required to wield power (most legislatures in democratic countries), governments may repeatedly fall into and out of power. This may cause polarization and policy lurch, or it may encourage compromise, depending on other aspects of political culture. McGann argued that such cycling encourages participants to compromise, rather than pass resolutions that have the bare minimum required to "win" because of the likelihood that they would soon be reversed. Within this atmosphere of compromise, a minority faction may accept proposals that it dislikes in order to build a coalition for a proposal that it deems of greater moment. In that way, majority rule differentiates weak and strong preferences. McGann argued that such situations encourage minorities to participate, because majority rule does not typically create permanent losers, encouraging systemic stability. He pointed to governments that use largely unchecked majority rule, such as is seen under proportional representation in the Netherlands, Austria, and Sweden, as empirical evidence of majority rule's stability.