Majority rule

For the Canadian comedy series, see Majority Rules! For the band, see Majority Rule (band).

In social choice theory, the majority rule (MR) is a social choice rule that says that, when comparing two options (such as bills or candidates), the option preferred by more than half of the voters (a majority) should win.

In political philosophy, the majority rule is one of two major competing notions of democracy. The most common alternative is given by the utilitarian rule (or other welfarist rules), which identify the spirit of liberal democracy with the equal consideration of interests. Although the two rules can disagree in theory, political philosophers beginning with James Mill and continuing through to the present day have nevertheless long argued the two can be reconciled in practice, with majority rule being a valid approximation to the utilitarian rule whenever voters preferences are similarly-strong. This position has found strong support in many social choice models, where the socially-optimal winner and the majority-preferred winner tend to overlap.

Majority rule is the most common social choice rule worldwide, being heavily used in deliberative assemblies for dichotomous decisions, e.g. whether or not to pass a bill. Mandatory referendums where the question is yes or no are also generally decided by majority rule. It is one of the basic rules of parliamentary procedure, as described in handbooks like Robert's Rules of Order.

Alternatives

Plurality rules

Pie charts plurality (left) and majority (right)

One alternative to the majority rule is the set of plurality rules, which includes ranked choice-runoff (RCV), two-round plurality, or first-preference plurality. This is often used in elections with more than two candidates. In these elections, the winning candidate is the one with the most votes after applying some voting procedure, even if a majority of voters would prefer some other candidate.

Cardinal rules

Main articles: Utilitarian rule, Cardinal utility, and Rated voting

The utilitarian rule, and cardinal social choice rules in general, take into account not just the number of voters who support each choice but also the intensity of their preferences.

Philosophers critical of majority rule have often argued that majority rule does not take into account the intensity of preference for different voters, and as a result "two voters who are casually interested in doing something" can defeat one voter who has "dire opposition" to the proposal of the two, leading to poor deliberative practice or even to "an aggressive culture and conflict."

Supermajority rules

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.

Properties

May's Theorem

Main article: May's Theorem

Kenneth May proved that the simple majority rule is the only "fair" ordinal decision rule, in that majority rule does not let some votes count more than others or privilege an alternative by requiring fewer votes to pass. Formally, majority rule is the only decision rule that has the following properties:

• Anonymity: the decision rule treats each voter identically (one vote, one value). Who casts a vote makes no difference; the voter's identity need not be disclosed.
• Neutrality: the decision rule treats each alternative or candidate equally (a free and fair election).
• Decisiveness: if the vote is tied, adding a single voter (who expresses an opinion) will break the tie.
• Positive response: If a voter changes a preference, MR never switches the outcome against that voter. If the outcome the voter now prefers would have won, it still does so.
• Ordinality: the decision rule relies only on which of two outcomes a voter prefers, not how much.

Other properties

Voting paradox

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. Because majority rule requires an alternative to have majority support to pass, majority rule is vulnerable to rejecting the majority's decision.

Properties

May's Theorem

Main article: May's Theorem

According to Kenneth May, majority rule is the only "fair" decision rule. Majority rule does not let some votes count more than others or privilege an alternative by requiring fewer votes to pass. Formally, majority rule is the only binary decision rule that has the following properties:

• Fairness: This can be separated into two properties:
  • Anonymity: the decision rule treats each voter identically. Who casts a vote makes no difference; the voter's identity need not be disclosed.
  • Neutrality: the decision rule treats each alternative equally. This is unlike supermajoritarian rules, which can allow the status quo to prevail even though it received fewer votes.
• Decisiveness: the decision rule selects a unique winner.
• Monotonicity: If a voter changes a preference, MR never switches the outcome against that voter. If the outcome the voter now prefers would have won, it still does so.

Majority rule meets these criteria only if the number of voters is odd or infinite. If the number of voters is even, ties are possible, violating neutrality. Some assemblies permit the chair to vote only to break ties. This substitutes a loss of anonymity for the loss of neutrality.

Other properties

Voting paradox

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.)

Limitations

Arguments for limitations

Minority rights

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.

Erroneous priorities

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."

Other arguments for limitations

Seeds For Change argued that majority rule can lead to poor deliberative practice or even to "an aggressive culture and conflict." 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. Buchanan and Tullock argue that unanimity is the only decision rule that guarantees economic efficiency.

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 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 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.

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

Other arguments

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.

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 system criterion
• Voting system

Further reading

• Black, Duncan (1958). The theory of committees and elections. Cambridge: Cambridge University Press. OCLC 387017.
• Farquharson, Robin (1969). Theory of voting (D.Phil. thesis). Oxford University. ISBN 9780300011210. OCLC 51803346.
• Volk, Kyle (2014). Moral minorities and the making of American democracy. Oxford: Oxford University Press. ISBN 9780199371914.
• Corneo, Giacomo; Neher, Frank (December 2015). "Democratic redistribution and rule of the majority" (PDF). European Journal of Political Economy. 40 (A): 96–109. doi:10.1016/j.ejpoleco.2015.08.003. S2CID 55606246.
• Novak, Stéphanie; Elster, Jon, eds. (2014). Majority Decisions: Principles and Practices. Cambridge: Cambridge University Press. ISBN 9781107054097.