Majority rule

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In social choice theory, the majority rule (MR) is a social choice rule which 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.

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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. [1] Although the two rules can disagree in theory, political philosophers beginning with James Mill have argued the two can be reconciled in practice, with majority rule being a valid approximation to the utilitarian rule whenever voters share similarly-strong preferences. [1] [2] This position has found strong support in many social choice models, where the socially-optimal winner and the majority-preferred winner often overlap. [3] [4]

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. [5] Mandatory referendums where the question is yes or no are also generally decided by majority rule. [6] It is one of the basic rules of parliamentary procedure, as described in handbooks like Robert's Rules of Order. [1]

Alternatives

Pie charts plurality (left) and majority (right) Plurality versus Majority.png
Pie charts plurality (left) and majority (right)

Plurality rules

A common alternative to the majority rule is the plurality-rule family of voting rules, which includes ranked choice voting (RCV), two-round plurality, and first-preference plurality. These rules are often used in elections with more than two candidates. Such rules elect the candidate with the most votes after applying some voting procedure, even if a majority of voters would prefer some other alternative. [5] [7]

Cardinal rules

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, [8] leading to poor deliberative practice or even to "an aggressive culture and conflict"; [9] however, the median voter theorem guarantees that majority-rule will tend to elect "compromise" or "consensus" candidates in many situations, unlike plurality-rules (see center squeeze).

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. [4] 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

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: [10] [11]

Agenda manipulation

If voter's preferences are defined over a multidimensional option space, then choosing options using pairwise majority rule is unstable. In most cases, there will be no Condorcet winner and any option can be chosen through a sequence of votes, regardless of the original option. This means that adding more options and changing the order of votes ("agenda manipulation") can be used to arbitrarily pick the winner. [12]

Other properties

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.

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. [13] 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.

Instability

Some social choice theorists have argued cycling leads to debilitating instability. [5] Buchanan and Tullock note that unanimity is the only decision rule that guarantees economic efficiency and eliminates the possibility of cycling in all cases. [5]

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. [5]

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. [5] 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. [14]

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."[ citation needed ]

Amartya Sen has noted the existence of the liberal paradox, which shows that permitting assigning a very small number of rights to individuals may make everyone worse off. [15]

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). [14]

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. [15]

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. [5]

See also

Related Research Articles

<span class="mw-page-title-main">Condorcet paradox</span> Self-contradiction of majority rule

In social choice theory, Condorcet's voting paradox is a fundamental discovery by the Marquis de Condorcet that majority rule is inherently self-contradictory. The result implies that it is logically impossible for any voting system to guarantee that a winner will have support from a majority of voters: for example there can be rock-paper-scissors scenario where a majority of voters will prefer A to B, B to C, and also C to A, even if every voter's individual preferences are rational and avoid self-contradiction. Examples of Condorcet's paradox are called Condorcet cycles or cyclic ties.

<span class="mw-page-title-main">Condorcet method</span> Pairwise-comparison electoral system

A Condorcet method is an election method that elects the candidate who wins a majority of the vote in every head-to-head election against each of the other candidates, whenever there is such a candidate. A candidate with this property, the pairwise champion or beats-all winner, is formally called the Condorcet winner or Pairwise Majority Rule Winner (PMRW). The head-to-head elections need not be done separately; a voter's choice within any given pair can be determined from the ranking.

<span class="mw-page-title-main">Arrow's impossibility theorem</span> Proof all ranked voting rules have spoilers

Arrow's impossibility theorem is a key result in social choice theory, showing that no ranking-based decision rule can satisfy the requirements of rational choice theory. Most notably, Arrow showed that no such rule can satisfy all of a certain set of seemingly simple and reasonable conditions that include independence of irrelevant alternatives, the principle that a choice between two alternatives A and B should not depend on the quality of some third, unrelated option C.

<span class="mw-page-title-main">Voting</span> Method to make collective decisions

Voting refers to the process of choosing officials or policies by casting a ballot, a document used by people to formally express their preferences. Republics and representative democracies are governments where the population chooses representatives by voting.

<span class="mw-page-title-main">Copeland's method</span> Single-winner ranked vote system

The Copeland or Llull method is a ranked-choice voting system based on counting each candidate's pairwise wins and losses.

<span class="mw-page-title-main">Smith set</span> Set preferred to any other by a majority

The Smithset, sometimes called the top-cycle, generalizes the idea of a Condorcet winner to cases where no such winner exists. It does so by allowing cycles of candidates to be treated jointly, as if they were a single Condorcet winner. Voting systems that always elect a candidate from the Smith set pass the Smith criterion. The Smith set and Smith criterion are both named for mathematician John H Smith.

Independence of irrelevant alternatives (IIA) is an axiom of decision theory which codifies the intuition that a choice between and should not depend on the quality of a third, unrelated outcome . There are several different variations of this axiom, which are generally equivalent under mild conditions. As a result of its importance, the axiom has been independently rediscovered in various forms across a wide variety of fields, including economics, cognitive science, social choice, fair division, rational choice, artificial intelligence, probability, and game theory. It is closely tied to many of the most important theorems in these fields, including Arrow's impossibility theorem, the Balinski-Young theorem, and the money pump arguments.

Majoritarianism is a political philosophy or ideology with an agenda asserting that a majority, whether based on a religion, language, social class, or other category of the population, is entitled to a certain degree of primacy in society, and has the right to make decisions that affect the society. This traditional view has come under growing criticism, and liberal democracies have increasingly included constraints on what the parliamentary majority can do, in order to protect citizens' fundamental rights. Majoritarianism should not be confused with electoral systems that give seats to candidates with only a plurality of votes. Although such systems are sometimes called majoritarian systems, they use plurality, not majority, to set winners. Some electoral systems, such as instant-runoff voting, are most often majoritarian – winners are most often determined by having majority of the votes that are being counted – but not always. A parliament that gives lawmaking power to any group that holds a majority of seats may be called a majoritarian parliament. Such is the case in the Parliament of the United Kingdom and the Parliament of Saudi Arabia and many other chambers of power.

<span class="mw-page-title-main">May's theorem</span> Social choice theorem on superiority of majority voting

In social choice theory, May's theorem, also called the general possibility theorem, says that majority vote is the unique ranked social choice function between two candidates that satisfies the following criteria:

<span class="mw-page-title-main">Condorcet winner criterion</span> Property of electoral systems

A Condorcet winner is a candidate who would receive the support of more than half of the electorate in a one-on-one race against any one of their opponents. Voting systems where a majority winner will always win are said to satisfy the Condorcet winner criterion. The Condorcet winner criterion extends the principle of majority rule to elections with multiple candidates.

<span class="mw-page-title-main">Median voter theorem</span> Theorem in political science

In political science and social choice, the median voter theorem states that if voters and candidates are distributed along a one-dimensional spectrum and voters have single-peaked preferences, any voting method that is compatible with majority-rule will elect the candidate preferred by the median voter.

<span class="mw-page-title-main">Majority winner criterion</span> Property of electoral systems

The majority criterion is a voting system criterion applicable to voting rules over ordinal preferences required that if only one candidate is ranked first by over 50% of voters, that candidate must win.

<span class="mw-page-title-main">Social choice theory</span> Academic discipline

Social choice theory is a branch of welfare economics that extends the theory of rational choice to collective decision-making. Social choice studies the behavior of different mathematical procedures used to combine individual preferences into a coherent whole. It contrasts with political science in that it is a normative field that studies how a society can make good decisions, whereas political science is a descriptive field that observes how societies actually do make decisions. While social choice began as a branch of economics and decision theory, it has since received substantial contributions from mathematics, philosophy, political science, and game theory.

In single-winner voting system theory, the Condorcet loser criterion (CLC) is a measure for differentiating voting systems. It implies the majority loser criterion but does not imply the Condorcet winner criterion.

<span class="mw-page-title-main">Borda count</span> Point-based ranked voting system

The Borda method or order of merit is a positional voting rule that gives each candidate a number of points equal to the number of candidates ranked below them: the lowest-ranked candidate gets 0 points, the second-lowest gets 1 point, and so on. Once all votes have been counted, the option or candidate or candidates with the most points is/are the winner or winners.

<span class="mw-page-title-main">Instant-runoff voting</span> Single-winner ranked-choice electoral system

Instant-runoff voting is a single-winner, multi-round elimination rule that uses ranked voting to simulate a series of runoff elections. In each round, the candidate with the fewest first-preferences is eliminated. This continues until only one candidate is left. Instant runoff falls under the plurality-with-elimination family of voting methods, and is thus closely related to rules like the two-round runoff system.

<span class="mw-page-title-main">Ranked voting</span> Voting systems that use ranked ballots

Ranked voting is any voting system that uses voters' rankings of candidates to choose a single winner or multiple winners. More formally, a ranked system is one that depends only on which of two candidates is preferred by a voter, and as such does not incorporate any information about intensity of preferences. Ranked voting systems vary dramatically in how preferences are tabulated and counted, which gives them very different properties. In instant-runoff voting (IRV) and the single transferable vote system (STV), lower preferences are used as contingencies and are only applied when all higher-ranked preferences on a ballot have been eliminated or when the vote has been cast for a candidate who has been elected and surplus votes need to be transferred.

There are a number of different criteria which can be used for voting systems in an election, including the following

<span class="mw-page-title-main">Comparison of voting rules</span> Comparative politics for electoral systems

This article discusses the methods and results of comparing different electoral systems. There are two broad ways to compare voting systems:

  1. Metrics of voter satisfaction, either through simulation or survey.
  2. Adherence to logical criteria.

A jury theorem is a mathematical theorem proving that, under certain assumptions, a decision attained using majority voting in a large group is more likely to be correct than a decision attained by a single expert. It serves as a formal argument for the idea of wisdom of the crowd, for decision of questions of fact by jury trial, and for democracy in general.

References

  1. 1 2 3 Ball, Terence and Antis Loizides, "James Mill", The Stanford Encyclopedia of Philosophy (Winter 2020 Edition), Edward N. Zalta (ed.).
  2. Jean-François Laslier (2011). And the loser is... Plurality Voting. ISBN   978-3-642-42955-2. ISSN   2267-828X. Wikidata   Q108664719.{{cite book}}: |journal= ignored (help)
  3. Pivato, Marcus (2015-08-01). "Condorcet meets Bentham" (PDF). Journal of Mathematical Economics. 59: 58–65. doi:10.1016/j.jmateco.2015.04.006. ISSN   0304-4068. We show that if the statistical distribution of utility functions in a population satisfies a certain condition, then a Condorcet winner will not only exist, but will also maximize the utilitarian social welfare function.
  4. 1 2 Krishna, Vijay; Morgan, John (2015). "Majority Rule and Utilitarian Welfare". American Economic Journal: Microeconomics. 7 (4): 339–375. doi:10.1257/mic.20140038. ISSN   1945-7669. JSTOR   43949040.
  5. 1 2 3 4 5 6 7 Anthony J. McGann (2002). "The Tyranny of the Supermajority: How Majority Rule Protects Minorities" (PDF). Center for the Study of Democracy. Retrieved 2008-06-09.{{cite journal}}: Cite journal requires |journal= (help)
  6. Vatter, Adrian (2000). "Consensus and direct democracy:Conceptual and empirical linkages". European Journal of Political Research. 38 (2): 171–192. doi:10.1023/A:1007137026336.
  7. Aubin, Jean-Baptiste; Gannaz, Irène; Leoni-Aubin, Samuela; Rolland, Antoine (July 2024). "A simulation-based study of proximity between voting rules".{{cite journal}}: Cite journal requires |journal= (help)
  8. "An Anarchist Critique of Democracy". 2005. Archived from the original on 2008-04-29. Retrieved 2008-06-09.
  9. "What's wrong with majority voting?". Consensus Decision Making. Seeds for Change. 2005. Retrieved 2006-01-17.
  10. May, Kenneth O. (1952). "A Set of Independent Necessary and Sufficient Conditions for Simple Majority Decision". Econometrica. 20 (4): 680–684. doi:10.2307/1907651. JSTOR   1907651.
  11. Mark Fey, "May's Theorem with an Infinite Population", Social Choice and Welfare, 2004, Vol. 23, issue 2, pages 275–293.
  12. Cox, Gary W.; Shepsle, Kenneth A. (2007). "Majority Cycling and Agenda Manipulation: Richard McKelvey's Contributions and Legacy". In Aldrich, John Herbert; Alt, James E.; Lupia, Arthur (eds.). Positive Changes in Political Science. Analytical perspectives on politics. Ann Arbor, Michigan: University of Michigan Press. pp. 20–23. ISBN   978-0-472-06986-6.
  13. Przeworski, Adam; Maravall, José María (2003-07-21). Democracy and the Rule of Law. Cambridge University Press. p. 223. ISBN   9780521532662.
  14. 1 2 Ben Saunders (2008). "Democracy-as-Fairness: Justice, Equal Chances, and Lotteries" (PDF). Archived from the original (PDF) on September 10, 2008. Retrieved September 8, 2013.
  15. 1 2 McGann, Anthony J. (2006). The Logic of Democracy: Reconciling Equality, Deliberation, and Minority Protection. University of Michigan Press. ISBN   0472069497.

Further reading