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Majority rule is a decision rule that selects one of two alternatives, based on which has more than half the votes. It is the binary decision rule used most often in influential decision-making bodies, including the legislatures of democratic nations. Some scholars have recommended against the use of majority rule, at least under certain circumstances, due to an ostensible trade-off between the benefits of majority rule and other values important to a democratic society. Most famously, it has been argued that majority rule might lead to a "tyranny of the majority", and the use of supermajoritarian rules and constitutional limits on government power have been recommended to mitigate these effects. Recently some voting theorists have argued that majority rule may actually be the best rule to protect minorities.

Distinction

Though plurality (first-past-the post) is often mistaken for majority rule, they are not the same. Plurality makes the options 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 fewer than fifty percent of the votes cast in its favor.

Use

Being a binary decision rule, majority rule has little use in public elections, with many referendums being an exception. However, 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 the default rule prescribed in books like Robert's Rules of Order. The rules of order of most groups additionally prescribe the use of a supermajoritarian rule under certain circumstances, a two-thirds rule, for example, to reopen debate on a measure that has already been decided. One exception is Rusty's Rules of Order, which serves as the standing orders of the Industrial Workers of the World, which is a simplification of Robert's Rules that prescribes the use of majority rule only.

Properties

May's Theorem

According to May majority rule is notable, because when it is considered among a set of reasonable decision rules, it is the only one that is fair, where fair is being used in a narrow sense to indicate that majority rule doesn't 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.

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.

Limitations on Majority Rule in Various Contexts

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. Supermajoritarian 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, privileging 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. Some argue that when there are multiple minorities and one is protected (or privileged) by the supermajoritarian 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. Who gets to vote and a definition of inalienable rights 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 to this 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.

Referendums

Manipulability by voters in a two-option case doesn’t constitute a problem with simple majority voting, since in a two option case, it is impossible to manipulate the result by voting strategically. May states that, since group choice must depend only upon individual preferences concerning the alternatives in a set, a pattern of group choice may be built up if we know the group preference for each pair of alternatives.

However, majority rule may lead to quite different results if one votes separately on several single issues or if one puts these issues together and votes once on the corresponding bundles of alternatives.

An example may demonstrate this.

Suppose there are 3 voters, A, B and C, who have to decide 3 issues each with 2 alternatives: s or t, v or w, and x or y.

When a certain alternative is collectively chosen, voters either get a certain additional quantity of hours of leisure or their hours of leisure are reduced by a certain quantity. It is further assumed that each voter prefers more hours of leisure to less.

The 6 alternatives and the corresponding outcomes for the voters are given in the tables below:

:::{| class="wikitable"
!
!width="30"|A
!width="30"|B
!width="30"|C
|align="center"|s:
|align="center"|0
|align="center"|0
|align="center"|0
|align="center"|t:
|align="center"|1
|align="center"|1
|align="center"|-3


:::{| class="wikitable"
!
!width="30"|A
!width="30"|B
!width="30"|C
|align="center"|v:
|align="center"|0
|align="center"|0
|align="center"|0
|align="center"|w:
|align="center"|1
|align="center"|-3
|align="center"|1


:::{| class="wikitable"
!
!width="30"|A
!width="30"|B
!width="30"|C
|align="center"|x:
|align="center"|0
|align="center"|0
|align="center"|0
|align="center"|y:
|align="center"|-3
|align="center"|1
|align="center"|1


From the tables one can see that for A and B alternative t is better than s, that for A and C alternative w is better than v, and that for B and C alternative y is better than x. Therefore t, w and y are the majority alternatives and thus the collective choice.

Now we put the 3 issues together. We get bundles of 3 alternatives each, for instance t+w+y and s+v+x, on which to vote. The bundles correspond to the following outcomes for the voters, consisting in hours of leisure (or quantities of any other good):

:::{| class="wikitable"
!
!width="30"|A
!width="30"|B
!width="30"|C
|align="center"|s+v+x:
|align="center"|0
|align="center"|0
|align="center"|0
|align="center"|t+w+y:
|align="center"|-1
|align="center"|-1
|align="center"|-1


The table shows that now a majority prefers s+v+x to t+w+y. This result is quite the opposite of the former results gained by voting separately on each issue. The bundle s+v+x now is preferred not only by a majority of voters but is even unanimously preferred by all the voters. This means that s+v+x is superior to t+w+y according to the Pareto criterion. Voting on each issue separately may thus lead to suboptimal results. This is a consideration against “direct democracy” and the indiscriminate use of referendums on single issues.

Some voting theorists argue that because referendums are not subjected to the same level of deliberation that laws are before being passed, they have a tendency to privilege the status quo. Because Switzerland requires constitutional amendments to be passed by referendum, its failure to give women suffrage before 1972 is used to support this claim.Glazer, Amihai and McGann, Anthony. "Direct Democracy and the Stability of State Policy". 18 October 2005. <<A href="http://www.economics.uci.edu/docs/2005-06/Glazer-15.pdf" target="_blank"> http://www.economics.uci.edu/docs/2005-06/Glazer-15.pdf>. 25 November 2008.

Other Arguments for Limitations

Some argue that majority rule can lead to poor deliberation practice or, worse, "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 Democracyargue that "two voters who are casually interested in doing something" can defeat one, even if the one has "dire opposition" to the proposal of the two. It has been common for voting theorists to say that cycling leads to debilitating instability. Buchanan and Tullock argue that unanimity is the only decision rule that guarantees economic efficiency.

Supermajoritarian 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 -- two thirds or three fourths, for example. For example, US jury decisions require a the support of at least 10 out of 12 jurors or even unanimous support. This supermajoritarian concept follows directly from the presumption of innocenceon 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

Some voting theorists argue that majority rule helps protect minority rights, at least in settings in which deliberation occurs. This, so the argument goes, is because cycling insures that it's in the interest of parties that lose to a majority to remain part of the group's process, because a winning vote can easily be overturned by another majority. Furthermore, if a minority wishes to overturn a decision, it need form a coalition with only enough of the group members to ensure that more than half approves of the new proposal. (Under supermajoritarian rules there can be occasions on which a minority needs to form a coalition consisting of something greater than a majority to overturn a decision.) In support of the view that majority rule protects minority rights better than supermajoritarian rules some point 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. Majority rule will, proponents say, fare better than supermajoritarian rules, because under majority rule a participant will always have to convince more than half the group at the very least, while under supermajoritarian rules a participant might only need to persuade a minority. Furthermore, proponents argue that because of cycling it is in the interest of participants to compromise, rather than strive to pass resolutions that only have the bare minimum required to "win". Arguing for another benefit of majority rule, voting theorists say 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 does not treat weak and strong preferences equally. 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 Netherlandsmarker, Austriamarker, and Swedenmarker, for example -- as empirical evidence of majority rule's stability.

Bibliography

  1. May, Kenneth O. 1952. "A set of independent necessary and sufficient conditions for simple majority decisions", Econometrica, Vol. 20, Issue 4, pp. 680–684.
  2. Mark Fey, " May’s Theorem with an Infinite Population", Social Choice and Welfare, 2004, Vol. 23, issue 2, pages 275–293.
  3. A Przeworski, JM Maravall, I NetLibrary Democracy and the Rule of Law (2003) p.223
  4. McGann, Anthony J. The Logic of Democracy: Reconciling, Equality, Deliberation, and Minority Protection. Ann Arbor: University of Michigan Press. 2006. ISBN 0-472-06949-7.
  5. Rousseau. The Social Contract. bk. 4, ch. 2.


See also



Further reading

  • Black, D.: The Theory of Committees and Elections, Cambridge 1958
  • Farquharson, R.: Theory of Voting, Oxford 1961



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