Majority voting

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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 notable in that it is the binary decision rule used most often in influential decision-making bodies, including the legislatures of democratic nations. Some people have recommended against the use of majority rule, at least under certain circumstances, due to an alleged trade-off between the benefits of majority rule and other values important to democracy. Most famously, it has been feared that majority rule leads to a "tyranny of the majority", and the use of supermajoritarian rules have been recommended in its place. Recently some voting theorists have argued that these fears are unfounded and majority rule may actually be the best rule to protect minorities.

Contents 1 Distinction 2 Use 3 Properties 3.1 May's Theorem 3.2 Voting on single issues and suboptimality 3.3 Other Properties 4 Criticism 4.1 Minority Rights 4.2 Intensity of Preferences 4.3 Deliberation 4.4 Instability 5 Bibliography 6 See also 7 Further reading

Distinction

Though plurality (first-past-the post) is often mistaken for majority rule, the rules are not the same.^[1] Plurality makes an alternative that has more or the most votes the winner. This is equivalent to majority rule when there are only two alternatives. However, when there are more than two alternatives, it is is possible for plurality to choose an alternative that has had fewer of the votes cast in its favor.

Use

As a binary decision rule, majority rule has little use in elections. 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.^[2]

Properties

May's Theorem

Majority rule is notable, because when it is considered among a set of reasonable decision rules, it stands alone as the only fair voting system. Stated more formally, majority rule is the only binary decision rule that has the following properties:^[3][4]

• 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.

Voting on single issues and suboptimality

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:

	A	B	C
s:	0	0	0
t:	1	1	-3

	A	B	C
v:	0	0	0
w:	1	-3	1

	A	B	C
x:	0	0	0
y:	-3	1	1

From the tables you 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):

	A	B	C
s+v+x:	0	0	0
t+w+y:	-1	-1	-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 referenda on single issues.

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.

Criticism

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 of dubious value.^[1] 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. 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 their equal rights can be decided beforehand as a separate act^[5], 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 would note 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 would also add the following: First, constitutional rights, being words on paper, cannot by themselves offer protection. Second, 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.^[6]

In stark contrast to fears of a "tyranny of the majority", some voting theorists have recently begun to say that majority rule protects 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 member's to insure 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 one might point out that cloture rules in the US Senate were used to prevent the extension of civil liberties to racial minorities.^[1] 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.^[7]

Intensity of Preferences

Some have asserted that majority rule fails to measure the intensity of preferences. For example, in An Anarchist Critique of Democracy it is argued 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.^[8] Other theorists say there will be times when a faction might want to support the proposal of another faction in exchange for support of a proposal it believes to be vital; it is in the interest of such a faction to report its true preferences.^[1]

Deliberation

Majority rule is sometimes dismissed, because it supposedly leads to poor deliberation practice or, worse, "an aggressive culture and conflict"^[9]. Other voting theorists have argued that deliberative democracy flourishes best under majority rule. Majority rule will, they 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.^[7] Furthermore, 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".^[6]

Instability

It has been common for voting theorists to claim that cycling leads to systemic instability. McGann holds a contrary view based on his observation that majority rule is the rule that maximizes a minority's ability to form a coalition that could overturn an undesirable position and that therefore a rationally self-interested being behind a Rawlsian veil of ignorance would choose majority rule. Based on this, McGann argues that though cycling may lead to an instability of policy, it makes it more likely that it will be in the best interest of everyone to continue to participate, because there are fewer permanent losers. The fact that governments that use majority rule that largely goes unchecked -- the governments of the Netherlands, Austria, and Sweden, for example -- are stable provides empirical evidence of majority rule's stability.^[1]

Bibliography

1. ^ ^{a b c d e} Anthony J. McGann (2002). "The Tyranny of the Supermajority: How Majority Rule Protects Minorities" (PDF). Center for the Study of Democracy. Retrieved on 2008-06-09.
2. ^ "How to Hold a Good Meeting and Rusty's Rules of Order" (PDF). Retrieved on 2008-06-09.
3. ^ May, Kenneth O. 1952. "A set of independent necessary and sufficient conditions for simple majority decisions", Econometrica, Vol. 20, Issue 4, pp. 680–684.
4. ^ Mark Fey, "May’s Theorem with an Infinite Population", Social Choice and Welfare, 2004, Vol. 23, issue 2, pages 275–293.
5. ^ A Przeworski, JM Maravall, I NetLibrary Democracy and the Rule of Law (2003) p.223
6. ^ ^{a b} 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.
7. ^ ^{a b} Ben Saunders (2008). "Democracy-as-Fairness: Justice, Equal Chances, and Lotteries" (PDF). Retrieved on 2008-06-09.
8. ^ "An Anarchist Critique of Democracy" (HTML) (2005). Retrieved on 2008-06-09.
9. ^ "What's wrong with majority voting?" (HTML). Consensus Decision Making. Seeds for Change (2005). Retrieved on 2006-01-17.

See also

• Majority criterion
• Majority loser criterion
• Mutual majority criterion
• Voting paradox
• Voting system criterion
• Voting system
• NIBMAR

Further reading

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

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