Majority rule
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Majority rule is a characteristic of political systems in which the majority of a population plays a role in decision-making. Political systems with majority rule are majoritarian while those with minority rule are minoritarian.
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[edit] Majority Voting
Voting systems are often designed to select among options (such as candidates or alternative courses of action) according to the majority wishes. When there are only two alternatives the choice of the majority can be determined without any problems: whichever option gets more votes is declared the collective choice. If both alternatives get the same number of votes or there are more than two alternatives, a more complex voting process is necessary.
[edit] What is the majority choice?
In cases with more than two alternatives under consideration, it is more difficult to say which alternative is preferred by the majority, as the following example will show, where a group of five individuals (A, B, C, D, E) has to choose one out of four alternatives (w, x , y, z). We assume that each individual can order their alternatives in terms of preference. That is, each individual would prefer overall that a particular alternative is chosen but has second, third, and fourth place alternatives if their first place alternative does not receive enough votes to win. Suppose these preferences are:
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A B C D E 1. y y x z w 2. z x z x x 3. w z y y y 4. x w w w z
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The question is: which of the alternatives is preferred by the majority? Different voting systems have different ways of deciding the winner.
Plurality voting selects the winner with the most first-choice votes. Note that this winner may not necessarily be the choice of the majority. In this example, y would be declared the winner because it gets two first-place votes whereas the other ones get only one. But is y the alternative the majority prefers? Alternative y is wanted by A and B, but two individuals are not a majority in a group of five.
In this example, there is an alternative x which is preferred to y the majority of C, D, and E. Consequently alternative y cannot be what the majority wants, and plurality voting does not select the majority choice. If we eliminate y from the race, z becomes the first place winner by virtue of the votes of A and D, but this is still not a majority. In fact, x is still preferred to z by the majority of B, C, and E.
This line of thought was formalized by the French scholar Condorcet (1743-94) who proposed to compare each alternative with each other. If an alternative in all cases receives a majority of votes, this alternative represents the will of the majority. “That motion, if any, which is able to obtain a simple majority over all the other motions concerned, is the majority motion.” (Duncan Black, The Theory of Committees and Elections, Cambridge 1958, p. 18.) Modern voting systems are usually designed to select the so-called Condorcet winner, although many real elections still use simple plurality voting, which is the only method possible if each voter can list only one candidate on their ballot (as opposed to preference voting).
[edit] Majority rule with coalitions
Up to now it was assumed that everyone votes “sincerely” for his favourite alternative. But in many cases voters are able to improve their position by adopting a certain strategy of voting. If one looks upon voters as persons maximizing their utilities, the assumption of sincere voting will not work.
If one assumes instead that voters know the preferences of the other voters and are able to make binding agreements on how to vote, the whole scene changes.
As the example above demonstrates, under such conditions w, y, and z become unstable results, for in each case there is a majority of individuals preferring x to that result. In terms of game theory one could say that the Condorcet winner is the only point of stable equilibrium in the cooperative game of voting.
If voters
- know the preferences of the other voters,
- make binding agreements on how to vote and
- vote rationally according to their own interest
then an existing Condorcet winner will win in all voting systems giving equal weights to the individual preferences.[citation needed]
Therefore all these voting systems are in accordance with majority rule.
The proof of this theorem is rather easy. If for instance a candidate y rather than the Condorcet winner x is chosen, those individuals preferring x to y could have established a winning majority coalition on the basis of x, what would have been better for each member of the respective coalition. A voting system which gives equal weights to the voters will only then produce a result other than the Condorcet winner when one exists in the case of irrational behavior, imperfect information, or inability to enforce binding contracts.
There is, however, the possibility that no Condorcet winner exists because of circular majorities: x > y and y > z and z > x. In this case, the group is said to have intransitive preferences. There is no stable point of equilibrium in the theoretical model of the voting process. In real life this is no great problem because whenever the voting process delivers no result the status quo normally will be chosen. Under real-life conditions there are "frictions" not considered by the theoretical model, which will stop the circular movement. For example there may be costs of changing partners and establishing a new majority coalition.
[edit] Voting on single issues and suboptimality
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:
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A B C s: 0 0 0 t: 1 1 -3
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A B C v: 0 0 0 w: 1 -3 1
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A B C x: 0 0 0 y: -3 1 1
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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):
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A B C s+v+x: 0 0 0 t+w+y: -1 -1 -1
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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 rather strong argument against “direct democracy” and the indiscriminate use of referenda on single issues.
[edit] Criticism of Majority Rule
[edit] Majority rule and minority rights
Under majority rule, it is possible for 51% of the population to make choices which are against the interests of the other 49% of the population. For example, the majority could vote to strip all land and money from the minority. This possibility is known as the tyranny of the majority.
One way to safeguard against such scenarios is to guarantee certain rights. Who gets to vote and their equal rights can be decided beforehand as a separate act[1], 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.
[edit] Why Half?
A majority is defined as "more than half", but there's no fundamental reason that this should this be the deciding number. Certain voting systems require larger majorities, such as the two-thirds (66%) supermajority required to pass a constitutional amendment in the United States.
Going even further, there are groups which require all decisions to be made by consensus, that is, unanimous agreement. Clearly, consensus decision-making in all cases would be ideal, but it is not clear how to achieve this in practice, especially for large groups or very contentious issues.
[edit] Further Reading
- Black, D.: The Theory of Committees and Elections, Cambridge 1958
- Farquharson, R.: Theory of Voting, Oxford 1961
[edit] References
- ^ A Przeworski, JM Maravall, I NetLibrary Democracy and the Rule of Law (2003) p.223
