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The Majority Alternative
I.) Voting procedures and the tendency towards the majority alternative
The majority principle states that the collective choice should be that alternative which, if pairwise compared with each of the other alternatives, in all cases gains a majority of votes. This alternative is called the "majority alternative". This terminology follows that of Duncan Black, who defined: "That motion, if any, which is able to obtain a simple majority over all of the other motions concerned is the majority motion. Similarly in an election, that candidate, if any, who is able to obtain a simple majority over each of the others, is the majority candidate." [Cf. D.Black, The Theory of Committees and Elections, Cambridge 1958, p.18] Because the method of pairwise comparison was invented by the french philosopher CONDORCET (1743-94), it is also known as "Condorcet winner".
The majority alternative is not one version of the Principle of Majority among others but it is of special importance. However this special importance is revealed only, when voters are allowed to build coalitions and develop collective voting strategies in order to get the best possible outcome for themselves. If these conditions are fulfilled, then an existing majority alternative will be chosen:
In any kind of voting system, which gives equal weight to individual preferences, an existing majority alternative will win, if all voters act with perfect rationality when forming coalitions.
BLACK and most of the studies in collective choice assume "sincere" voting. Therefore they do not analyse voting as a cooperative game, and the special role of the majority alternative could not be detected by them.
The theorem about the majority alternative stated above can be easily proved.
If for instance it is not the majority alternative m but some other alternative x which is chosen by the voting procedure, then those individuals preferring the majority alternative m in comparison with x could have formed a winning majority coalition on the basis of m. This result is better for each member of the coalition than x.
Therefore a result other than an existing majority alternative is impossible, if everyone knows the preferences of the other voters and acts rationally.
II.) Problems of the principle of majority
If one excludes the more difficult problem that there is a "paradox of voting" with no majority alternative at all because of circular majorities (x > y > z > x), the question of democratic legitimacy is the normative question: under which conditions may the majority alternative be regarded as an acceptable approximation to the collective interest?
The first problem which may arise with any voting system concerns the
assumption that voters know their own interests sufficiently well. If their
preferences are based on disinformation, affected by logical errors,
influenced by fear of sanctions, determined by subconscious motives etc. then the
voters preferences do
not express their "enlightened" interest. Therefore a majority alternative
determined on the basis of such unqualified preferences may not be acceptable as
approximating the collective interest.
The second normative problem of majority rule arises from the fact that in determining the majority alternative only an ordinal measurement of individual interests is necessary. The fact that the same decision may be of different importance or "salience" for the voters is neglected in voting procedures, which give each individual equally one vote.
A certain mitigation of the problem may occur where coalitions are formed over a whole series of decisions or when the voter has to decide between large bundles of alternatives. If the individuals most heavily affected are not the same but vary from decision to decision, the degree of salience of the whole series of decisions may tend to equalize with respect to the individuals.
But the majority decision is questionable as an approximation to the collective interest in those cases where for the loosing minority the decision is of greater salience than for the winning majority and where this difference is not compensated for by the degree of quantitative superiority that the majority possesses.
A third problem of the majority system arises from the fact that the set of voters can never be identical with the set of those individuals whose interests are affected by the decision - for example if the interests of future generations are affected. Who takes care of these interests if voters express only their individual interests?
A fourth problem when applying the majority system arises from the enormous costs of getting information and making decisions, if everyone has to articulate his interest with respect to every decision. In most cases the improvement of the decision in approximating the collective interest will not suffice to outweigh the costs of the decision process necessary to determine the majority alternative.
A fifth problem of the majority system stems from an unequal distribution of social power. Powerful minorities may limit the range of feasible alternatives by connecting with an alternative consequences, which make the alternative in question undesirable for a majority of the voters. For instance, capital-owners will withdraw capital and transfer it to other countries, if a socialist party gets the majority.
III.) How to deal with the shortcomings of the principle
Having briefly stated the four major weaknesses of a majority system the question arises, whether these weaknesses can be removed by modifications of the majority system.
The most promising of these modifications are the election of representatives (which shall not be discussed here) and the decentralization of decision-making by splitting up the whole set of possible decisions into various subsets of "domains of decision", so that everyone is no longer involved in every decision but that each individual is competent for only a restricted number of domains. If those individuals who are not - or only slightly - affected by a decision, are eliminated from the corresponding voting body a certain equalization of the degree of affectedness may be reached.
In addition the problem of sufficiently enlightened interests of the individuals is much easier to be solved with decentralization, for the number of decisions an individual is confronted with may be reduced considerably. As the individual only has to decide those issues by which it is affected to a certain degree, one may assume that there will be greater motivation to gather the necessary information. In addition, decision-costs are greatly reduced, because the number of individuals involved in any decision is much smaller. In the extreme cases where there are individual domains of decision only one individual has to decide.
The decentralization of decision-making thus seems to be an effective means to deal with at least some of the short-comings of the majority system. On the other hand new problems arise. One has to demarcate domains of decision and to appoint the individuals belonging to each domain. Problems of coordination between the different domains have to be solved so that a highly complicated structure of decision-making may result.
At this point only preliminary ideas concerning the criteria of demarcation and appointment can be presented. One principle of demarcating different domains of decision should be to combine those decisions, which are mutually interrelated. If decision 1 would alter the factual situation relevant for decision 2 and vice versa, both decisions have to be made connectedly. The task then is to identify those decisions which are mutually interrelated in this way. This task is complicated by the fact that the domains of decision normally have to be demarcated in advance without knowing exactly which kind of decision has to be made in the future.
A guideline for appointing the individuals to the different domains of decision should be the degree of importance or "salience" that this domain has for the respective individual. The degree of salience of a decision for an individual would be measured by the difference of individual utility between the best and the worst alternative. Thus an interpersonal comparison of utility differences is needed and all the questions associated with this concept rise again.
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Last review 03.06.2008 / Eberhard Wesche
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