Back to Overview
Review Question
Next
 


 

Majority Rule and Economic Efficiency

Some economists have suggested that one way to view the decisions that are made in the market is to see them as the result of dollar voting. Consumers are, in a way, voting when they decide to buy a product. If enough of them cast their dollar votes for the product, the product will be profitable to produce. If there are not enough dollar votes cast for a product, it will not be profitable for a business to produce it, and it will not be produced. Decisions reached with dollar voting are not always economically efficient. Public goods, for example, will not be produced because of the free-rider effect. In this section we will look at the results of majority voting and find that it too can lead to economically inefficient results.

Not all political voting is based on majority voting. In most elections only a plurality is needed; that is, the winner is the one with the most votes even if he or she gets less than 50%. In contrast, in elections in which a majority is needed, a run-off election is held if no one gets a majority. In most rules of order, a vote to close discussion or to change the rules requires a two-thirds vote. In most jury trials in the United States, a unanimous vote is required to convict a person.

Economists, in fact, have often been attracted by the requirement of unanimity. With such a rule, only moves that harmed no one would be allowed. But for such a rule to work--that is, for any but the most trivial motions to gain passage--the gainers would have to be able to buy off losers. Once payments are allowed, however, a serious bargaining problem arises. Any one person can hold up passage of a bill that benefits everyone until the others pay him. Requirements for unanimous passage simply do not work well in large groups, and therefore they are never used. In order to get the benefits of collective action, individuals must agree to accept some outcomes that they do not want and on which they are outvoted.

Majority voting works better, but it too can have serious problems. For example, there may be no equilibrium solution. Consider the voting that results from the preferences in the first table below. If these three people vote to see whether policy "paper" or policy "rock" should be selected, they will choose "paper". (Smith and Doe vote for "paper" and Jones votes for "rock".) If they vote to see whether policy "rock" or "scissors" should be selected, they will choose "rock". (Smith and Jones vote for "rock" and Doe votes for "scissors".) Because policy "paper" is preferred to "rock" and policy "rock" is preferred to "scissors", one might expect that policy "paper" is preferred to "scissors", but this is not the case. If they vote for policy "scissors" or "paper", they will choose "scissors". (Jones and Doe prefer "scissors" to "paper".)

A Voting Paradox
Paper beats rock, rock beats scissors, but it does not follow that paper beats scissors!

.

Most Preferred
.
Least Preferred
Smith's Ordering
Paper
Rock
Scissors
Jones' Ordering
Rock
Scissors
Paper
Doe's Ordering
Scissors
Paper
Rock

Even if there is a policy that clearly wins, there is no reason to expect that this policy will be economically efficient. This can be shown using a second table that contains the marginal valuations that three people have for a public good. Recall that a public good is one that is non-rival, which means that when one person uses it, this use does not reduce the amount available to others. Thus, the total extra value that the group obtains from each unit of the good can be obtained by adding the individual marginal valuations. For example, if one unit is produced, the benefits Tom receives are $18, the benefits Dick receives are $19, and the benefits Harry receives are $50, so the total benefit of the first unit is $87.

Demand for a Public Good
Amount of Good
Marginal Value
to Tom
Marginal Value
to Dick
Marginal Value
to Harry
Sum of
Marginal
Values
1
$18
$19
$50
$87
2
17
18
10
45
3
16
17
2
35
4
15
16
0
31
5
14
15
0
29
6
13
14
0
27
7
12
13
0
25

Suppose that the extra cost of the good in the table above is $43.50. If this good is provided by dollar voting in the marketplace, only one will be bought. At a cost of $43.50, neither Tom nor Dick will buy any. Tom, for example, finds it a bad decision to spend $43.50 for something that gives him benefits worth $18. The one unit that is provided will be bought by Harry, who finds it worthwhile to spend $43.50 to get benefits of $50. However, the economically efficient amount is two because the second provides benefits of $45.00, greater than its cost.

The market operating on the basis of dollar voting is inefficient here, but a political process operating on a principle of majority voting may also be inefficient. Suppose that the extra cost is split equally among the three voters (or that each must pay $14.50 for each unit produced). Tom wants four units produced, Dick wants five, and Harry wants only one. Majority voting will result in four being produced. Tom and Dick will outvote Harry below four, and Tom and Harry will outvote Dick above four. This democratic solution is not economically efficient. The extra value to the group that the fourth unit contributes is $31, but its extra cost is $43.50.

In this simple case of majority voting, the median or middle voter has his wants satisfied best. People on the extremes are unlikely to be satisfied. The inefficiency results because this simple voting scheme ignores intensity of preferences.

In modern complex societies, few issues are decided by direct voting. There are too many issues to decide in this way, and the amount of knowledge needed to make those decisions is much larger than any ordinary citizen will want to have. (Recall the discussion of the rationally ignorant vote.) Yet many societies want the preferences of citizens to determine the course of public policy. To make citizen preferences matter, the society can elect representatives who, in the name of the electorate, vote on issues. To analyze how voting will take place in this system, we need to make an assumption about what motivates the elected representative.


Back to OverviewReview QuestionNext
Copyright Robert Schenk