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Paper beats rock, rock beats scissors, but it does not follow that paper beats scissors! |
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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.
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to Harry |
Marginal Values |
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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.