Lecture Notes2

ECO 4554 Economics of State and Local Government Lecture Notes PUBLIC CHOICE Key Points 1. The alternative selected by a community using simple majority rule voting is the alternative preferred by the median voter(s), that is, the voter(s) whose preferred alternative is the median of the distribution of all voters’ preferred alternatives. 2. Simple majority rule is not necessarily the most efficient voting rules for at least five reasons: (1) it may not choose the efficient alternative, (2) there may not be an alternative that is uniquely preferred by a majority of voters, (3) it does not guarantee that all voters have an equal voice, (4) it is not the lowest cost voting rule, and (5) it does not reflect how strongly voters feel about the alternatives. Synopsis When government provides goods, decisions about how much of each good or service to supply and how to supply them are made by a collective decision or political process, usually voting. The application of economic analysis to the study of political processes is called "public choice". We begin with a simple model of voting using simple majority rule. We derive the most fundamental result of public choice, the median voter theorem, which says that simple majority rule voting chooses the alternative that is preferred by the voter(s) with the median preference. Next, we show that simple majority rule is not necessarily the most efficient voting rule, that other voting rules are often more efficient than simple majority rule. There are at least five reasons that simple majority may not be the most efficient voting rule. We look at the five reasons. We then look briefly at cumulative voting or point voting as an alternative to simple majority rule. Finally, we consider a political process where bureaucrats have some monopoly power over the political agenda. Voters cannot choose among all possible alternatives but can choose only among the alternatives presented to them by the bureaucrats. We look at the reversion model as an example of a monopoly bureaucratic model of voting. Lecture Notes I.

Simple majority rule A.

Assumptions 1.

The costs of the good or service are divided equally among all individuals in the group.

2.

Voting is binary, meaning that the voters choose between only two options (for example, shall the level of expenditure increase, yes or no?). 1

ECO 4554: Economics of State and Local Government Public Choice

3. B.

C.

Decisions are made in a referendum in which every voter participates (direct democracy, not a representative system).

Median voter theorem: Under assumptions (1)-(3) above, the quantity of a good or service or the level of expenditure chosen by simple majority rule is the quantity or expenditure level preferred by the median voter. See Power Point Slides Figure 2-1. 1.

Median voter: The median voter is the individual whose preferred quantity or expenditure level is the median of the distribution of preferred quantities or expenditure levels of all voters.

2.

Suppose there are three voters, Huey, Dewey, and Louie. Huey prefers $2500 per pupil of education expenditure, Dewey prefers $5000 per pupil, and Louie prefers $7500 per pupil. Dewey is the median voter. According to the median voter theorem, if the decision is made by simple majority rule, annual education expenditure will be $5000 per pupil.

Applications of the median voter theorem in the economics of state and local government 1.

2.

Intergovernmental grants a.

When a community receives a matching grant for urban mass transit, does the community increase its own spending on mass transit?

b.

The effect of a matching grant is to reduce the price to the community’s voters. If a voter’s demand for transit services is elastic, that voter’s preferred expenditure increases when the price decreases. If the voter’s demand is inelastic, the voter’s preferred expenditure decreases when the price decreases.

c.

The effect of the grant depends only on the elasticity of demand of the median voter. If the median voter’s demand is elastic, mass transit expenditure increases no matter whether the average community demand is elastic or inelastic. If the median voter’s demand is inelastic, mass transit expenditure decreases.

d.

The “average” demand of the community’s voters or the demand of the typical voters does not matter. The result depends only on the demand of the median voter.

Property taxes a.

Why do some communities rely more heavily on property taxes to finance local education than other communities?

b.

Suppose the voters believe renters do not pay property taxes. Therefore, if education is funded by property taxes, renters can free ride on the community’s education expenditures.

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ECO 4554: Economics of State and Local Government Public Choice

D. II.

c.

One might suppose, then, that a community with a large amount of rental property would not rely on property taxation to finance education, but this is not necessarily the case.

d.

Whether or not the community uses property taxes to fund education depends on whether the median voter in the community is a renter or a property owner. If the median voter is a renter, s/he would prefer to finance education using property taxes. However, if the median voter is a homeowner, s/he would prefer to use other taxes so that renters cannot free ride. If there is a large amount of rental property in the community, it is more likely that the median voter is a renter and such a community is more likely to rely on property taxes.

The median voter theorem is a useful model for analyzing and predicting the outcome of simple majority rule voting.

Problems with simple majority rule A.

B.

Simple majority rule is not necessarily the most efficient voting rule. 1.

Process problems: The voting process using simple majority rule may be less efficient than the voting process using other voting rules because other rules (1) may provide greater equality of political influence and (2) may have lower costs.

2.

Outcome problems: The voting outcome using simple majority rule may be less efficient than the outcome using other voting rules because (1) the outcome of simple majority rule voting may not be the economically efficient quantity or expenditure level, (2) the outcome of simple majority rule voting may not be unique because of the cyclical majority or paradox of voting, and (3) other voting rules more closely reflect the strength or intensity of voter preferences.

3.

We consider each of these in turn.

Majority rule does not guarantee that all voters have an equal voice in the political process. 1.

With simple majority rule, all voters have the same number of votes, but an equal distribution of votes alone does not guarantee equal political power or influence.

2.

The degree of political power depends on many things other than just the number of votes assigned to each individual. For example, the political power of wealthier individuals and groups, of individuals and groups who have more time to devote to political activity (labor unions and their members), and of individuals and groups who are more intensely interested in and affected by the outcome (activists and special interest groups) is greater than their share of the votes. Conversely, the political power of other groups is less than their share of the votes. 3

ECO 4554: Economics of State and Local Government Public Choice

C.

Majority rule may not be the lowest cost voting rule. 1.

2.

Any voting rule involves two types of costs. a.

Administrative cost: The cost of conducting an election and reaching a decision. The longer it takes to reach a decision under a voting rule, the greater are its administrative costs. For example, simple majority rule is often more costly than plurality rule if there are more than three alternatives because simple majority may require a second runoff election.

b.

External cost of an adverse decision: When an alternative is chosen using a voting rule, there are winners and losers. Those who favor the winning alternative are imposing external costs on those who oppose it. Proposal A may be favored by 51 percent of the voters, but all the voters will pay for Proposal A. The 51 percent who prefer Proposal A are imposing an external cost on the 49 percent who oppose Proposal A.

Political decision costs and the voting rule a.

We can characterize a voting rule by the percentage of votes required to support an alternative in order for it to be adopted. For example, simple majority rule requires 50% plus one of the votes to adopt an alternative. Unanimous consent requires 100%. To close debate in the U.S. Senate requires a super-majority of 60%. Amending the constitution requires a two-thirds super-majority. On the other hand, decisions involving more than two alternatives with no run-off election require only a plurality, meaning more votes than any other alternative even if it is less than 50%.

b.

Administrative cost 1) Getting unanimous agreement is likely to be extremely timeconsuming. Therefore, a rule of unanimous consent has high administrative cost. 2) At the opposite extreme, a dictatorship where a single voter makes the decision for the entire community has very low administrative costs since it requires the agreement of only one voter to select an alternative. 3) As the percentage of voters required to agree increases, the administrative cost also increases.

c.

External cost 1) A rule of unanimous consent imposes no external cost on any individual because each voter has a veto over the outcome. There are no losers so no external costs are imposed on any voter. 4

ECO 4554: Economics of State and Local Government Public Choice

2) A dictatorship, on the other hand, potentially imposes an external cost on all voters except the dictator. 3) As the percentage of voters required to agree increases, the external cost decreases. 3.

The lowest cost political decision rule See PowerPoint Slides Figure 2-2. a.

The lowest cost voting rule is the rule that minimizes the sum of the administrative cost and the external cost. Simple majority rule is not necessarily the lowest cost rule. The lowest cost rule could be either larger or smaller than a simple majority.

b.

In the diagram below, costs are measured vertically. The percentage of voters required to adopt an alternative is measured horizontally. Dictatorship (one vote) is at the left and unanimity (100% of the votes) is at the right. The curve labeled A shows the administrative cost. The curve E shows the external cost of an adverse decision. The social cost of voting, S, is the vertical sum of A and E.

Cost S A

E 0%

40%

100%

In this illustration, the lowest cost voting rule is a 40% plurality rule. [Note: The point at which A and E intersect has no special significance. It is simply the voting rule at which administrative cost and external cost are exactly equal. It does not necessarily correspond to the lowest point on the S curve.] c.

Higher administrative costs relative to external costs favor less stringent voting rules, pluralities instead of simple majorities. Higher external costs relative to administrative costs favor more stringent voting rules, super-majorities instead of simple majorities. Whatever the administrative and external costs, there is no reason to believe that simple majority rule, precisely 50% plus one, is always the lowest cost voting rule.

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ECO 4554: Economics of State and Local Government Public Choice

D.

Simple majority rule often does not choose the economically efficient alternative. See PowerPoint Slides Figure 2-3 and Example 2-1. 1.

2.

3.

If the tax system imposes on the median voter a share of the marginal cost of the good exactly equal to her/his share of the marginal social benefit, then the quantity preferred by the median voter is the efficient quantity. Simple majority rule would then result in choice of the efficient quantity. a.

Suppose Huey’s marginal benefit is 50% of the marginal social benefit, Dewey’s marginal benefit is 30% of the marginal social benefit, and Louie’s marginal benefit is 20% of the marginal social benefit. Dewey is the median voter.

b.

If the tax system assigns 30% of the marginal cost to Dewey, Dewey’s tax share is exactly equal to his share of the benefits. Dewey’s preferred quantity is the efficient quantity, so simple majority rule chooses the efficient quantity.

However, if the tax system imposes on the median voter a share of the marginal cost that is different from her/his share of the marginal social benefit, then the median voter prefers some quantity other than the efficient quantity. Simple majority rule does not choose the efficient quantity. a.

If the tax system assigns less than 30% of the marginal cost to Dewey, his share of the marginal social benefit is greater than his share of the marginal social cost and he prefers a quantity greater than the efficient quantity.

b.

If the tax system assigns more than 30% of the marginal cost to Dewey, his share of the marginal social benefit is less than his share of the marginal social cost and he prefers a quantity smaller than the efficient quantity.

Efficiency and the distribution of taxes a.

Simple majority rule is guaranteed to result in an efficient outcome only if the costs are distributed exactly in proportion to the marginal benefits. In other words, only with a Lindahl equilibrium tax system where the distribution of taxes is perfectly correlated with the distribution of benefits does simple majority rule always choose the efficient quantity. See PowerPoint Slides Figure 2-4.

b.

However, with a Lindahl equilibrium tax system, every voting rule chooses the economically efficient alternative. Simple majority rule is neither better nor worse than any other voting rule.

c.

Even if the distribution of taxes is not perfectly correlated with the distribution of marginal benefits, the quantity chosen using simple majority rule is likely to be more efficient with taxes or user charges based on willingness-to-pay than with taxes based on ability-to-pay. 6

ECO 4554: Economics of State and Local Government Public Choice

d.

E.

Examples of benefit taxes and user fees include gasoline taxes to finance highways, property taxes to finance fire protection, and sewer charges based on water consumption.

The quantity chosen by simple majority rule may not be unique or determinate or stable. 1.

2.

There may be no one quantity or expenditure level that is uniquely preferred by a simple majority of the voters. a.

Simple majority rule may cycle among the alternatives with each alternative able to defeat at least one other alternative.

b.

This is referred to as the cyclical majority or the paradox of voting.

Cyclical majority or paradox of voting: an illustration a.

Assumptions •

There are three voters (Huey, Dewey, and Louie).

•

They choose among three possible levels of education expenditure per pupil.

•

Their preferences are described in the following table where 1 indicates most preferred and 3 least preferred: Rank 1 2 3

b.

Huey $7500 $5000 $2500

Dewey $5000 $2500 $7500

Louie $2500 $7500 $5000

Voting is binary so that at each round of voting, voters may choose between only two of the three alternatives. Voting proceeds in the following order: Round 1 2 3 4 5

Issue $5000 vs. $7500 $7500 vs. $2500 $2500 vs. $5000 $5000 vs. $7500 $7500 vs. $2500 etc.

Winner $7500 $2500 $5000 $7500 $2500

What is the majority’s preferred alternative? There isn’t one. None of the alternatives is clearly preferred by a simple majority of the voters. Each alternative can defeat at least one other alternative. No alternative can defeat all of the others. 3.

Agenda control and simple majority voting 7

ECO 4554: Economics of State and Local Government Public Choice

a.

Voting continues to cycle among the alternatives with no determinate outcome unless there is some restriction on voting or termination rule. But any such restriction or rule is arbitrary.

b.

Examples of termination rules include • • • •

c.

4.

limiting the number of proposals that can be offered limiting the number of times that an alternative can be voted on setting a final date on which voting ceases establishing a rule that a proposal once defeated may not be reintroduced in a later vote.

If there is a termination rule, the alternative that is finally chosen depends as much on the order in which the alternatives are considered, or the agenda, as on the preferences of the voters. The individual or group that controls the agenda has disproportionate influence over the outcome.

Single peaked preferences a.

The cyclical majority or paradox of voting does not occur if preferences are single-peaked. When preferences are single-peaked, simple majority rule always has a unique determinate result. There is one alternative that can defeat all others. See PowerPoint Slides Figure 2-5.

b.

In the illustration of the cyclical majority above, preferences are not single-peaked. Louie’s preferences are inconsistent in a sense because he prefers $2500 to both of the larger alternatives but he prefers a much larger expenditure, $7500, to a moderately larger expenditure, $5000. He prefers either extreme to the middle. Rank Huey

1

2

Louie Dewey

3

2500

5000

7500

Expenditure per Pupil

c.

Suppose that we change Louie’s preferences. Suppose for example that he prefers $5000 to $7500. Now, his preferences are single8

ECO 4554: Economics of State and Local Government Public Choice

peaked and there is no cycle. Simple majority rule chooses $5000 per pupil no matter in what order the alternatives are considered. (Verify this by working through the voting rounds in b.2 above with this new set of preferences.) Rank Huey

1

2

Dewey Louie

3

2500

5000

7500

Expenditure per Pupil

d.

F.

III.

There is some evidence that single-peaked preferences are more likely to occur in larger groups than in small. If so, the importance of cycling may decrease as group size increases.

Majority rule does not reflect the intensity of individual voter preferences. 1.

The outcome of a simple majority voting rule depends only on the rank orderings of individual preferences. The outcome is independent of the intensity of individual preferences.

2.

To see this, note that an increase in the median voter's demand results in an increase in the quantity of the good. If the strength or intensity of the median voter’s demand increases, then the quantity of the good also increases. However, an increase in any other voter’s demand has no effect on the quantity chosen. No matter how strong the demands of other voters, only the demand of the median voter matters.

3.

An alternative voting rule that better reflects the strength or intensity of voters’ preferences is cumulative voting.

Cumulative voting (or point voting): An alternative to simple majority rule A.

Illustration 1.

Suppose that each individual in the group is given 10 points to assign in any way s/he wishes.

2.

The table below shows each voter’s rank order of preference among the three alternatives and each voter’s assignment of points to the alternatives. 9

ECO 4554: Economics of State and Local Government Public Choice

Expenditure per pupil $7500 $5000 $2500

B.

Huey Rank 1 2 3

Points 5 3 2

Rank 3 1 2

Points 1 5 4

Louie Rank 3 2 1

Points 1 3 6

3.

With simple majority rule, only rank matters, and $5000 per pupil is chosen by simple majority rule. With cumulative voting, the alternative with the greatest point total is the winner. This is $2500 per pupil, and so $2500 per pupil is chosen by cumulative voting.

4.

With simple majority rule, the alternative preferred by the greatest number of individuals wins without regard to how strong or how weak their preferences are. With cumulative voting, the most strongly or intensely preferred alternative wins without regard to how the voters rank the alternatives.

Advantages and disadvantages of cumulative voting 1.

Advantage: Cumulative voting may result in outcomes that are preferred by everyone to the simple majority rule outcome because it takes strength or intensity of preference into account, not just rank order.

2.

Disadvantages: Cumulative voting • • •

IV.

Dewey

entails greater administrative costs can be strategically manipulated by individual voters or groups may be subject to cyclical majority.

Monopoly bureaucratic voting models A.

Monopoly in the private sector and in the public sector 1.

The objective of suppliers in the private market is to maximize profits subject to the constraint imposed by consumers’ demand or willingness-to-pay. A monopolist maximizes profits by limiting supply below the competitive equilibrium quantity. At a lower quantity, consumers are willing to pay a higher price which provides the monopolist with higher profits.

2.

Monopoly bureaucratic voting models adapt the analysis of monopoly suppliers in the private market to government agencies and the bureaucrats who run them. Assume that the objective of bureaucrats is to maximize their agency’s budget subject to the constraint imposed by the voters’ demand or willingness-to-pay as expressed through voting. The bureaucrats exercise monopoly power because they control the agenda. Just as the private monopolist limits the quantity supplied to consumers, the monopoly bureaucrats use their control of the agenda to limit the alternatives on which voters can vote.

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ECO 4554: Economics of State and Local Government Public Choice

B.

C.

An example of a monopoly bureaucratic voting model: The reversion model 1.

The reversion model, which is used in Oregon school budget referenda, is an example of a monopoly bureaucratic model.

2.

The bureaucrats propose a budget to the voters. The voters may either approve the proposed budget or reject it. If they reject it, then the budget reverts to some pre-determined level such as last year’s budget or some percentage of last year’s budget. The pre-determined level, called the reversion level, is usually specified by law.

3.

Thus, voters cannot choose among all possible budgets. They can only choose between the proposed budget and the reversion budget.

An example of the reversion model See PowerPoint Slides Figure 2-6. 1.

The diagram below shows the median voter’s demand for road construction and the median voter’s share of the marginal cost of road construction.

$

A

Median Voter’s Tax Share

B

QR

QV

Median Voter’s Demand QB

Miles of Road Construction

The median voter prefers QV miles of road construction. This is the quantity that maximizes the median voter’s consumer surplus. 2.

Suppose the bureaucrats’ proposed quantity is QB. If voters reject the proposal, then the budget reverts to QR. Thus, the median voter cannot vote for her/his preferred quantity, QV, but can only choose between the bureaucrats’ proposed quantity, QB, and the pre-determined reversion quantity, QR.

3.

Both QR and QB provide less consumer surplus than QV. If the median voter accepts the bureaucrats’ proposed quantity, the loss in consumer surplus is area B. If the median voter rejects the bureaucrats’ proposed quantity in favor of the reversion quantity, the loss in consumer surplus is area A. If the bureaucrats propose a budget so that area B is smaller than area A, the median voter accepts the bureaucrats’ proposed budget. If the bureaucrats 11

ECO 4554: Economics of State and Local Government Public Choice

propose a budget so that area B is larger than area A, the median voter rejects the bureaucrats’ proposed budget. 4.

The largest quantity that voters would accept is QB where area A=area B. To ensure that voters accept their proposal, bureaucrats who want to maximize their budget might propose a budget so that area B is just slightly smaller than area A. Because they control the agenda, the bureaucrats are able to increase the agency budget beyond the median voter’s preferred level, QV. [Note that the distance from QV to QB equals the distance from QV to QR only when the demand curve is a straight line. Comparing the loss in consumer surplus between QV and QB to the loss in consumer surplus between QV and QR is always correct no matter how the demand curve is shaped.]

5.

Is a lower or a higher reversion level better? a.

A higher reversion level is better for the voters. The higher is , the lower is . A higher reversion level reduces the maximum possible loss to the voters from rejecting the bureaucrats’ proposal and therefore limits the bureaucrats monopoly power.

b.

A lower reversion level is better for the bureaucrats. The lower is the pre-determined reversion quantity, the greater is the voters’ loss if they reject the bureaucrats’ proposal and the larger the quantity that bureaucrats can get the median voter to approve. In fact, the best reversion quantity for the bureaucrats is zero so that if the median voter refuses to accept the bureaucrats’ proposed quantity, there will be no road construction at all. This is an “all-or-none” or “take–it-orleave-it” system, which gives the bureaucrats maximum monopoly power.

c.

Example: Whenever the National Park Service budget is reduced, the Park Service announces that it will close the Washington Monument. Either we fund the Park Service at their desired level or the Washington Monument is history. Surely, there are other, less visible ways that the NPS could reduce their budget, but the Washington Monument is always at the top of the list. This strategy maximizes the monopoly power of the bureaucrats at the National Park Service.

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