UD-9

In this chapter, we introduce another reason why the provision of public goods by means of a democratic government is likely to be inefficient. This is also another reason why we can expect government failure in a democracy. It is that it is practically impossible in reality for majority voting to result in the optimal supply of a public good. We demonstrate this point by using some simple models of direct democracy. In addition, we show that most voters are likely to be dissatisfied with the quantity of any particular public good that is supplied collectively. Most would prefer a different quantity.

Part one of the chapter defines the economic idea of efficiency in the supply of a public good. Part two discusses the efficiency of public goods supply when the amount supplied is decided by simple majority rule and when the tax for the public good is shared equally. Part three does the same except that it assumes that the tax paid by each person varies with his income. Part four shows that simple majority rule decision-making may lead to the supply of a good which benefits some people but which causes greater harm to other people. Part five briefly discusses how our conclusions would have to be modified under a supra-majority rule. As mentioned in Chapter Five, this is a collective decision-making rule that requires more than a 50+% majority for a public good to be supplied.

In the models of this chapter, it is assumed that the decision to supply one public good is made separately from the decision to supply other public goods. In real democracies, this is not the case. Part six discusses this fact and how it bears on the conclusions reached in earlier parts. The chapter ends with a brief conclusion.

The economic theory of a public good begins by assuming that the good is a pure public good (see Chapter Three).

Economists teach that it is efficient to produce a pure public good if the collective benefits are greater than the costs. Assuming that the good can be broken down into small units, this implies that it should be supplied up to the quantity where the sum of the marginal benefits equals the marginal cost.

Figure 9-1 shows this for the simple case of two people and constant production costs. D_a is the demand of consumer A, and D_b is the demand of consumer B. The optimal quantity is q*, where the vertical sum of the two demands (D_a+b) = MC. To show efficiency when there are many members of the collective, we would simply increase the number of demand curves.

The efficient quantity of a public good: the quantity at which the sum of the marginal benefits equals the marginal cost.

Before going on, it is worth pausing to consider why, under the usual economic assumptions, we say that the quantity q* is efficient. Efficiency refers to resources. It implies that it is not possible to shift a resource from one use to another without reducing the money value of surplus (or benefit) from production and distribution. Thus, when we say that q* is efficient, we mean that when the resources are used to produce q* units of the good, they yield more surplus than if they were used elsewhere. Because we assume constant costs, surplus consists entirely of surplus to consumers, or consumers’ surplus. The area of the triangle EFP in the figure represents this consumers’s surplus.

We can better understand efficiency by comparing it with inefficiency. In figure 9-1, consider the resources needed to produce the last unit, the q*th unit. For example, if the efficient quantity is 100, then the q*th unit is the 100^th unit. The resources needed to produce that unit could be used to produce other goods. Suppose that they are shifted to some other industry, or industries. Then the number of units of the public good produced would be q*-1, as shown in figure 9-2. When we say that q* is the efficient quantity, we mean that the resources needed to produce the q*th (100^th) unit, given that q*-1 (99) units arealready being produced, are worth more if they are used to produce that unit than if they are used to produce the other goods. In figure 9-2, the value of the resources in other industries that are needed to produce the q*th unit (i.e., the opportunity costs) are equal to the area bcgf. The value of those same resources if they are used to produce the q*th unit is acgf. There is a net surplus to the collective of consumers of abc. Similarly, the worth to the collective of producing the q*+1th unit is less than the worth of the other goods that could be produced with the same resources. The cost is the same, cdhg. The value if they are used to produce the q+1th unit is cehg. The net loss to the collective of consumers is cde.

We can use figure 9-1 to help us discuss interaction between the two people. Suppose that A and B both live in a competitive market economy. Suppose further that the good is a public good for only A and B. Others in the economy feel no effects from its production. Finally, assume initially that A and B act independently. Neither recognizes that the other benefits from the good. In other words, although we as outsiders know that the good is a public good, both A and B look upon it as a private good. Under these assumptions, each would make a private decision about how much to buy.

Let us assume at first that A and B make their decisions to buy at exactly the same time. To maximize his satisfaction, A would buy q_a from competing suppliers. This is the quantity at which his personal value, or marginal benefit, in terms of money, just equals the price he must pay. B would buy q_b. The total bought would be q_a+b.

Each person would gain more satisfaction than he had expected because he did not anticipate the other's purchase. He would be pleasantly surprised. However, neither would be fully satisfied with this outcome. We can see why by putting ourselves in the shoes of A and B, respectively. We begin with A. A only decided to buy q_a but he was able to consume the amount q_a+b. Because of the additional amount purchased by B, the benefit from the last unit he bought was only equal to c. Yet he paid a price of p for it. So he would regret having purchased so much. If he expected the same thing to happen again, he would want to reduce his purchases to zero, since at q_b, the price he must pay for an additional unit, p, is greater than his marginal benefit. A would want to be a complete free rider.

Now let us put ourselves in B's shoes. She decided to buy q_b but, as in the case of A, she was able to consume q_a+b. She also would regret her purchase. Unlike A, she would not wish that she had reduced her purchases to zero. She would wish that she had reduced them to q_b - q_a. She would only want to be a partial free rider.

Now let us suppose that A reduces his purchases to zero and B reduces her purchases to q_b - q_a. Neither would be fully satisfied with this outcome either. Each would want to consume more and would wish that he had bought more.

We do not need to discuss this very unrealistic case further. It is enough to point out that for A and B to reach a situation where they would be permanently satisfied under the assumed demand and supply conditions, they would have to make virtually an infinite number of adjustments. Long before this happened, each would figure out that there was another human like herself who was making choices to buy. Given that they live in a peaceful society, each would want to seek out the other for negotiation in order to avoid so many future errors in judgment.

Negotiation could have many outcomes. As we have said, q* is the efficient quantity. However, there is no reason to think that the two individuals would believe this and that they would agree to an outcome of q*. Each has an incentive to conceal his preferences from the other in order to gain the advantage in bargaining.

Figure 9-1 looks very much like the ordinary demand and supply diagram of private markets that we see in the economics textbooks. But you should not be deceived. It is different for a very important reason. The ordinary diagram of a competitive market for a private good shows two things. First it shows the most efficient quantity and price. Second, it shows the quantity and price that buyers and sellers would tend to achieve under the assumed conditions of competition among suppliers and price-taking consumers. In economic jargon, the latter is called an equilibrium. The diagram of public goods supply only shows efficiency. Because there is no competition among suppliers and because individuals have a tendency to conceal their demands for public goods, it does not show an equilibrium toward which there is a tendency.

The quantity q* is the one at which the net gains to consumers, in terms of money, are as high as possible. Given that the marginal cost is MC, if any smaller or larger amount was produced, the consumers' gains, or surplus, would be lower. The consumers' surplus, if q* is supplied, is represented by the triangle EFP in figure 9-1. This surplus may be divided up in any conceivable way, yet there would still be efficiency in the economic sense.

Economics identifies the most efficient quantity, not the best distribution of gain. It does not make recommendations about who should receive the gain, except insofar as the distribution affects the amount of the surplus that is produced. Assume that A and B agree to demand q*. The total cost is P x q*. Would the agreement be fair? One should not look to economics for an answer.

Ordinary people are concerned with distribution, however. The distribution of the cost burden has a lot to do with whether people are satisfied with their public goods interaction. In the simple interaction among two people, if one is dissatisfied, he can simply opt out. In other words, he can decide not to cooperate with the other. For example, if A was dissatisfied, he could always decide to quit the agreement and buy his optimum quantity q_a, regardless of what B decided to do. The worst that would happen is that the other would respond by deciding to produce nothing. If a public good is bought by the government, however, the cost of opting out is ordinarily very high. One can opt out only by refusing to pay taxes.

In a large collective with a market economy, where public goods are supplied by means of a representative democratic national government, the cost burden is in the form of mandatory taxes. How it is divided among members of the collective is determined by the decisions of elected legislators. Suppose that the legislature decides to cause the optimal amount of a pure public good to be produced. However, the tax burden that results from this decision is distributed in such a way that the benefits to many people are lower than their taxes. Then those people will be dissatisfied and may want to leave the country.

Local Public Good – a public good that only yields benefits to those who happen to live in a geographical area where the good is supplied.

Up to this point, we have only discussed pure public goods. Such public goods benefit everyone. In everyday life, there are no pure public goods. All real public goods have a range limitation. Consider what economists call a local public good -- one that only yields benefits to those who happen to live in a geographical area where the good is supplied. Such a good is usually supplied by towns, city governments or states. It may be available in different tax jurisdictions at different quantities and tax prices.

In this event, individuals who are dissatisfied in one community may be inclined to move to a different community, where the combination of tax price and quantity of the public good is closer to their own preference.

If members of a collective make decisions to produce public goods by using simple majority rule, will their decisions result in an efficient quantity in the economic sense? Will members be satisfied with the outcome? The aim of this section is to help us find out. We begin with a list of alternative proposals to supply a public good. Then we try to predict which one will be chosen, given that each voter votes according to her preferences.

The alternative proposals facing a collective in everyday life are very complex. The most we can do here is to consider some simple proposals that we can relate to the two-person model shown in figure 9-1. We assume that each proposal consists of two parts (1) a designated quantity of a fixed-quality public good and (2) a tax price sharing plan. Proposals in everyday life are more complex in three ways. First, public goods vary in "quality." As a result, members of a collective have a range of quality choices. Second, there is virtually no limit to the number of tax schemes that can be used to finance a public good. Third, proposals to supply one public good are often considered jointly with proposals to supply other public goods. We discuss these complexities in part six.

Using the model of figure 9-1 as an analogy, assume that there are many members of a collective each of whom has a demand for a single public good. Assume further that each member of the collective agrees to pay an equal share of the cost of supplying the collectively-decided quantity. Under these conditions, a decision about how much to supply could easily be made by majority vote. Because individuals have different demands, some would prefer a large quantity while others would prefer a small quantity. Under a simple majority rule, the quantity preferred by the median voter would win the vote. The median voter analysis of Chapter Seven would apply.

Given realistic assumptions within this model, there would be neither efficiency nor full satisfaction with the quantity supplied except by coincidence. Our method of demonstrating this is to first identify the configuration of demands that would have to exist for efficiency and full satisfaction to be achieved. Then we argue that such a configuration would not exist in reality.

Under the equal-sharing rule, the size of each member's tax bill rises with the quantity of the public good supplied. In addition, it equals 1/nth of the total tax bill, where n is the number of members in the collective. If we assume constant marginal costs of supply, as we did in the case of figure 9-1, a collective decisions to supply two units would require each person to pay twice as much tax as one unit. Each person's tax price per unit would be MC/n. Her tax bill would be MC/n x q, where q is the quantity of the public good supplied. The marginal tax price for each citizen is shown as a horizontal line, MC/n, in figure 9-3.

Efficiency and full satisfaction would be achieved if all demands were alike. In this case, each consumer-voter's demand would be 1/nth of the collective demand. Referring to figure 9-3, each voter would have the same demand curve, say D_m, which is labeled the average demand voter. Since all voters are alike, each would be the median voter. The median voter's (i.e., every voter's) optimum is q* since this is where his demand crosses his tax price line. The quantity q*, of course, is the same as the efficient quantity for the collective. Thus there would be quantity efficiency.

In addition, each voter would be fully satisfied with q*, given the tax price. No voter would want a larger or smaller amount.

Figure 9-3

AN INDIVIDUAL FACING AN EQUAL-SHARING

RULE

Realistically, members' demands differ. So let us vary the example slightly by assuming that consumers have unequal demands. Assume that the sum of the demands and, therefore, the average demand is the same as in figure 9-3. If the median voter has an average demand (one that is equal to D_m), the efficient quantity would still be supplied, since the median voter would favor it. There would be quantity efficiency.

In a collective of n members, not only are consumers' demands likely to differ, the median voter's demand would most likely not equal 1/nth of the collective demand. Suppose that the median voter's demand is lower than 1/nth of the collective demand. Then he would vote for a quantity that is lower than q*. If his demand is higher, he would vote for a higher quantity than q*. In either case, majority voting would lead to an inefficient amount of the public good.

In everyday life, voter demands differ. If we assume that they do and if everyone's tax price is the same, most voters will be dissatisfied with the median voter's choice. To see this, assume as before that the median voter’s demand equals the demand of the average demand voter. In figure 9-3, we have drawn the demands of a high-demand voter (H) and a low-demand voter (L), D_h and D_l. H's preferred quantity is q_h. L prefers a zero amount of the good. Thus, both voters would not be satisfied. Full satisfaction could be achieved at the quantity q* if individuals were charged different tax prices. For example, H and L would be satisfied with q* if their respective tax prices were p_h and p_l.

Under any rigid tax-sharing rule, there is unlikely to be either efficiency or full satisfaction with the quantity of a public good supplied as a consequence of majority rule decision-making.

When we say that individuals would be dissatisfied with the outcome, we mean only that they would prefer a larger or smaller quantity of the public good. Even if there is dissatisfaction in this sense, each person's total benefit may still be greater than her tax costs. In other words, although a person would want a larger or smaller quantity, she may not want the government to stop supplying that good.

Moreover, even if a majority of consumers of a particular public good prefers that the government stop supplying it, they may benefit from the government's supply of public goods in general. Other public goods may give them much greater benefits than their tax bills.

If we consider local public goods, individuals may have the alternative of moving to a locality where their gains are higher or losses lower.

Note that if some low-demand voters opt out of the system by, say, moving to another locality, the remaining members of the collective would have to pay a higher tax share.

Although we have limited our discussion to an equal-sharing rule, the conclusion applies to any rigid tax-sharing rule. The median voter theorem deduces that under the assumed conditions, the quantity will be determined by the preference of the median voter. Once a rule is established, the only way that complete satisfaction with the collective decision could be achieved is to vary the tax price according to whether a voter-consumer has a low or high demand.

By definition, a rigid tax-sharing rule does not permit this.

In this part, we consider the more complex case of an income tax. The goal of an income tax is to charge high-income people a higher tax than lower-income people. More accurately, the goal is to discriminate in the size of the tax charged on the basis of the income that an individual would have earned. Real tax systems cannot achieve this ideal very well. As soon as people find out that their incomes will be taxed, they look for ways to avoid the tax.

We can identif y three problems associated with trying to achieve the goal. The first is the problem of defining income. If the legislature or chief executive (the government) defines income as money income, some individuals can more easily shift to self-sufficient activities and to earning income-in-kind through barter. This tendency can be countered by defining income as any flow of satisfaction that an individual receives because he has performed some service or made some investment. Under this definition, receipts of in-kind income would be taxable. However, the government then encounters huge problems of comparing incomes. Government agents would have to find some way to compare the satisfactions received from the different in-kind services. The problem faced by government agents is to discover the various means of concealment and to administer an appropriate penalty for concealment. We do not expect them to succeed very well in this. Because individuals differ in their abilities to conceal their incomes, an income tax cannot be completely fair. In other words, it cannot fully achieve its goal.

Real tax systems cannot completely succeed in taxing people on the basis of their ability to earn income because:

1. Individuals have different incentives and abilities

to shift from activities that result in taxable income to activities that do not.

2. Individuals have different incentives and

abilities to shift from legal to illegal enterprises.

3. Individuals have different incentives and abilities

to evade the tax.

The second problem is that such a tax encourages illegal enterprises relative to legal ones, since the illegal ones cannot be taxed. The third problem is that people have different abilities to defend themselves against the charge of tax evasion. High-income members of the collective typically find it profitable to employ highly skilled lawyers to argue their cases in court. In addition, they are in a better position to bribe tax collectors and judges.

Not only can real tax systems not achieve the ideal that is implied in the concept of an income tax, real-world democratic governments typically use their tax systems for other purposes. Legislators may set the schedule of income taxes lower for heads of households than for single people because voters with families constitute a stronger political force. They may also grant tax breaks to individuals who use their income to improve their education, who make employment-creating investments, who have unusual medical bills, who make donations to charity, who use child care services, and so on.

Obviously, we cannot consider each and every possibility. Thus, we confine our discussion to a strictly proportional income tax with no deductions or exemptions.

We also assume no tax avoidance.

As before, let us define q* as the most efficient quantity. For a proportional income tax to result in q* under the assumptions of the model in figure 9-3, q* would have to be the most preferred quantity to the median voter. This is highly unlikely. To understand why, we consider two cases. In the first, we assume that all individuals have the same demand. In the second, we assume that demands differ.

To help us understand the position of a taxpayer, consider figure 9-4, which uses the same assumptions as those used in the earlier discussions. We assume that there is a collective of n members and that each taxpayer has the same demand: D_n. In addition, we assume that the median voter receives the average income. Under these conditions, the collective would choose q*. Put yourself in the shoes of the median voter shown in the diagram. You earn an income equal to the average for the collective. Therefore you will have to pay a tax price of MC/n = p_n. For example, suppose that the collective has 60 members and that the cost of one unit is $600. Then for each unit, your tax price (p_n) would be $10. Your preferred output would be q*, the efficient output. This is the output that the collective would choose because you are the median voter.

Now suppose that you earn an income that is twice as much as the average. Under the same conditions, your tax price would be $20 per unit. In figure 9-4, $20 = p₃. You would prefer that none of the public good be supplied because p₃ is higher than your demand curve. But, of course, the median voter prevails. If you earned half as much as the average, your price would be $5 (p₁). You would prefer the larger quantity of q₁, since the line .5MC/n crosses your demand line at that point.

To understand why it is unlikely that the median voter under a proportional income tax would choose the efficient quantity, we must consider the distribution of income. Let us start with two extreme distributions. Suppose that one person earns so much more than everyone else that he pays more than one half of the total taxes. Assume that the rest of the income is distributed equally. Then everyone else's tax price, including that of the median voter, would be less than one half of the marginal cost. In figure 9-4 it would be less than p_l = $5. Thus the median voter would demand a quantity that is greater than q₁. This is inefficiently large.

At the other extreme, suppose that 49 per cent of the voters earn no income. Assume further that the total income is evenly distributed among the other 51 per cent of the voters. Then, the tax price to the median voter would be slightly less than twice p_n, or p₃ = $20. The quantity of the public good demanded would be zero. This is clearly not efficient either.

In the capitalist systems that we know, the median income is typically less than the average (1/nth) of the total income earned by all members. Under the circumstances, if all voter preferences were the same and if everyone voted, the quantity of the public good demanded by the median voter would tend to be inefficiently large on this account.

Of course, the demands for a given public good are not identical, as we have assumed. They vary for a number of reasons. Let us consider a couple of extreme examples. First, we can suppose that the height of the demand for the public good varies directly and proportionally with income. In this case, a proportional income tax that was evenly applied, that contained no exemptions or deductions, and that individuals did not try to avoid would result in the median voter having the median income. Under the assumed conditions, the efficient quantity of the public good would be chosen. Moreover, each voter would be fully satisfied with the resulting output. High income voters would pay high tax prices and, as a result, demand a moderate amount of the good. Low demand voters would pay low tax prices and also demand a moderate amount of the good.

Another extreme is where the height of the demand for the public good varies inversely and proportionally with the demand. In this case, a proportional tax would again result in the optimal quantity of the public good. However, tax prices would be just the opposite of what would be needed for people to be satisfied with the collective outcome. High income-earners, who have low demands, would be extremely dissatisfied. They would be under great pressure to opt out or revolt against the system if they could. Low income-earners who have high demands would press for an even larger quantity.

Under an income tax, there is unlikely to be either efficiency or full satisfaction with the quantity of a public good supplied as a consequence of majority rule decision-making.

None of these extremes corresponds to reality. We consider them in order to help us better understand how income distribution effects the quantity of the public good that is chosen and why there may be dissatisfaction with the collective choice.

In Chapter Four we discussed the "external costs of collective decision-making." We pointed out that an individual would be wary of participating in a majority-rule, collective decision-making procedure. He would want to be assured that others' decisions were not so much against his interest that his participation turned out to be a mistake. In fact, majority decision-making may result in the supply of goods for which the total money costs are greater than the money benefits. We can illustrate the potential problem by using the median voter model developed in Chapter Seven.

Figure 9-5 differs from the median voter model in figure 7-1 in two ways. First, the expenditure axis is moved upwards so that for each voter, there is a range in which the expenditures are positively harmful. This reflects our assumption that each voter must pay an equal share of the tax bill. Second, the preferences are not symmetrical. B is harmed by every possible expenditure. His optimum is at point b. An expenditure of 0b will do him less harm than a smaller or larger expenditure. Nevertheless, all the expenditures are harmful to him. If either A or C is able to attain his optimum, they will both enjoy a net benefit of some amount.

In a vote, the median voter theorem will apply, as we showed in Chapter Six. Thus, an expenditure of 0a would be chosen. For illustrative purposes, let us use the lines to measure absolute satisfaction in terms of money.

Then, if a is chosen, A would gain 0a', B would lose 0b', and C would gain 0c'. The loss to B would exceed the combined gains to A and C.

We would not presume to know the gains or losses to the individuals in any specific case. Our aim here is only to show that even though a majority may agree and benefit from a simple majority decision, we may be inclined to judge that the result is worse than if no decision had been made.

If possible, B would not want to allow spending on this good to be put on the agenda. In other words, he would want to block the issue from being brought up for a vote. Assuming however that items can be added to the agenda if a majority approves, this item would be added because A and C would approve.

Although a majority may benefit from and vote to adopt a particular proposal, one who takes account of the intensity of preferences may judge that the collective would have been better off if it had rejected it.

It is worth pointing out that although this good yields simultaneous benefits to all three parties,

there is no quantity for which the sum of the benefits from it would exceed the cost of producing it. Thus we might be inclined to call this a public "non-good," or public "bad." The essential point is that the harm and the others' benefits are joint, given the equal-sharing rule. Also, by assumption, no one can be excluded from the effects.

We can use a similar model to show that a majority may not approve an expenditure even though the sum of the benefits is greater than the costs. Consider the preferences represented in figure 9-6. The benefits to A of selecting a are 0a'. The combined harm to B and C is 2 x 0b'. Since 0a' is greater than 2 x 0b', efficiency requires that the good be supplied. Yet the majority would vote against supplying any quantity of the good. If a majority was required for the item to be put on the agenda, B and C would block it from being put on.

Although a majority may be harmed by and reject a particular proposal, one who takes account of the intensity of preferences may judge that the collective would have been better off if it had accepted it.

Up to this point, we have discussed a simple majority rule of 50+ per cent. Let us briefly consider how our conclusions would have to be modified if a greater majority was required to pass a bill. Consider a case of five voters whose preferences are of equal intensity and are evenly distributed about the preference of the median voter. Figure 9-7 shows such a case. Assume that for a collective decision to be made, a 2/3rds majority is required.

We can gain an understanding of the problems raised by a 2/3rds majority by comparing important pairs of alternatives. Let us put ourselves in the shoes of the voters and ask how they would vote on some of the pairs. Consider a comparison in the range between 0 and a. Let us select a point f midway between 0 and a. We compare it with a point that is also within this range but to the right of f. On the basis of the preferences in the figure, everyone would vote for the expenditure to the right of f. By using similar comparisons, we can deduce that point a would be preferred by all voters to any point left of a. Thus in a paired comparison a would defeat any point to the left of a by more than a 2/3rds majority.

Next consider expenditures in the range between a and b. Four of the five voters prefer b to any expenditure to the left of b. Only A prefers expenditures to the left of b. Thus, in a two-thirds majority vote, b could defeat any point to the left of b by more than the required 2/3rds majority.

Now let us begin at the other end -- at $1 million. All voters would vote for e in preference to any point to the right of e. And four of the five voters would vote for d as compared with any point to the right of d. Thus d could defeat all points to the right of d by more than the required 2/3rds majority.

This analysis shows that points to the left of b and to the right of d would always be defeated in a 2/3rds majority vote by any point between b and d. Thus we can say with confidence that in an exhaustive vote, a 2/3rds majority would not choose either points to the left of b or points to the right of d. But what can we say about points between b and d?

If we compare any two points within this range, we can see that none can obtain a 2/3rds majority over the other. Consider point g. If a paired-comparison vote is taken between b and g, 3/5ths of the voters would prefer g. However this is not enough to achieve the necessary 2/3rds majority. The same is true for a paired-comparison vote between b and c. Consider a paired-comparison vote between g and h. Two voters would vote in favor of g, two would vote in favor of h, and one voter would be indifferent.

We have considered only the simplest, small numbers case. Because of this, our analysis cannot be strictly applied to every supra-majority rule. However, the conclusion is generally applicable if the number of voters is large.

Let us state our conclusion about an exhaustive-vote, large-numbers collective decision subject to a supra-majority rule. Under these conditions, and in the general case, a collective decision can only be made through some kind of compromise. This is possible in the example of figure 9-7 since for each voter, some decision is better than no decision (the status quo). Exactly what the compromise would be is not evident. If vote buying is allowed, it is possible that some voters would try to buy the votes of the others. If it is not allowed, then vote-trading may occur. Suppose that the collective is considering more than one issue. Then voters who would otherwise vote against a particular project may agree to change their votes if other voters agree not to vote against a project that they favor. Whatever outcome emerges, it must emerge from negotiation and not from paired voting on single issues. We discuss vote-trading in the next chapter.

An exhaustive-vote, collective decision subject to a supra-majority rule will not yield a unique outcome. The outcome must emerge from negotiation and not from paired-comparison voting.

We can look at the supra-majority rule in a different way. We can say that under supra-majority rule, only a minority is required to block any particular expenditure from being adopted. This has led some writers to argue that a supra-majority rule amounts to potential tyranny by the minority. For the simple case discussed here, these writers are correct. In more complex cases, there are several ways around this problem. First tax plans can be devised to persuade people who otherwise would be members of a blocking minority to vote in favor of some issue. Second, issues can be combined and then voted on as a single issue. Third, there may be several dimensions of service quality. In this event preferences for more or less of one quality dimension can be traded off against preferences for more or less of a different quality dimension. We shall gain some insight into these possibilities in the next chapter.

In real democracies, collective decisions are not made directly by voters. They are made indirectly through legislative representatives. The public goods on which these representatives vote often have a number of quality dimensions. Take a decision to supply the repair of government-owned streets. Quality may refer to the durability of the repairs, the nature of the surface after the repairs (different degrees of smoothness); complementary services such as improved drainage and reinforced roadbeds; and the virtually infinite possible locations of the surfaces that can be repaired. In an actual collective decision involving government streets, the legislature must decide on each of these dimensions.

In addition, real legislative representatives often consider proposals to spend on several different public goods at the same time. A single legislative bill on transportation may contain proposals to spend on roads, bridges, rail systems and airports.

Besides this, the taxes needed to finance spending bills are not equally shared. Tax plans can be very complex. We have pointed out that many tax systems base the size of the taxpayers's tax on the amount of her income. We have also noted that tax size may be adjusted on the basis of such things as whether the taxpayer has a large family, invests in education or job-creating activities, contributes to charity, or uses child care services. In addition, a government may have several kinds of taxes. For example, the tax laws may specify that half of the government revenue used to pay for a public good would come from the income tax, a fourth from a sales tax, and a fourth from a property tax. Clearly the system of financing public goods can be very complex. In fact, we cannot even fully describe the possibilities. Because of this, we cannot imagine a ballot that includes all of the possible tax plans.

Finally, legislatures in everyday life do not impose a separate tax for each public good. In most cases, the same overall taxes are used to finance all of the public goods. As a result, a taxpayer who wants to calculate the tax price of any particular public good (roughly) must divide the total spending on that good by her share of the total tax. Suppose, for example, that one hundred miles of road are built at a cost of $10 million dollars, making the cost per mile of road equal to $100,000. If you pay 1 millionth of the total tax bill, the tax price to you per mile is $.10. To make such a calculation, you would have to know the cost of the road per unit and your per cent of the total tax bill.

Most people do not ordinarily make such calculations and, therefore, do not ordinarily know their tax prices. The reason may be that it is often unprofitable in large elections for individuals to improve their decision-making ability. They remain rationally ignorant (see Chapter Seven). It may seem odd that members of the collective do not demand that their legislators try to estimate the personal tax price of various spending bills. It would seem to be a good idea for every new spending proposal to contain such an estimate so that voters can know whether they are getting a good deal from their legislators.

In this chapter we have considered enough simple cases to get a general idea of the inefficiency of majority rule. When we try to apply our theoretical model to what we can realistically assume about individuals' preferences, their distribution of income, and real tax systems; we must conclude that we have no particular reason to believe that the quantity of a single public good that is chosen by majority rule in a direct democracy would be close to the theoretically efficient quantity. Also we have no reason to believe that a majority of voters will be satisfied with the quantity of any single public good that is supplied.

1. Use the diagram of a two-person demand for a public good to show the efficient quantity. Be careful to label your diagram properly. In words, describe the curves and the assumptions you have made in drawing them.

2. Referring to the diagram of a two-person demand for a public good, explain why the efficient quantity is, in fact, the efficient quantity.

3. Referring to the diagram of a two-person demand for a public good, explain why the efficient quantity is not an equilibrium. In your discussion, put yourself in the shoes of the two demanders.

5. The text argues that if a collective adopts a rigid tax-sharing rule, two things are likely: (1) the quantity chosen through majority voting will not be efficient and (2) most voters are likely to be dissatisfied. Referring to a graph, use words to present the logic behind this conclusion.

7. The goal of an income tax is to discriminate according to the amount of income that an individual would have earned in a market economy. Tell three problems associated with a government's effort to achieve that goal.

8. Suppose that all members of the collective have the same demand for a public good but that their incomes differ. The tax-sharing rule is that members will be taxed according to a proportional income tax. There is no tax evasion. Assume further that the collective decision on how much to buy is made by simple majority vote. Thus the median voter theorem would apply. The text says that under these circumstances it is likely that a quantity that is larger than the most efficient quantity of the public good would be demanded. Explain the text's reasoning.

9. Suppose that the demands of members of a collective vary directly and proportionately with income. Thus those members with high demands also have high incomes. The tax-sharing rule is that members will be taxed according to a proportional income tax. There is no tax evasion. Assume further that the decision on how much to buy is made by simple majority vote. Thus the median voter theorem would apply. Would the collective decision be efficient? Would consumers be satisfied? Explain.

10. Suppose that the demands of members of a collective vary inversely and proportionately with income. Thus those members with high incomes have low demands and those with low incomes have high demands. The tax-sharing rule is that members will be taxed according to a proportional income tax. There is no tax evasion. Assume further that the decision on how much to buy is made by simple majority vote. Thus the median voter theorem would apply. Would the collective decision be efficient? Would consumers be satisfied? Explain.

11. Assume that voters must pay taxes to obtain the benefits of a public good. Adapt the simple 3-person median voter model of chapter 7 to show that the what we judge to be the total benefits of a majority vote decision may be lower than the total costs. Note that you must assume that the utilities of different voters can be compared to answer this question.

12. Assume that voters must pay taxes to obtain the benefits of a public good. Adapt the simple 3-person median voter model of chapter 7 to show that the collective may decide to demand zero units even though we judge that the benefit of a majority vote decision is greater than the total costs. Note that you must assume that the utilities of different voters can be compared to answer this question.

13. Compare simple majority rule with supra-majority rule. Discuss the probability that laws that yield net collective losses will be passed and the probability that laws that yield net collective benefits will be passed.

14. One of the disadvantages of supra-majority rule decision making is that for decisions to be made, there must be a compromise. Use the median voter model to show that this is true for the simple case of a 2/3rds majority and 5 voters.

Gunning’s Address
J. Patrick Gunning
Professor of Economics/ College of Business
Feng Chia University
100 Wenhwa Rd, Taichung
Taiwan, R.O.C.
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