UD-7

The purpose of this chapter and the next is to discuss elections. Public Choice has developed three rather simple but major insights regarding elections. The first concerns the act of voting. Public Choice theorists have pointed out that it is not usually profitable for a voter to use his voting right for the purpose of influencing government. The money value of the benefits that a voter expects from public goods or other government actions due to his vote are not higher than the money value of the benefits he must give up in order to vote. This observation has led them to ask deeper questions about why people vote and why they acquire information about candidates and issues. The second insight concerns how candidates or political parties can win votes. Public Choice theorists have discovered that if they make some simple assumptions about voter preferences and about candidates or parties, they can show that, if political candidates and parties aim to win elections, they will ordinarily avoid taking extreme positions on issues. This idea is called the median voter theorem. This theorem helps explain why it often appears that there is very little difference between the positions taken by opposing candidates in a two-party election. The third insight deals with majority voting. Public Choice theorists show that under fairly typical voting conditions, the candidate or policy that is chosen may not be the one that most people would regard as best. This basic insight is called the voters' paradox.

In this chapter, we consider the first two of these insights. Part one discusses the decision to vote and to improve information. Part two presents the simple median voter theorem for the case of direct democracy, where voters vote directly on issues. We expand on these simple ideas and describe the third insight in Chapter Eight.

When Public Choice theorists consider the decision to vote, they focus on three rather obvious but often neglected facts. The first is that a person's gain from an election is really a comparative gain. Consider an election competition between two candidates, A and B. If A is elected, the voter expects certain benefits and tax costs. The same is true if B is elected. The gain from an election is equal to the difference between the two. Suppose that you expect candidate A to build a new park near your home and candidate B to repair a road that you frequently use. In other respects you expect the two candidates to be the same. The gain to you from the election is the difference between (1) your benefit minus your tax cost if the park is built and (2) your benefit minus your tax cost if the road is built.

The second fact is that the gain from an election is not the same as the gain from voting. The gain from voting is the gain you expect from carrying out the action of casting your ballot. Suppose that your gain from the election in a two-person race is $1,000. In the above example, building the park is $1,000 more valuable to you than repairing the road. If A wins, you expect to gain $1,000 more or to lose $1,000 less than if B wins. Your gain from voting is much lower. It equals the $1,000 times the probability that your single vote will affect the outcome. Suppose that a million people vote. Assume that you know nothing about how the other 999,999 people will vote. Then the probability that your vote, by itself, will cause A to win is about 1/1,000,000. As a result your gain from voting is approximately one tenth of a penny ($1,000/1,000,000 = $.001). Thus, even if a person gains (or loses) substantially from an election, his gain from voting may still be quite small.

The third neglected fact is that time has alternative uses. There is an opportunity cost of using your time to vote. If voting takes an hour's time, the hour must come at the expense of overtime work, housework, an hour's entertainment, and so on. Continuing with our example, suppose that an hour of your time is worth $10. Suppose further that there are a million voters whose votes you do not know. Then you would have to expect the election of A to be worth approximately $10 million dollars more to you than the election of B for your voting to be worthwhile. Obviously, not too many people would expect such a big gain from an election.

Rational voter hypothesis: a "rational voter" will vote when his expected money value of the difference between the candidates' election times the probability that his vote will influence the election is greater than the opportunity cost of voting.

Public Choice theorists have put these facts together in a formal model of the voting decision. Let V₂ - V₁ be the money value of the difference between two candidates, let P be the probability that the vote will influence the outcome, and let C be the opportunity cost of voting. Then a person will choose to vote if:

This is called the rational voter hypothesis. In words, it says that a "rational voter" will vote when his expected money value of the difference between the candidates' election times the probability that his vote will influence the election is greater than the opportunity cost of voting.

When Public Choice theorists squarely faced the logic of the rational voter hypothesis, they were naturally led to ask why anyone votes.

If such a high gain from election is required, why don't some elections have no voters? One answer is that there are "sociological" factors, such as ethical values, indoctrination, or social pressure, which economists do not usually take into account. Let S represent a voter's evaluation of "sociological" factors. Public Choice theorists point out how strong the influence of these other factors must be to motivate a person to vote. In terms of an inequality, a "rational voter" will vote if

Since P (V₂ - V₁) is likely to be small for most voters, the most important consideration is whether S is greater than C.

Let us use the numbers from the previous example as an illustration. Suppose that you will gain $995 if the park is built but that you will lose $5 if the road is repaired with your tax money. Thus, if A wins the election, you will enjoy a net gain $1,000. Assume as before that there are one million voters and that your opportunity cost of voting is $10. Then

There is a second reason why elections always have some voters . The smaller the number of people who vote, the greater the probability that a single individual's vote will effect the outcome. As long as some voters perceive a significant difference between candidates, we can be sure that some will vote. In an election with a million people, suppose that 999,989 decided not to vote. Then the probability that one person's vote would influence the outcome would rise from about one in a million to about one in ten. If your gain from the election was $1,000, your gain from voting would be about $100.

Public Choice theorists have also focused on the choice of a voter to try to improve his decision-making. To what extent can we expect voters to devote time and energy to learning about differences between candidates? A single voter's incentive to improve his knowledge depends on his estimated profit from voting -- P (V₂ - V₁) - C -- after the learning occurs. If this amount is negative, the voter would not want to improve his knowledge. We have already seen that the size of P depends on the number of other people who the voter expects to vote. This implies that, other things equal, a voter in a large election would devote less time and energy to improving his knowledge about candidates than a voter in a small election.

Reasons why elections always have some voters

1. Sociological factors outweigh the

negative profitability of voting.

2. The lower the number of voters in an

election, other things equal, the greater the probability that a person's vote will influence the outcome.

Note that an individual may decide to vote even though he is uninformed. The sociological factors may outweigh his loss from voting. For example, he may feel social pressure to vote. However, he is not likely to feel the same strength of social pressure to acquire information about issues or candidates.

Another interesting point is that the amount of resources devoted to increasing one's knowledge is likely to be inefficiently small. This is due to the public goods character of some knowledge. Let us divide knowledge into two types: knowledge that is useful to only a single voter and knowledge that is also useful to other voters. The individual has an incentive to produce the optimal amount of the first type. However, he does not have an incentive to produce the optimal amount of the second type because of the difficulty of selling it. Such knowledge is a public good. This is because of (1) jointness and (2) the costs, once information is transferred, of preventing others from obtaining the knowledge without paying for it. An example is knowledge about previous wrongdoing by a candidate. Many voters would benefit from such knowledge. However, in deciding whether to produce it (i.e., to pay the costs of conducting an investigation and publishing the results), a single individual would ordinarily take account only of his own benefits. We discussed this problem in Chapter Five. There we suggested that freedom of speech and the press and other rights would encourage the supply of information by those who are motivated to search for it. Even with these provisions, however, we should not expect the most efficient amounts of knowledge to be produced.

The lack of knowledge needed to make an informed voting decision due to a person's low gain from voting is called rational ignorance. Voters in a democracy remain partly ignorant of candidates and of their positions on issues because the personal costs of acquiring additional information is greater than the personal benefits (it is "rational" to do so).

Rational Ignorance: Voters in a democracy remain partly ignorant of candidates and of their positions on issues because the personal costs of acquiring additional information is greater than the personal benefits.

If sociological factors are very important in leading a person to vote, then he may choose to vote regardless of his uncertainty or his perceived difference between candidates. Consider a person who knows so little about the candidates that V₂ - V₁ is very low. He also calculates that it is not worth improving his information. He may still decide to vote because sociological factors outweigh the cost of voting. But how will he decide which candidate to vote for? He may use some other criterion than money-calculated gain. For example, suppose that the voter is a member of a church group and that the church leader urges all members to vote for a candidate who is a member of the congregation. Then he may be inclined to vote for the candidate even though he does not know whether the vote will benefit him.

Since the voter knows so little about candidate differences, the desire to please the church leader need not be large for it to decisively influence his vote.

As mentioned above, sociological factors are less important in the decision to acquire information. As a result, even if voters lose substantially from a particular politician's actions, they may not find out about the true cause of their loss. For example, a voter might be inclined to vote for a candidate who promises to "get tough on drugs" by raising the penalties to suppliers. Assume that in doing this, he is mainly influenced by the preachings of a church leader or other community leader. Because of his lack of incentive to learn about the effects of laws, he remains ignorant of the fact that strict drug laws induce adult drug producers and distributors to hire juveniles, who will commit more murders. He may blame the increased street violence on other factors. And he may fail to pay attention to the fact that otherwise law-abiding children find it profitable to carry out violent criminal activity.

Sociological factors give citizens a reason to vote even though their money-calculated profit from voting may be negative. But these factors are not important in the decision to acquire the knowledge needed to make an informed voting decision.

Sociological factors are more important in some circumstances and societies than in others. They appear to be more important in new democracies that were previously communitarian, socialist, or tribal. In such new democracies, social pressure on an individual to vote may be very strong relative to the pressure to vote informatively.

We have suggested that the major reason why individuals vote may be that they feel a social or moral obligation. We have also said that this same obligation has much less effect on the decision to learn about the candidates and issues. Finally we have pointed out that the optimal amount of some information (the public goods type) will not be supplied because of the free rider problem, although the media may make this problem less serious. What do these observations imply about the efficiency of elections as a means of identifying the best agents to cause public goods to be supplied? We consider each of these items in turn.

First, how do social or moral obligations relating to voting affect the efficiency of elections? To answer this, we must recognize the differences among people. Some people are apparently very sensitive to what they believe are the opinions of others, some people are less sensitive, some people are not sensitive at all, and a small minority are apparently contrarian. They go against the social conventions and choose not to vote just because others say they should vote. Some people have habitualized the voting act. They always vote because "it is right." Some of these moralists impose social sanctions on others. If you let it be known that you are planning not to vote, a moralist may try very hard to convince you that only bad people decide not to vote. Other habitual voters do not care what others do and they do not sanction neighbors who decide not to vote. Some voters presumably vote only if the personal gains of voting exceed the personal costs. Still other people never vote and never think about voting. Thus social or moral factors are different for different people and affect different people in different ways.

Let us try to imagine a two-candidate election in which all voters vote. Now compare the imagined outcome with one in which the only citizens who voter are those for whom S > C - P (V₂ - V₁). We have good reason to expect that the outcome of the two elections will differ. To see this in a simple way suppose that there are two candidates, A and B, and that A barely wins the election. Suppose further that all of his votes come from voters who feel a social obligation to vote even though they have less information about candidates than the typical other voter and non-voter. On the other hand, B receives all the votes of the voters who pay no attention to sociological factors. Moreover, a survey of only non-voters shows that B is their overwhelming favorite. We would surely be wrong to conclude that the election of A best represents the preferences of the collective "as a whole." It would be more correct to say that the voting is not an efficient representation of voter preferences for candidates.

Second, consider how the choice to improve decision-making ability affects our view of the efficiency of the election process. Because of the limited incentive to improve one's decision-making regarding the choice among political candidates, we would expect more errors in the collective choice of one candidate over another than in, say, a house buyer's choice of one real estate agent over another. Considering this factor alone, voter disappointment with elected officials and regret of their decision to vote for them would not be surprising. A voter may say: "If I had only known more about those candidates, I could have made a better choice."

Finally, consider the free rider problem in the supply of information. The information that people want is about (1) the physical effects of the supply of a public good and (2) the personal tax costs. Information about the physical effects has the characteristic of jointness. Moreover, if A discovers the information and tells B, it is very difficult for A to stop B from telling C. So it also has the characteristic of nonexclusion. Information about tax costs is usually joint because taxes are practically always shared. And it is nonexclusive for the same reason as information about the physical effects. Given the public goods character of this information, we would expect that the information supplied would be less than the efficient quantity. As before, a candidate may be correct to complain about voter ignorance and to claim that the election process is inefficient.

Why the Rational Voter Hypothesis Suggests that Democracy is an Inefficient Means of Causing Public Goods and Corrections of Market Failures to be Supplied

1. The outcome of an election is un-

likely to represent a cross-section of voters' preferences

2. Voters are rationally ignorant

3. Some information about candidates

and the effects of a policy is has public goods characteristics

When we write in these passages of the inefficiency of the election process, we are not saying that there is some better process that we can think of. We are merely pointing out that it is incorrect to argue that the election process is as efficient in selecting among candidates as we can imagine it being. This is what we typically do when we consider market failure. Just as markets are not as efficient as they could be in providing incentives to supply public goods, elections are not as efficient as they could be in selecting agents to cause public goods to be supplied.

It is obvious that collective decisions cannot give everyone what she wants. People with atypical preferences will not be as pleased as those whose preferences are more average. Public choice theorists have formalized this observation by inventing the median voter theorem.

To understand the theorem, we must build a model of an imaginary voting situation.

The simplest model assumes direct democracy. This is a system of government in which voters vote directly on issues. Laws are made by voters, not by their representatives in a legislature. Perhaps the best example is the town meeting. Direct democracy was used by most of the ancient Greek city-states. It is still used today by some cantons in Switzerland and by some local governments in the United States. However, it has been replaced in most of the democratic countries by a representative democracy.

We begin with the smallest number of people for whom majority rule is relevant -- three persons. Assume that the three make their collective decision by direct vote. A possible issue is the amount of police services. In deciding how much he wants the community to spend on this, each voter takes into account two things: (1) the benefit he expects from the services and (2) his personal tax cost. Regarding benefit, we assume that the greater the amount of police service, the more benefit he receives. Regarding tax cost, we assume that each person must pay a larger tax bill for a larger police force than for a smaller one. They may have an equal-sharing tax agreement or a system that allows different individuals to pay different shares.

We also assume that no one wants a society without police. Thus, at very low levels of police service, an increase of a dollar in police service is worth more to each person than the dollar cost. As higher and higher levels are provided, the situation changes. At some level, an increase in a dollar spent on police service becomes worth less than the additional tax cost. In the eyes of each voter, the police force has grown too large. Another way to say this is that for each voter, some intermediate amount of spending is optimal. His preferences are less well satisfied if spending is either less than the optimum or more than it. And the farther away the majority choice is from his optimum, the less well off he is. Finally, we assume that the three individuals have different preferences.

In figure 7-1, the horizontal axis shows various possibilities for spending on police services, from zero to one million. Tht three dark lines with peaks at A, B, and C, respectively represent the optima of three voters, A, B and C. B's preferences are represented by the line that peaks at point B, A's by the line that peaks at point A, and C's by the line that peaks at point C. The figure helps us see the three optima relative to each other.

The median voter refers to the voter whose optimum is in the middle of the group. In this example, A is the median voter because the optimum amount of police services for him, a, is between the optima of B and C.

Referring to figure 7-1, suppose that the voters vote according to simple majority rule on the size of the police budget. In addition, suppose that each voter votes independently. He does not allow another voter to influence his vote, as he might do if he sold his vote. Next suppose that each possible expenditure size is pitted against every other size. In other words, a vote is taken on whether people prefer a budget of 0 or $1, $1 or $1 million, $500,000 or $500,001, and so on until all the possibilities are exhausted. We call such a case an exhaustive vote. Finally suppose that the cost of voting is very small for each voter.

Median voter: On an issue in which voters may have preferences ranging from a small to large amount, he is the voter for whom the number of voters preferring more is equal to the number of voters preferring less.

Under these circumstances, the outcome would be a. Expenditure size a could defeat every other expenditure size. Suppose that votes are taken between a and some larger police budget, i.e. some point to the right of a. Both A and B would prefer a. Only C would favor the larger budget. On the other hand, suppose that votes are taken between a and some smaller police budget, i.e. some point to the left of a. Both A and C would prefer a. It follows that a majority would vote for budget a against any other budget. Thus, if a simple majority, exhaustive vote was held, the optimum of the median voter A would be chosen.

This simple proposition is the median voter theorem. It states that under specific conditions, the outcome of an exhaustive majority vote on an issue will be the optimum of the median voter. The conditions include (1) all voters vote, (2) voters vote according to their true preferences, (3) voters have different views, (4) there is an odd number of voters, (5) there are no costs of voting, and (6) voter preferences are single-peaked.

This theorem can be applied to any odd number of voters. Suppose there are one hundred and one voters, each with a different optimum. Now make an array of the voters' optima in the same way that we did in figure 7-1. In other words, the voter whose optimum is at the lowest amount of police services lies to the left of all the others. We can call him the first voter. The second voter's optimum lies slightly to the right of him but to the left of the third voter. And so on. The one hundred-first voter's optimum would be to the far right. In this array, the median voter would be the fifty-first one. His optimum would be in the middle of all the rest. If we make the other assumptions also, the budget preferred by the fifty-first voter would be chosen in a majority vote.

Median voter theorem: Under specific conditions, the outcome of an exhaustive majority vote on an issue will be the optimum of the median voter.

A good deal of empirical research has been built upon this model. It has been found useful in predicting the size of school budgets, government policies on conservation, etc. We shall see below that it also may be used to explain why political parties try to adopt platforms and positions that are similar.

It is difficult to make a collective decision-making model without ultimately saying something about whether the model leads to good or bad results. In this example, we have assumed simple majority voting. As a result, the median voter's preference predominates. Is the choice of the median voter's optimum the "best" policy for this imaginary community? To answer this question, we must be willing to compare benefits among individuals. Suppose that we make the judgment that collective benefit should be maximized. Then we can say that the median voter's optimum would be "best" if two conditions hold: (1) voters have roughly the same intensity of preferences or if the voters to the left of the midpoint feel just about as strongly as the voters to the right, and (2) the positions on the left and right are roughly symmetrical. This point is intuitively obvious for our three-voter model in figure 7-1. As we move left from point a, for example, B's benefit rises but the benefit of both A and C fall. If we count each person's benefit equally and if the optima are symmetrical, this means that there is a decline in benefit over the group as a whole.

Figure 7-2

DIFFERENT PREFERENCE INTENSITIES

If preference intensities differ and if we regard taking account of such differences as important, we may judge the median voter outcome to be undesirable.

Suppose that inten-sities of preferences differ substantially. In the three-person example, it is possible that B would feel much more strongly about the issue than either A or C. We can represent this by drawing B's peak higher than the peaks of A and C. In this case, we might judge that some point between b and a would be better than a. We may judge that the median voter outcome is not desirable. Figure 7-2 illustrates this situation.

Figure 7-3

DISTRIBUTION OF VOTER PREFERENCES

and attempt to see what we can deduce from the median voter model about real-world democratic politics. To make it easier to deal with more realistic problems, we convert our diagram to another form and we change our assumptions about preferences. In figure 7-3, we assume that there is a large number of voters. The vertical axis represents the number of voters whose optima lie at various levels of police services. For example, the expenditure level of t is most preferred by N₁(say 100) voters. Expenditure level m is most preferred by N₂ (say 400) voters.

We assume that the median voter's peak is at expenditure level m. The number of voters who share this peak is represented by the distance am = N₂. Note that more voters (namely, gb voters) prefer expenditure level g over any other expenditure level. Thus the distribution is not symmetrical. The unique property of m is that the number of voters who prefer larger expenditures than this amount is equal to the number who prefer smaller expenditures. There is an equal number of voters who prefer an expenditure on the median voter's left as there are who prefer an expenditure on his right. This is represented by the fact that the area under the curve to the left of m equals the area under the curve to the right. (The lightly shaded area equals the darkly shaded area.) Because the area to the left of g is greater than the area to the right of g, we know that more voters prefer budgets to the left than to the right.

Let us imagine an election in which citizens vote for one of two candidates based solely on the position each candidate takes on the single issue of the level of police services. Imagine, for example, a previously elected mayor who is running for reelection against a single rival. Assume that the preferences are like those in figure 7-3 and that everyone votes.

We know that the mayor's best strategy is to advocate a budget that corresponds to the median voter's highest preference, or peak. Let us call this the median voter strategy. Since the mayor cannot know the exact preferences of voters, she must make a guess. Suppose that she makes a mistake and decides to campaign for a police budget that is "too low." Let us represent her choice by a campaign position such as t in figure 7-3. If her opponent believes that the mayor's position is to the left of the median voter's optimum, he would be wise to choose a position as close as possible to t, yet somewhat to the right of it. He would prefer this position to, say, position m because of his uncertainty about voter preferences. It is true that if he chooses m or even some position slightly to the right of m, he would still win. But he does not know this. A possible choice is c. In this circumstance, both candidates would campaign by offering voters less police protection and a higher crime rate than the median voter wants.

Median voter strategy: the strategy by a candidate in an election of choosing a position on an issue that is most preferred by the median voter.

Of course, this result depends on the assumption that the mayor makes a mistake. It is clearly in her interest to try to find m and to take that position. If she chooses m, her challenger could not defeat her by choosing a different position.

In this analysis, we assumed that voters always vote for the alternative that is closest to their optima. The tendency for a candidate to adopt a position that is closest to the optimum of the median voter would be less pronounced if voters sometimes do not vote at all or if they become confused when alternatives are too close together. In this case, the distribution of the voters (how many are on each side and how close they are to the median) becomes important. To determine the optimal strategy for a candidate under these circumstances requires a more detailed analysis. It does not, however, effect the general thrust of the median voter principle.

We pointed out that the optimal position for a candidate to take is one that is very near to the opponent even if the opponent is far away from the preference of the median voter. Let us suppose that he does this, as in the example of figure 7-3. Specifically suppose that one candidate chooses position t and that her rival responds by choosing position c. The rival will win the election. After he is elected, will he actually put the policy associated with position c into effect?

Assuming that the candidate plans to run for reelection or, if not, that he aims to promote his political party's choice, there are two considerations. First, if he does not adopt c, voters may not believe his (or his party's) promises in the next election. Second, if he does adopt c, voters might believe that after the next election he will again adopt c. If they believe this, and assuming that preferences do not change, a new challenger would have a good opportunity to replace him. The challenger would only have to choose a position to the right of c but to the left of the median voter. Even if the incumbent responded by choosing a position closer to the center than the challenger, the voters may not believe him.

There is no clear solution to this problem because it is due to how voters expect a candidate to act. Such expectations depend on a variety of factors that Public Choice theorists do not ordinarily study. It is enough to point out here that a voter's choice depends on the policies he expects the candidate to adopt after he is elected and not upon the policies that the candidate happens to say he will adopt. The clever politician not only knows this and takes into account, he also tries to predict changes in voters' preferences and opinions regarding credibility.

The median voter theorem in strict form applies only if there are two candidates. Suppose that there are three candidates and that the election rule states that the candidate with the largest number of votes wins ( a plurality rule). Then models of the sort we have been discussing do not yield a stable outcome. It is possible to compute an optimal strategy for one candidate, given that the other two have taken specific positions. In other words, suppose that you are a candidate and that you know exactly which positions the other candidates have chosen. Suppose further that the other candidates cannot change their positions after they choose them. Then we could find a position that would maximize the votes you would receive. We could specify your optimum strategy exactly. The problem is that it is ordinarily not profitable for any candidate to stick exactly to his previously-announced position. Vote-maximizing candidates would want to adjust to a rival's latest shift in position.

Our first thought might be that the three candidates would cluster at the middle in order to attract the most votes, just as two candidates tend to be very close together. This is not so. Figure 7-4 represents preferences in the same way as figure 7-3. The difference is that we assume that the preferences are symmetrical around the median voter. This time there are three candidates: C (conservative), S (socialist), and L (liberal). Suppose at first that they are closely bunched around point a. They all promise the median amount of spending on police services. We would expect the voters to be more or less equally divided among the three candidates. Each would receive approximately one-third of the votes. Now consider what would happen if one of the candidates moves a little bit away?

Assume that candidate S moves to position b while the other candidates remain at a. We can now determine the number of voters who are closer to b than to either of the other two candidates. The dotted line divides voters into two groups: those who would vote for S and those who would vote for one of the other two candidates. By making the shift, S loses votes in the center of the distribution, but he gains all votes to the left of the dotted line. Clearly, S has improved his position in relation to the other two candidates.

A candidate does not want to take a position that is too extreme. If he moves too far from the median voter's optimum, he will win less than one-third of the votes.

Let us suppose that two of the three candidates move away from the center in such a way that all three receive an equal share of the vote. Figure 7-5 shows such a movement. S takes position s, C takes the center position c, and L takes position l. In this case, both S and L could gain by shifting back toward the center. For example, if S simply shifted to s', he would gain more votes.

Deciding which position to take in a multi-candidate election requires a good deal more skill on the part of candidates, and mistakes are more likely. In a two-candidate election there is a simple operational rule for the politician: try to find out what the other candidate is doing and take a position very close to her but on the median voter's side. With a three-candidate system, no such simple rule exists. Candidates must make difficult decisions and we can expect frequent errors.

Figure 7-5

THREE CANDIDATE INTERDEPENDENCE

1. Tell what it means to say that the gain from an election is a comparative gain.

2. Tell the difference between an individual's gain from election and his gain from voting.

4. Describe the rational voter hypothesis. Using symbols is not sufficient. You must tell what the symbols mean to a voter by putting yourself in the voter's shoes.

5. When economists recognized the rational voter hypothesis, they were led to ask why anyone votes. They gave two answers. Describe and explain each answer.

6. Many people vote because of "sociological" factors. Tell how strong such factors must be to explain why a person votes.

7. Use the rational voter hypothesis to explain why a person may remain uninformed about the candidates or issues even though he decides to vote.

8. Given the costs of producing information about candidates for political office, is the amount of information produced about candidates likely to be optimal from the standpoint of voters? Explain by distinguishing between information that is only useful to a single voter and information that is useful to many voters at the same time.

9. Some Public Choice scholars have made the following argument. "Many people vote in spite of the low probability that their vote will influence the outcome of an election. This suggests that when they vote they are not thinking first of their personal gain. Instead, sociological factors are the deciding influences." If sociological factors are indeed the deciding influence on a voter's choice to vote, then his choice among candidates may also be primarily influenced by sociological factors. However, the same sociological factors play little role in the decision to produce information. It follows that the sociological factors involved in voting may lead a person to vote against his interest. More specifically, he may vote in a way that is different than he would vote if he had perfect information. Give an example that is different from those in the text to show that you understand this argument.

10. "It is not surprising that voters would regret their choices in an election and that they would occasionally want to impeach a previously elected politician." According to the text, how can we explain that voters' decisions may be more frequently regretted than other decisions?

12. In the simple model of three voters, is the median voter outcome desirable? Explain. In your explanation, take account of the possibility that the intensities of preferences may not be the same.

14. Assume that there are many voters, a single issue, that voter preferences are single-peaked, and that there are two candidates. Draw a graph showing the hypothetical number of voters who favor each point on the issue scale. Use this graph to demonstrate the optimal position for a candidate, assuming (1) that he is uncertain about voter preferences and (2) his opponent has already chosen a position that is not optimal. Don't forget to explain your graph in words by telling what is measured on the axes and what the graph represents.

15. Consider a two-candidate election. Suppose that the first candidate chooses a position that is far away from center. The second candidate then chooses a position designed to maximize the number of votes. After the second candidate is elected, should he attempt to implement the policies that he promised the voters? Assume that his main goal is to get reelected in a subsequent election. Explain. (Hint: there is no definite answer.)

16. Assume that there are many voters, a single issue, that voter preferences are single-peaked, and that there are three candidates. Draw a graph showing the hypothetical number of voters who favor each point on the issue scale. Use this graph to demonstrate the interdependence among the three candidates. Don't forget to explain your graph in words by telling what is measured on the axes and what the graph represents.

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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