January 16, 2003

Chapter 8

More on Voting and Elections

Real voting and elections are much more complex than our simple models might lead us to think. There are many reasons for this, some of which are discussed in future chapters. Two important factors are political parties and pressure groups. Political parties help candidates obtain votes; and some candidates help parties gain votes for other party candidates. Parties are also instrumental in selecting which people will be candidates for which seats. Pressure groups are like clubs. There are different kinds. Some pressure groups mainly bring voters together in voting blocs, others mainly raise funds in an effort to influence elections or politicians' decisions, and still others mainly put collective voting pressure on political parties to only accept or support candidates who express views that are acceptable to them. We discuss political parties and pressure groups in Chapter Twelve.

  The purpose of this chapter is to introduce three other types of complexities to help us understand voting in everyday life. First, in real elections, candidates must take positions on many issues. We show that to take the center position on each issue may be a less optimal strategy than to take extreme positions on some issues. Second, voting choices can be influenced by advertising. As a result, acquiring money or other resources for a campaign is an important part of a candidate's means of obtaining votes. A politician can obtain such money or resources by adopting a platform that appeals to special interests. Third, some elections proceed in stages. When this occurs, there is a possibility of what Public Choice scholars have called the voters’ paradox. In addition, two forms of strategic behavior may become profitable. The first is agenda manipulation. This occurs when political party leaders try to manipulate the stage sequence, or order of voting, for the purpose of raising the chances that their preferred candidate will be chosen. The second is strategic voting. We say that voters vote strategically when they cast their vote for a candidate who they do not prefer in order to beat out a rival who they regard as the top competitor of their preferred candidate.

  Part one of this chapter extends the median voter analysis to situations in which voters elect representatives to vote on multiple issues. Part two presents a model of a candidates choice of platform in which campaign spending for the purpose of persuasion plays a part. Part three describes the voters' paradox, agenda manipulation, and strategic voting. For simplicity, we continue to assume direct democracy.

1. MULTIPLE ISSUES AND THE TENDENCY

TOWARD THE CENTER OF OPINION

  So far, our discussion of voting and elections has assumed that candidates for election are elected on the basis of the position they take on a single issue. Obviously, the voters in modern democracies are interested in many issues. Can the simple median voter model be extended to cases in which candidates must take positions on many issues? In these cases, will candidates try to adopt a median position on the issues? The answer is yes and no. In a two-candidate election, a vote-maximizing candidate would attempt to take positions that are at what we shall call the "center of opinion."

  The "center of opinion" is not the same as the peak of the median voter's preference on one issue. It refers to a sort of average of many issues. We can get an idea of what this means by thinking about the median voter for a case where there are many issues. Obviously, it is very unlikely that the same person would be the median voter on every issue. Suppose that you are the median voter on the police budget. Others prefer either a much larger or a much smaller budget. You may also want a relatively large education budget and a relatively small highway budget. Someone different would be the median voter on the education budget; and still a different person is likely to be the median voter on the highway budget.

  Now let us shift our viewpoint to that of a candidate. We call a set of positions on different issues a platform. A candidate aims to construct a platform that will maximize her probability of being elected. She can do this by choosing positions on each issue that will, when considered together, win more votes than some alternative. Suppose that she makes a platform designed to appeal only to you. Then she would support a moderate police budget, a large education budget, and a small highway budget. It is evident that she might lose to a candidate with a different platform -- perhaps one that appealed to voters who preferred a smaller amount of school spending and a larger amount of highway spending. The center of opinion platform describes a hypothetical platform that, when pitted against all others in an exhaustive vote, would defeat them. We can use the term center of opinion strategy to refer to the effort by a candidate to construct a center of opinion platform. We can also say that a candidate aims to appeal to the center of opinion.

  We say that the center of opinion is hypothetical for two reasons. First, no candidate could know exactly what it is. Second, there may be many platforms (a locus of platforms) that are equally capable of defeating others but not capable of defeating each other consistently.

Conditions Under Which a Median Voter Strategy is Not Optimal

  To help us understand the center of opinion strategy, let us define a different strategy. We can call it the median voter strategy. A candidate that used this strategy would try to take a median position on each issue. He would adopt a strict median voter platform.

To see how the center of opinion strategy differs from this, we can try to imagine a set of voter preferences for which appealing to extreme positions would be an optimum strategy. Consider a simple case of three voters and three issues: spending on police, spending on highways, and spending on education. Assume that figure 8-1 shows the preferences for spending on police. It is identical to figure 7-1. Figure 8-2 shows the preferences for spending on highways and education, respectively. The highway graph shows that C has intense preferences for a large amount of highway spending, while the other two voters have moderate preferences for their optima. The education graph shows that B has intense preferences for a small amount of education spending, while the others have moderate preferences for their optima. The median voter on all three issues is A.

                                            Figure 8-1

 

                  PREFERENCES OF THREE VOTERS

  Under the assumptions, suppose that a candidate adopted a median voter platform. Then he would lose the election if his competitor chose the appropriate extreme positions on highways and education. Suppose the competitor chose a platform of large highway spending, small education spending and moderate police spending. He would capture C's vote because of his position on highways and B's vote because of his position on education. He would lose A's vote to a candidate who followed a median voter strategy. But he would win the election.

  This example suggests that a platform designed to appeal to extremes on different issues may be able to attract minorities of voters who have intense preferences. When the votes from the different minorities are added together, the total may be higher than that which could be achieved by a median voter platform. This implies that in order to adopt a center of opinion strategy, a candidate may have to take extreme positions on some issues. Thus, the center of opinion strategy may be quite different from a median voter strategy. Of course, a candidate could not know precisely which strategy is a "center of opinion" strategy because he cannot exactly know the true preferences of voters.

                                            Figure 8-2

 

                              VOTER PREFERENCES

  Is the outcome associated with the center of opinion strategy desirable? As in the case of two issues (see Chapter Seven), to make such a judgment, we must be willing to compare benefits among individuals. One important difference is that when there are many issues, a candidate who adopts the center of opinion strategy tries to appeal to extremists on specific issues if their demands are intense. It is difficult to know whether this is desirable or not. It depends on one's point of view.

Multiple Candidates

  It is very difficult to analyze a multi-candidate, multi-issue case. The best we can do here is to provide some hints based on our simple models. First, we can consider a very simple but unrealistic case in which the same person is the median voter on every issue. In this part that in a two-candidate election, the center of opinion strategy would be the same as the median voter strategy. Each candidate would tend to adopt it. But suppose there are more than two candidates. Our analysis of three candidates and two issues in Chapter Seven showed that if all candidates clustered around the center, one candidate could gain by moving away from the center, although not if he moved too far away.

  Next, suppose that all of the candidates move away from the center and that, as a result, each receives an equal share of the votes. Then, on the basis of our discussion in Chapter Seven, a candidate who adopts a position to the extreme left or extreme right could take away votes from a competitor by moving closer to the center. In this sense, there is a tendency for candidates to cater to the median voter even in the multi-candidate case.

  Second, we can consider a case where different voters have different extremes on different issues and where the preferences toward extreme positions are relatively intense. In this case, our purely logical analysis does not help us very much. In order to identify the optimum platform, a candidate would have to find out not only the preferences and distribution of voters, but also the intensity of their preferences toward different issues.

2. CAMPAIGN SPENDING

  Public Choice started as a branch of economics. The simplest economic theory -- the one we learn in economics textbooks -- assumes that consumers have fixed demands for goods and that producer-entrepreneurs respond to those demands by trying to produce goods that will enable them earn a profit. In fact, of course, consumers do not have fixed demands. When the typical shopper visits the supermarket, for example, she explores new products and tries to judge whether she has a demand for them. She ordinarily does not make such judgments in isolation. She may consult with others, read newspapers, and so on. She is alert to advertisements, although she recognizes that ads may be biased and deceptive. She knows that she could be led to make errors.

  Advertisers know that consumers are alert so they put their products in distinctive packages and sometimes invest large sums of money to make the packages attractive. It is also common for sellers to supply free or discount samples in order to give consumers opportunities to try new products. In addition, advertisers recognize that consumers make errors. Some have developed sophisticated ways to prompt mistakes and to exploit them. For example, sellers may pay retailers to display their products in preferred locations in order to discourage consumers from considering, locating, or sampling a competitor's product. Sometimes the consumers discover deceptions, sometimes not. Since discussion of advertising and deception requires some amount of expertise in psychology and sociology, economists usually do little more than mention these possibilities. In this section, however, we will incorporate them into a model in order to help us understand elections in everyday life.

  Candidates for political office are somewhat like the suppliers of private goods. They know that voters are uncertain about which candidate is most likely to act in their interest. So they give voters information to distinguish them from other candidates and they package and display themselves in a way that they believe is most attractive. Also, knowing that the judgments of many voters are imperfect, they have developed sophisticated ways to deceive and to exploit defects in voter decision-making. They take lessons in speech-making; hire expert writers; advertise; obtain endorsements from respected community members, pressure groups, or political parties; and employ expert press agents. In these actions also, they try to discover and exploit the sociological factors that influence voters' decisions to vote. All of these things require money. As a result, candidates and political parties use their personal funds and they try to raise additional funds.

  A common way to raise campaign funds is to appeal to special interests. Examples of special interests are a businessperson, a wealthy property owner, a corporation, an industry council, a labor union, and a fund-raising consumers' or taxpayers' group. In the case of a chief executive, the special interest typically makes a campaign contribution because it expects to be treated favorably by a government bureau under his direction. In the case of a legislator, the special interest typically contributes campaign funds in exchange for the candidate's promise to vote for or against particular bills. Such a promise may be part of a publicly-announced platform or it may be secret. A campaign contribution need not involve money. It may consist of services, such as help with rallies, producing and distributing leaflets, and so on.

A Model

  Figure 8-3 is a simple model that shows the costs and benefits to a political candidate of exchanging his administrative decision or a vote on legislation for a campaign contribution. It represents two characteristics of campaign contributions in elections: one positive and one negative. On the positive side, after a candidate obtains such contributions, she can use them in a variety of ways to sway voters. On the negative side, in order to attract campaign funds from special interests, a candidate must sacrifice the votes of voters who prefer that he follow policies other than those that favor the special interests.

  Costs and benefits in the graph are defined in terms of votes gained and lost. The horizontal axis measures the amount of campaign spending. For simplicity we assume that it is measured in money. The vertical axis represents the number of votes. We assume that as more money is spent on a candidate's campaign, the candidate gains votes but that she gains them at a decreasing rate. The curved line G represents this assumption. Beyond some amount -- 0a in the figure -- there is no additional gain from campaign spending. Voters are saturated with campaigning.

                                            Figure 8-3

 

        VOTING IN ORDER TO RECEIVE CAMPAIGN

                                    CONTRIBUTIONS

  Also in the figure is line L. This line represents the loss in votes that soliciting campaign contributions is likely to cause. Exactly how such a loss would occur depends on the nature of laws that regulate campaign contributions. At one extreme, suppose that campaign contributions are legal and open. In other words, suppose that there is no law against making and receiving contributions of any amount, so long as the contributor or candidate announces the amount and identity of the contributor. In the U.S., campaign contributions must be made public. As a result, newspaper reporters can find them out and report them. The U.S. also regulates campaign contributions in various ways, including a limitation on the amount that can be contributed by a single individual or organization. In this case, astute voters know that elected politicians are likely to favor campaign contributors in their administrative decisions or legislative votes. Since the interests of many voters differ from those of the campaign contributors, such voters have a tendency to shift, other things equal, to another candidate. Or they may decide not to vote at all.

  At the other extreme, suppose that the campaign contributions are illegal and concealed from voters. In this case, the prospective loss in votes is due to the possibility that voters will discover the contributions and then shift their votes. In addition, candidates or contributors face other costs due to the prospect that the illegal contributions will be discovered by election officials and that they will have to pay a penalty.

  Line L assumes that the amount of votes lost plus other costs is a constant function of the amount of campaign contributions. Making these simplifying assumptions allows us to show a maximizing position for the tradeoff between (1) additional votes that must be sacrificed in order to attract contributors plus other costs and (2) the additional votes that are gained by using increased amount of campaign contributions to sway voters.

  In the model, there is a net gain from accepting campaign contributions up to point e, where the marginal gain equals the marginal loss. The total gain in votes due to the combination of fund raising and campaign spending equals the shaded area between the G and L curves from the origin to the amount 0s.

  At point e, additional campaign spending would still bring votes. However, there is no additional net gain to the candidate because the votes she would lose by further catering to special interests on bills or bureau actions is greater than the votes she would gain from additional persuasion.

  This model assumes that in order to obtain campaign resources, a candidate must please campaign contributors by adopting a platform or making promises that are different from otherwise. Suppose that additional campaign funds are merely given to the candidate. In this case, the candidate would have no obligation to change her platform in order to cater to the special interest. She would happily accept the funds; since she can use them to persuade additional voters without changing her platform. Consider a candidate who is very wealthy. She could use her wealth to gain votes through campaign spending without having to give up votes by appealing to the special interests. This explains why, other things equal, wealthy individuals have an advantage in elections.

The Center of Opinion Platform and Campaign Spending

  The theory of candidate competition that we presented in Chapter Seven and in part one of this chapter assumes that voters' preferences for issues (public goods) are fixed. In order to compete effectively in elections, candidates try to identify those preferences and offer a platform that comes closest to the center of opinion. Contrary to this, the theory of campaign spending presented in this section assumes that voters do not fully know their preferences for public goods or how a candidate could best satisfy them. The candidates try to persuade voters that, compared with their competitors, they will be better agents in public goods supply. Which theory is right?

  The answer is that both are. In some cases, voters have relatively fixed preferences toward issues. In other cases, they do not. Thus, candidates not only try to identify voter preferences and satisfy them; they also use persuasion.

3. THE VOTERS' PARADOX

  To understand the voters' paradox, consider the simple case of a community with three voters, A, B, and C. Suppose that a wealthy person has just died. In her will, she specified that $1 million of her wealth be given to "the community." It can only be used for one of three projects: to build a park, a road, or a bridge. The location and other detailed specifications of each option are stated in the will. In case of disagreement over how to use the money, the decision must be made according to majority rule.

  Suppose that the preferences of the three voters are represented by table 8-1. A's first choice is the park, B's first choice is a road and C's first choice is a bridge. The second and third choices are given in the table.

   Now suppose that you are charged with the task of conducting a vote. Assume that the voters vote honestly. If you list all three alternatives on the ballot and ask voters to vote for their first choice, each alternative will receive one vote. No decision can be made. But now suppose that you ask voters to vote for the alternatives, one pair at a time. You might begin by giving voters the option of choosing between a park or a road. In this case, A would choose the park, B would choose the road, and C would choose the park. The park wins over the road. Now, in order to give the bridge a chance, you give voters the option of choosing between the park and bridge. A chooses the park, while B and C choose the bridge. Since the bridge defeats the park, and since the park had defeated the road, the bridge seems like the best collective choice.

  But now suppose that you try to check your result by giving voters a choice between the bridge and the road. A and B would vote for the road and C would vote for the bridge. The check fails. The road defeats the bridge.

  This is the paradox. Even though the park defeats the road and the bridge defeats the park, the road defeats the bridge in a paired comparison.

  You could have chosen a different order. But the result would have been similar. For example, you could have started with a vote between the road and bridge. The road would win. Then you could conduct a vote between the road and the park, in which case the park would win. But if you checked your result by putting the park against the bridge, the bridge would win.

  The voters' paradox shows that when there are more than two alternatives, we should not make paired comparisons, lest we mistakenly infer that a chosen alternative is preferred to one that is not chosen. We should consider all the alternatives together. If we do this in our example, we discover that the collective has no clear preference.

  Public Choice theorists have devoted a lot of research to the voters' paradox in order to better understand whether a collective decision is likely to truly reflect voters' preferences. The research is also relevant to voters and lawmakers, since they may be able to sway the outcome of an election to their advantage. Specifically, it is related to agenda manipulation and to strategic voting. Much of the work in these fields is highly mathematical and complex. However, a few simple examples can give us a good idea of the issues involved.

Agenda Manipulation

  Agenda setting in Public Choice means making a decision about the order in which issues or candidates will be compared. In our example, suppose that voters have decided to compare the three alternatives of park, road, or bridge by using paired comparisons. Assume that the voters do not realize the possibility of a voters' paradox. As a result, they decide to only make the paired comparison twice. In other words, they decide not to check their comparisons. Put yourself in the shoes of a government agent who is assigned the task of setting the agenda. Suppose that you have a definite preference for one of the alternatives. You prefer the park. Your preferences are like those of voter A in table 8-1. Under these conditions, if you know the preferences of the three voters, you can set the agenda in such a way that the park will be chosen. To do this, you should arrange for the first vote to be between the road and the bridge and for the second vote to be between the winner of the first vote and the park. As we have seen, the park would turn out to be the winner. If you chose a different order, the result would be different. Your goal should be to prevent voters from comparing the park with the bridge directly.

  This result suggests a possible advantage for clever people who are assigned the task of setting the agenda for elections or meetings where incomplete paired comparisons are made. If the preferences are such that a voters' paradox is present, they can manipulate the agenda to obtain their preferred outcome. Agenda manipulation means setting an agenda for the purpose of achieving a voting outcome that would otherwise not occur.

  There are a variety of ways to avoid this problem. For one example, the voters could demand a complete vote. Or they could adopt a point system like assigning 3 points to their first choice, 2 points to their second choice, and 1 point to their third choice.

  Agenda manipulation does not occur in elections since elections do not involve sequential paired comparisons. However, it may occur in votes on legislation or in small committees.

  Another point that is worth making is that for people who have experience in these things, the possibility of agenda manipulation is only common sense. If you know that a collective is planning to make a series of paired comparisons and if you have a definite preference for one of the options, you would surely want to delay a comparison involving your preferred choice until after the other alternatives have been compared and some have been eliminated from consideration. The lesser the number of competitors you must defeat, the better.

  The conditions that allow agenda manipulation to occur are present in the U.S. primary system of presidential elections within political parties. Party primaries are used to choose which candidate will run against the candidate of another party. The presidential candidate that polls the highest number of electoral votes throughout all the states ordinarily wins the party's primary. However, the different states conduct their party primaries on different dates. Naturally, the candidates who score high in a given primary are given greater media attention than those who score low. This means that a winner in the first state to have a primary -- New Hampshire -- receives greater publicity than a loser. Assuming that the publicity is good, it helps to influence the vote in states that hold their primaries later in time. Accordingly, it increases the probability of winning. Because of this, we might be inclined to think that a wise strategy would be for a candidate to spend her funds in such a way that she maximizes the probability of winning the first election. However, there may be an advantage to delaying one's spending. If the candidate believes that the most competitive rival may be defeated in early elections and that she can defeat the early winner, she may hold back spending her money until the rival is soundly beaten and either quits or loses substantial fund-raising capacity.

Introducing New Agenda Items

  So far, we have discussed simple majority rule under the assumption that the number of items on the agenda is given. Under this assumption, voters have only two ways to make the outcome different from what it would be if they voted according to their preferences: manipulating the agenda and strategic voting.(discussed below) It may also be possible to affect the outcome by introducing a new agenda item. In the example of the park, road an bridge; you might tip the balance in your favor by trying to add another item – say, a dam. Introducing the dam as an alternative may sway enough voters away from other alternatives to enable your preferred alternative to win the vote.

  When we turn our attention to the possibility of swaying a vote by introducing a new agenda item, we are led to view the collective decision-making process in a very different way. A person who introduces a new agenda item merely in order to help his preferred alternative win wants to subvert the process. His action is aimed at preventing the alternative that would otherwise be chosen to win the vote. To see the significance of this, suppose that the donor of the money described above does not specify how it must be used. Assume further that there are 100 voters participating in what is, at first, a simple two-issue vote, say whether to use the donated funds to build a park or a road. Assume that 98 voters prefer the park and only two prefer the road. By carefully introducing to the list of alternatives a minimum of 97 other carefully selected uses of the donated funds, they could assure that the road would get more first place votes than any of the other alternatives.

  This result is especially significant in an open voting forum like a legislature, where items can practically always be added to the agenda or to a legislative bill. It suggests that because of the possibility of agenda manipulation, there is no reason to believe that the project or bill that is actually chosen by majority rule will be most preferred by the “group as a whole.”

Strategic Voting

  Strategic voting refers to voting in a way that is different from your preferences with the goal of raising the probability that a preferred alternative will be chosen. Consider the preferences shown in table 8-2.

  Suppose that you are B and that the agenda is set to compare the park and bridge first. The winner will be put to a vote against the road. Assume that the other voters always vote in accord with their preferences. If you also vote in accord with your preference, you would vote for the park in the first vote and the park would win. In the second vote the park would defeat the road, which is your preferred choice. You would not be too unhappy because at least your second choice would be adopted. However, you could have done better. Suppose that you had voted against your preferences in the first vote. If you had voted for the bridge, the bridge would have won. In the second vote, the road would defeat the bridge. So your first choice would be adopted.

  If you knowingly do this, we say that you vote strategically or that you engage in strategic voting. The reason we use these terms is that your goal in voting is not to show your true preferences but to cause a more preferred alternative to be chosen than otherwise. Another way to say this is that you are treating the vote as a kind of game in which you adopt the best strategy to win.

  There is practically always some potential for strategic voting. Consider the earlier example of the voters’ paradox. Look again at the table 8-1. Assume as in the first example, that the agenda is set such that the first comparison is between the park and the road. The winner will be pitted against the bridge. Suppose that you are A. If you know the preferences of the other voters, you would expect that the lowest alternative on your preference scale would be chosen. You could improve your situation by changing your vote in the first round. Instead of voting for the park over the road, you could vote for the road over the park. Assuming that no one else changed his vote, the road would defeat the bridge in the second tally. This strategy would not enable you to attain your first choice. But it would enable you to cause a more preferred alternative to be chosen by the group than the bridge.

  Strategic voting may occur in sequential elections where there is a runoff. Consider five candidates in a single representative district system: A, B, C, D, and E. Assume that the two candidates who receive the highest number of votes are selected for a runoff election. The winner of the runoff wins the election. In this case, suppose that your favorite candidate is A. You believe that if everyone votes honestly, A and B will be in a runoff. However, you also believe that B will defeat A. Then you have an incentive to try to keep B from being in the runoff election. If you think that a vote for C will help C defeat B in the first election, then you have nothing to lose in the first election by voting for C. If enough people do this, then there may be a runoff between A and C, in which case you think A will win.

  Consider a second example. Assume that there is a series of elections in which the candidate with the lowest number of votes is eliminated. If the first election has no majority, one of the five candidates is eliminated. Then a second election is held and, if no candidate wins a majority, the lowest vote-getter is again eliminated. Still another election is held. The process continues until one of the candidates wins a majority. For example, if E receives the least number of votes in the first election and no other candidate receives a majority, she will be eliminated. Then, assuming that there is no majority, there will be a second election involving A, B, C, and D. If D receives the least votes yet no one receives a majority, a third election will be held among A, B, and C. Such a system may give a voter several opportunities to act strategically.

  Strategic voting can be a very serious threat to a system in which there are party primary elections. In such elections, members of the other party or independents who are planning to vote for the other party's candidate may be able affect the choice of the candidate in your party. To achieve their goal, they will vote for a candidate who is most likely to be defeated in the general election. Because of this possibility, the leaders of a political party that holds primaries must be wary of people who want to vote in their primary election but who are not known to be party loyalists.

  The ability to gain from strategic voting depends on the voter's knowledge of the votes that others would make. Someone who knows nothing about how others would vote cannot expect to gain. Correspondingly, those who spend time and energy acquiring knowledge of others voting preferences will have an advantage over those who do not.

4. CONCLUSION

  In Public Choice, we regard democracy as a means for members of a collective to cause public goods to be supplied. We discussed such goods in Chapter Three. One reason why members may want such goods supplied collectively is that producers in the market economy face a special difficulty in trying to learn about demands for goods that have the jointness characteristic. Because consumers have a propensity to act strategically by withholding information from other consumers, producers are less able to determine consumers' wants than they are in the case of private goods. There is market failure. A democratic government allows consumers to communicate their demands in a different way -- by voting. But democratic governments can fail also.

  In this chapter, we have seen that, in order to get elected, politicians have an incentive to identify individuals' preferences for public goods and to try to satisfy those preferences. However, identifying the optimal platform is difficult. Partly because of the uncertainty, we can expect politicians to take moderate positions on many issues. However, they can find that if the preferences of some voters are intense, they may maximize the votes they receive by taking extreme positions on some issues. Also in this chapter, we recognized that in order to attract campaign contributions, politicians must take positions on issues that deviate from the optimal platform. Finally, we saw how strategic voting and agenda manipulation may occur to make the outcome of an election or law-making process different from what it would be without these actions. All of these factors raise doubts about the ability of a representative democracy to yield outcomes that are better than what would be achieved in the market economy. In other words, they help us realize that besides market failure, there may also be government failure in the supply of public goods.

Questions for Chapter 8

1.   Define platform, median voter platform, center of opinion platform, center of opinion strategy, agenda setting, strategic voting.

2.   Explain why the center of opinion is hypothetical.

3.   Assume that voters must choose among candidates who have positions on several issues. Assume further that voter preferences are single peaked. We define a "median-voter" platform as one that appeals to the median voter on each issue. Describe voter preferences (1) for which this strategy is likely to succeed and (2) for which it is likely to fail.

4.   Under what conditions are the median voter strategy and the center of opinion strategy the same?

5.   Suppose that you are a typical voter who prefers candidate A over candidate B one month before the election. Explain why candidate B's campaign spending might cause you to change your vote? [Hint: there are several possible explanations.]

6.   Other things equal, do wealthy candidates have an advantage over poor candidates in a fair election? Explain.

7.   To obtain funds from special interests, a candidate must sacrifice votes. Explain why.

8.   Assume that a candidate has no initial money to spend on his campaign. However, he can raise campaign funds by promising special interests to vote for projects that they favor. When he votes for special interests he must give up votes because he cannot at the same time choose the optimal platform. Use a model of campaign spending to show the tradeoff between the votes lost by deviating from the optimal platform and votes gained through campaign spending. Identify the optimal amount of campaign money to raise and spend. (Make sure that you explain the lines and important points on the graph.)

9.   Without referring to a table or to a specific example, explain in words the voters' paradox. [You might pretend that you are trying to explain the paradox to your grandparents.]

10.   Suppose that you are a member of a collective that plans a series of pairwise comparisons among alternative policy options. If you have a preferred option and if you are the agenda setter, tell in general how you can maximize the probability that your option will win? Try first to answer this question without referring to a specific example. If you are not comfortable with your answer or wish to elaborate, you may present a table to illustrate it.

11.   Suppose that there are five candidates for an election: Ahmed, Fatima, Mohammed, Samar, and Saif. The election rules say that each voter has only one vote. They also say that unless a candidate receives 50% of the vote, there will be a runoff election between the top two vote-getters. In the first election, you believe that Mohammed will win a plurality (get the most votes) and that Fatima will be second. You are confident that Fatima will defeat Mohammed in the runoff because the majority of voters who prefer Ahmed, Samar, and Saif will switch to Fatima in the runoff. Explain how you can use strategic voting to improve Mohammed's chances of winning. In making your answer, what assumption are you making about how the other voters will vote in addition to the assumptions already stated?

12.   Explain how strategic voting can cause problems in a system where political parties conduct primary elections.

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J. Patrick Gunning
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Feng Chia University
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