978-0393919684 Chapter 15 Lecture Note

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CHAPTER 15

Strategy and Voting

Teaching Suggestions

Most students will be familiar with at least a few of the vari ous aggregation methods

used to determine winners in elections. You may want to poll the class and come up with a list

of different methods that they know about or have used. Even a simple discussion of this type

will lay the groundwork for coverage of the many methods available. This is another

opportunity to let the political science students in your class use their field knowledge and lead

the discussion, thereby engaging their interest. There are additional examples beyond those

found in the text; some of these are explained in the symposium on “Economics of Voting” in

the Journal of Economic Perspectives, vol. 9, no. 1 (winter 1995).

The best way to get students to appreciate that different voting methods can lead to

very different final outcomes is to have them work through an example. The John Allen Paulos

example found in Exercise S5 of this chapter is an excellent one; you can change the characters

to fit your own state, local, or university situation to make the idea more interesting to

students. Another classic example of how the choice of procedure can affect the outcome is

based on a Roman legal case, extracted from the letters of Pliny the Younger (see Robin

Farquharson, Theory of Voting [New Haven, Conn.: Yale University Press, 1969], pp. 6–7, or

Peter Ordeshook, Game Theory and Political Theory, pp. 54–55). Pliny, as a member of the

Roman senate, had a distinct preference for the particular aggregation rule that would lead to

his most-preferred outcome.

Many other examples of voting paradoxes can be found in the literature. Those who

want to emphasize political science applications may want to refer to William Riker’s

Liberalism Against Populism, some of the papers of Peter Fishburn (including “Paradoxes of

Voting,” American Political Science Review, vol. 68 [1974]), and the Farquharson and

Ordeshook books mentioned above.

For a more-detailed discussion of the Condorcet paradox, you can pick up on the idea

mentioned briefly in the text that in the City Council example, the paradox arose “because the

Council completely disagreed not only about which alternative was best but also about which

was worst.” This argument can be spelled out it more detail; doing so will help to clarify the

conditions under which an agenda setter will be able to determine the outcome.

In a three-by-three case (in which votes are cast “truthfully”), it is clear that a

Condorcet paradox can exist only when all three members rank a different alternative best. If

two members agreed on their favorite, that alternative would beat both others. As the text

implies, however, disagreement about the best alternative is not sufficient for the Condorcet

paradox to exist. In addition, the three voters must also disagree about which alternative is

worst.

Suppose that this isn’t true, so that the three voters (who each prefer a different

alternative) agree that one alternative, say A, is not the worst. In this case, alternative A is

ranked first by one voter, and second by the other two. Consider the voting outcome when

alternative A is matched against (for example) alternative B: A gets two votes, one from the

person who likes A best and one from the person who likes C best but prefers A over B.

Similarly, A gets two votes when matched against C, the second coming from the person who

likes B best but ranks A over C. When all three voters agree that A is not the worst outcome,

therefore, a Condorcet paradox cannot exist. We conclude that in the 3 x 3 case, a Condorcet

paradox exists only when there is complete disagreement among the voters; they must disagree

not only about which alternative is best but also about which is worst.

It is only when disagreement is so complete that the outcome can be determined by the

preferences of the agenda setter. This is intuitive; if there is “enough” agreement among the

voters, the voters’ preferences fully determine the outcome. The power to set the agenda is

decisive only when voters’ preferences are quite diverse. One can note also that the above

description is, of course, just another way to describe the well-known

double-peaked-preferences condition. In addition, it may be worth pointing out to students that

complete disagreement on rankings may be more likely if the three alternatives being voted on

are three completely different options—like spending money on a park, a library, or a clinic—

rather than a range of spending on a single program.

Another example that can be used in class comes from the story, mentioned briefly in

the text, concerning how opponents of a federal school-construction-funding bill were able to

defeat the bill by strategic voting. They voted in favor of an amendment, which they would

have opposed on its own merits, anticipating that the amended bill was more likely to fail than

the original bill was.

Bear in mind, however, that attempts to engage in such clever schemes sometimes fail.

The first federal law that banned discrimination on the basis of gender passed only as a result

of a failed strategic plan. The original bill banned racial discrimination (in certain contexts);

opponents supported adding the gender-discrimination language expecting it to sink the whole

bill. To their surprise, it passed.

For those of you with mathematically sophisticated students, you may want to spend

some time discussing the example of strategic voting with incomplete information in Section

4.C. If you carefully covered the material on incomplete information in Chapter 8, this is a

good opportunity to make the connection between the broad implications of information

asymmetries and the specific case of voting games. Exercise U7 considers the opposite case to

that described in the text (in which a possible center-type vote is assumed to vote truthfully). If

you want to do a more complete analysis of this example, you can refer to P. Ordeshook and T.

Palfrey, “Agendas, Strategic Voting, and Signaling with Incomplete Information,” American

Journal of Political Science, vol. 32, no. 2 (1988).

When covering the median voter theorem, you may find that students balk at the idea

that candidates all move toward the position of the median voter since this does not seem to be

observed in reality. In actual political campaigns, candidates will often take positions in order

to distinguish themselves from one another. It is worthwhile to explain to students that this

observation does not destroy the essential conclusions of the median voter theorem.

As the text notes, part of the reason why candidates may distinguish themselves is that

the median voter theorem does not hold when the political spectrum has two or more dimen –

sions. There are also institutional (and other) features that explain some differentiation between

candidates. A brief list includes:

A candidate may need to win a primary election, by appealing to a left- or

right-leaning subset of the total population, before running in the general election

campaign.

A candidate may attempt to increase the turnout of voters by appealing to her base

of supporters.

Prior public statements by a candidate may tie her to a particular position.

A candidate’s own belief system may lead some candidates to accept a reduced

chance of winning an election in order to promote what she believes are correct stands.

In spite of these factors, however, the basic conclusion of the median voter theorem—a desire

of candidates to move toward the middle of the political spectrum—still holds, even if the

candidates do not meet at the exact midpoint.

For example, candidates who must take relatively extreme positions in order to win a

primary often begin to moderate their positions as they move into the general election cam-

paign. Consider also a candidate who has represented a congressional district that leans more

to the left or the right than the candidate’s whole state. If this person runs for a statewide

office, she may modify some previous statements in order to sound more mainstream.

Candidates may also alter or hide their own personal views.

In all of these cases, a candidate may not be able to move into the exact middle of the

voter distribution because doing so would require the candidate to reverse some of her pre vious

positions. The loss of credibility that might result could be very damaging to the candidate.

Still, it is worth emphasizing that a candidate’s incentive to moderate her positions is quite

strong. Many candidates will behave in such a manner, up to the point at which the resulting

loss of credibility becomes too costly.