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Über dieses Buch

interest in a particular application, however, often depends on his or hergeneralinterestintheareainwhichtheapplicationistakingplace. My experience at Union College has been that there is a real advan­ tage in having students enter the course knowing thatvirtually all the applications will focus on a single discipline-in this case, political science. The level ofpresentation assumes no college-level mathematicalor social science prerequisites. The philosophy underlying the approach we have taken in this book is based on the sense that we (mathemati­ cians)havetendedtomaketwoerrorsinteachingnonsciencestudents: wehaveoverestimatedtheircomfortwithcomputationalmaterial,and we have underestimated their ability to handle conceptual material. Thus, while there is very little algebra (and certainly no calculus) in our presentation, we have included numerous logical arguments that students in the humanitiesand the socialscienceswill find accessible, but not trivial. The book contains five main topics: a m.odel of escalation, game­ theoretic models of international conflict, yes-no voting systems, political power, and social choice. The first partofthe text is made up of a single chapter devoted to each topic. The second part of the text revisits each topic, again with a single chapter devoted to each. The organizationofthe bookisbasedonpedagogicalconsiderations, with the material becoming somewhat more sophisticated as one moves through the ten chapters. On the other hand, within any given chap­ terthere is little reliance on material from earlierchapters, except for those devoted to the same topic.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Escalation

Abstract
Important examples of escalation are easy to find in political science, such as the buildup of American troops in Vietnam during the 1960s and the arms race of the 1960s, 1970s, and 1980s, to mention just two. Such escalatory behavior is driven at least in part by a desire to keep previous investments from having been wasted. In this chapter we consider a model of escalatory behavior introduced by the economist Martin Shubik and extensively analyzed by Barry O’Neill. This model is known as the dollar auction.
Alan D. Taylor

Chapter 2. Conflict

Abstract
One of the central concepts of political science is conflict, that is, situations where the actions of one individual (or group) both influence and are influenced by those of another. Real-world examples of such conflict situations tend to be enormously complex, and a considerable amount of influential work in political science deals with the analysis of particular conflict situations and the ramifications of literally dozens of subtle influences upon the events that took place.
Alan D. Taylor

Chapter 3. Yes-No Voting

Abstract
This chapter discusses voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. In these systems, each voter responds with a vote of “yea” or “nay.” A yes-no voting system is simply a set of rules that specifies exactly which collections of “yea” votes yield passage of the issue at hand. The following four real-world examples of yes-no voting systems will be used to illustrate several concepts introduced later in this chapter.
Alan D. Taylor

Chapter 4. Political Power

Abstract
One of the central concepts of political science is power. While power itself is certainly many-faceted (with aspects such as influence and intimidation coming to mind), our concern is with the narrower domain involving power as it is reflected in formal voting situations (most often) related to specific yes-no issues. If everyone has one vote and majority rule is being used, then clearly everyone has the same amount of “power.” Intuition might suggest that if I have three times as many votes as you (and majority rule is still being used in the sense of “majority of votes” being needed for passage), then I have three times as much power as you have. The following hypothetical example should suffice to call this intuition (or this use of the word power) into question.
Alan D. Taylor

Chapter 5. Social Choice

Abstract
Chapters 3 and 4 dealt with what we called “yes-no voting systems.” In these systems, voters are presented with a single alternative (such as a bill or an amendment) and they simply vote yes or no on that one issue. One could also view a yes-no voting system as one in which voters are choosing between two alternatives: the status quo and the issue at hand. Such a view, however, is seldom used, perhaps in part because we tend to think of choosing democratically among several alternatives only in situations where no alternative has an advantage built in by the rules of the voting system. In yes-no voting systems, as we’ve seen, the status quo often has such a built-in advantage.
Alan D. Taylor

Chapter 6. More Escalation

Abstract
This chapter contains proofs of two very pretty theorems dealing with auctions. The first is the result due to Barry O’Neill that prescribes optimal play (for rational bidders) in the dollar auction from Chapter 1. We prove this theorem in Sections 6.2 and 6.3. The second result we present is William Vickrey s celebrated theorem from the theory of auctions. This theorem, proved in Section 6.4, shows that honesty is the best policy in what is called a “second-price sealed-bid auction” or a “Vickrey auction.” In Section 6.4, we explain the sense in which a Vickrey auction is a “generalized Prisoners Dilemma.” Finally in the conclusion, we compare the degree to which the two theorems are truly normative. (Briefly, the former requires the knowledge that one s opponent is rational; the latter does not.)
Alan D. Taylor

Chapter 7. More Conflict

Abstract
In this chapter, we continue our study of 2 × 2 ordinal games (and variants thereof) with particular emphasis on game-theoretic models of international conflict. Section 7.2 contains an application of 2 × 2 ordinal games to the Yom Kippur War. This model, although enlightening, unfortunately fails to explain the actual sequence of events that unfolded. This shortcoming is rectified in Section 7.3 where we present a slightly altered version of the so-called theory of moves from Brams (1985a, 1985b, 1994). In Section 7.4 we consider the joint U.S.-Soviet policy of mutual assured destruction (“MAD”) from the 1960s, 1970s, and 1980s. This treatment of deterrence tries to take into account not only the actual preferences of each side, but also each side’s perception (perhaps better: fear) of the other’s preferences. In Section 7.5 we return to the issue of deterrence and follow Brams (1985a, 1985b) in considering a model of deterrence based on Chicken, but with the choice of strategies being “probabilistic.” This section also introduces the ideas of cardinal utilities and expected value, thus setting the stage for an introduction of 2 × 2 zero-sum games in Section 7.6.
Alan D. Taylor

Chapter 8. More Yes-No Voting

Abstract
In this chapter, as in Chapter 3, our primary interest is in yes-no voting systems that are not weighted. We begin by returning to the theorem in Chapter 3 that characterized the weighted voting systems as precisely those that are trade robust (meaning that an arbitrary trade among several winning coalitions can never simultaneously render all of them losing). A natural question suggested by this result is whether trade robustness really needs to be stated in terms of “several winning coalitions.” That is, perhaps a yes-no voting system is weighted if and only if a (not necessarily one-for-one) trade between two winning coalitions can never simultaneously render both losing. Recall that in showing that the procedure to amend the Canadian constitution is not trade robust we needed only two winning coalitions.
Alan D. Taylor

Chapter 9. More Political Power

Abstract
We continue our study of political power in this chapter, beginning in Sections 9.2 and 9.3 with two more quantitative measures of power. Both of these power indices were introduced in the late 1970s, the first appearing in Johnston (1978) and the second in Deegan-Packel (1978). These indices are similar in some ways to the Shapley-Shubik and Banzhaf indices introduced in Chapter 4, but they also differ in some important respects from these earlier ones as well as from each other. In Section 9.4 we build on work of Brams, Affuso, and Kilgour (1989) in applying all four of these different indices to measure the power of the president in the context of the United States federal system. It turns out, for example, that according to the Deegan-Packel index, the president has less than 1 percent of the power. The Johnston index, however, suggests that the president has 77 percent of the power.
Alan D. Taylor

Chapter 10. More Social Choice

Abstract
Chapter 5 dealt with what might be called “concrete social choice theory” in that specific social choice procedures were introduced and analyzed. The present chapter deals with what might be called “abstract social choice theory.” Rather than consider any particular social choice procedures, this chapter establishes some limitations on what kind of “better” procedures can ever be found. These are very striking results. They are not saying that certain kinds of procedures fail to exist in the sense that no one has yet discovered one, they’re saying it is absolutely pointless even to look—one will never be found.
Alan D. Taylor

Backmatter

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