# Positive Political Theory I

Collective Preference

Publication Year: 1999

Published by: University of Michigan Press

Series: Michigan Studies in Political Analysis

#### Cover

#### Frontmatter

#### Acknowledgments

The genesis of this book lies in graduate classes we taught at the University of Rochester, roughly through the decade 1986-1996. Many people have contributed to it in one way or another. We are very grateful to all of the students who have suffered through our classes at Rochester, offering constructive criticism, insight, and commentary on both the material itself and on our presentation thereof. Among these students we are particularly ...

#### Preface

Positive political theory is concerned with understanding political phenomena through analytical models which, it is hoped, yield insight into why political outcomes look the way they do and not some other way. Examples of such outcomes include the parties or candidates elected at various times, the bills adopted by legislatures, and decisions on going to war or designing a constitution. The models typically ...

#### 1. Choice and Preference

It is natural to think of individuals choosing what they prefer and it is precisely this intuition that supports, for instance, empirical work in which legislators' policy preferences are inferred from their observed voting behavior. Indeed, individual preference is occasionally defined in terms of choice. But there is no logical reason why this should be so. Individuals might make ...

#### 2. Power and Collective Rationality

Chapter 1 was concerned with the logical structure of concepts of preference and choice. This concern is motivated largely by the fact that whereas the choices of given individuals or societies are directly observable, preferences-even if they are known to exist - are not so apparent. Nevertheless, individuals are typically assumed to make choices based on some deeper notion of preference, and social choices are derived through some aggregation of these ...

#### 3. Restricting Outcomes

...Thus the domain condition used in the results derived so far involves only two substantive restrictions: that individual preferences be weak orders and that the set of alternatives be finite. With these restrictions, we saw in Chapter 2 how the set of decisive coalitions associated ...

#### 4. Restricting Preferences

Theorem 3.10 provided an axiomatic foundation for plurality rule; yet Corollary 3.2 demonstrated that unless the feasible set consists of only two alternatives, plurality rule can be "badly behaved" in that it can fail to generate a well-defined choice in all circumstances. One popular avenue out of this predicament comes from weakening the requirement of acyclicity over all logically possible preference profiles to requiring acyclicity only over some ...

#### 5. The Spatial Model

A maintained assumption of almost all of the previous discussion is that the set of alternatives facing society is finite. But there are many situations in which a finiteness assumption is inappropriate: the choice of tax-rates or expenditure levels, the allocation of time to various collective activities, the setting of maximal legal pollution levels or a minimum wage are more naturally considered ...

#### 6. Instability and Chaos

The core characterization results of the previous chapter suggest that cores are quite fragile in high-dimensional spaces, in the sense that they simply may not exist for relatively large sets of preferences. This intuition is especially transparent for the case of majority rule: Corollary 5.1 states that with an odd number of individuals, each with a distinct ideal point, preferences must be distributed in a very special way to support a nonempty ...

#### 7. Summary and Conclusions

...necessarily associated with existence of equilibria, it must be that minimal democracy is sacrificed. Indeed, by its focus on individual behavior and hence individual influence over collective decisions, the very essence of game-theoretic analysis calls out for such a sacrifice. Therefore, the collective preference and game theory approaches to the study of collective decision making differ not with respect to existence of solutions...

E-ISBN-13: 9780472022465

E-ISBN-10: 0472022466

Print-ISBN-13: 9780472087211

Print-ISBN-10: 0472087215

Page Count: 224

Illustrations: 42 drawings, 6 tables

Publication Year: 1999

Series Title: Michigan Studies in Political Analysis

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