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E-grāmata: How to Divide When There Isn't Enough: From Aristotle, the Talmud, and Maimonides to the Axiomatics of Resource Allocation

(University of Rochester, New York)
  • Formāts: EPUB+DRM
  • Sērija : Econometric Society Monographs
  • Izdošanas datums: 05-Sep-2019
  • Izdevniecība: Cambridge University Press
  • Valoda: eng
  • ISBN-13: 9781108168724
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How to Divide When There Isn't Enough: From Aristotle, the Talmud, and Maimonides to the Axiomatics of Resource AllocationPalielināt
  • Formāts: EPUB+DRM
  • Sērija : Econometric Society Monographs
  • Izdošanas datums: 05-Sep-2019
  • Izdevniecība: Cambridge University Press
  • Valoda: eng
  • ISBN-13: 9781108168724
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How to Divide When There Isn't Enough develops a rigorous yet accessible presentation of the state-of-the-art for the adjudication of conflicting claims and the theory of taxation. It covers all aspects one may wish to know about claims problems: the most important rules, the most important axioms, and how these two sets are related. More generally, it also serves as an introduction to the modern theory of economic design, which in the last twenty years has revolutionized many areas of economics, generating a wide range of applicable allocations rules that have improved people's lives in many ways. In developing the theory, the book employs a variety of techniques that will appeal to both experts and non-experts. Compiling decades of research into a single framework, William Thomson provides numerous applications that will open a large number of avenues for future research.

Recenzijas

'William Thomson, one of the greatest academic advisors in economics worldwide, and a leading scholar in the field of resource allocation, has been carefully developing this project for more than two decades. I believe the book will be considered a classic right after being published.' Juan D. Moreno-Ternero, Universidad Pablo de Olavide, Spain 'The design of rationing rules has inspired for nearly forty years a fascinating intellectual edifice of axiomatic postulates and mathematical results, reviewed here by the premiere author of that literature. Readers will recognize, or discover, William Thomson's superb pedagogical talent in a text that is comprehensive, self-contained, and luminously clear.' Hervé Moulin, Donald J. Robertson Chair of Economics, University of Glasgow 'The folksy title notwithstanding, this is an impressive study of modern economic design. The focus of the book is how best to adjudicate claims on a resource when the sum of those claims exceeds the amount or value of the resource. Thomson (Univ. of Rochester) displays his masterful command of the subject, of which he is certainly a prime architect The book's lessons apply to many real-world problems, among them bankruptcy claims, estate division, allocation of water rights, allocation of shares of the global carbon budget, and assignment of telecommunications frequencies Thomson intends the book, and the work it summarizes, to provide a conceptual basis that will inform wise/smart societal choices going forward.' K. J. Murphy, Choice ' this book is, simply, a masterpiece. It is highly recommended for the broad audience of mainstream economists and a must read for those interested in normative economics ' Juan D. Moreno-Ternero, Social Choice and Welfare

Papildus informācija

An introduction to the modern theory of economic design, it develops an up-to-date treatment of the adjudication of conflicting claims.
List of Figures
xii
List of Tables
xix
Acknowledgments xx
General Notation xxi
1 Introduction
1(20)
1.1 Claims Problems
1(2)
1.2 The Model
3(6)
1.3 Two Puzzles in the Talmud
9(2)
1.4 Three Approaches
11(5)
1.4.1 Direct Approach
12(1)
1.4.2 Axiomatic Approach
12(3)
1.4.3 Game-Theoretic Approach
15(1)
1.5 Historical Note
16(1)
1.6 Road Map
16(1)
1.7 How to Use This Book
17(1)
1.8 Concluding Comment
18(3)
2 Inventory of Division Rules
21(41)
2.1 An Inventory of Rules
22(23)
2.1.1 Proportional Rule
22(1)
2.1.2 Constrained Equal Awards Rule
23(3)
2.1.3 Constrained Equal Losses Rule
26(2)
2.1.4 Concede-and-Divide
28(3)
2.1.5 Piniles' Rule
31(1)
2.1.6 Talmud Rule
32(2)
2.1.7 Constrained Egalitarian Rule
34(3)
2.1.8 Random Arrival Rule
37(1)
2.1.9 Minimal Overlap Rule
38(5)
2.1.10 Rule Based on Random Stakes
43(2)
2.2 Families of Rules
45(15)
2.2.1 Sequential Priority Family
45(1)
2.2.2 Young's Family
46(7)
2.2.3 ICI and CIC Families
53(7)
2.3 Summary
60(2)
3 Basic Properties of Division Rules
62(32)
3.1 Balance
62(1)
3.2 Continuity
63(1)
3.3 Homogeneity
64(1)
3.4 Lower and Upper Bounds on Awards and Losses
65(10)
3.4.1 Defining Bounds
65(7)
3.4.2 Recursive Assignment of Lower Bounds
72(3)
3.5 Conditional Full Compensation, Conditional Null Compensation, and Related Properties
75(4)
3.6 Symmetry Properties
79(10)
3.7 Order Preservation Properties
89(5)
4 Monotonicity Properties
94(24)
4.1 Endowment Monotonicity and Related Properties
95(10)
4.2 Claim Monotonicity and Related Properties
105(10)
4.3 Inverse Sets Axioms
115(3)
5 Claims Truncation Invariance and Minimal Rights First
118(13)
5.1 Claims Truncation Invariance
119(4)
5.2 Minimal Rights First
123(8)
6 Composition Down and Composition Up
131(26)
6.1 Composition Down
131(9)
6.2 Composition Up
140(17)
7 Duality
157(25)
7.1 Duality for Rules
157(8)
7.2 Duality for Properties
165(6)
7.3 Duality for Theorems
171(1)
7.4 Characterizations
172(10)
8 Other Invariance Properties
182(18)
8.1 No Advantageous Transfer
182(2)
8.2 Claims Separability and Variants
184(3)
8.3 Convexity and Additivity Properties
187(8)
8.4 Rationalizing Rules as Maximizers of Binary Relations
195(5)
9 Operators
200(29)
9.1 Claims Truncation Operator
200(2)
9.2 Attribution of Minimal Rights Operator
202(3)
9.3 Convexity Operator
205(1)
9.4 Relating and Composing the Operators
206(8)
9.5 Preservation of Properties under Operators
214(8)
9.5.1 Properties Preserved under Claims Truncation
215(3)
9.5.2 Properties Preserved under Attribution of Minimal Rights Operator
218(1)
9.5.3 Properties Preserved under the Composition of the Claims Truncation and Attribution of Minimal Rights Operators
219(2)
9.5.4 Properties Preserved under Convexity
221(1)
9.6 Extension Operators
222(5)
9.7 Summarizing
227(2)
10 Variable-Population Model: Consistency and Related Properties
229(41)
10.1 The Variable-Population Model
230(1)
10.2 Consistency and Related Properties
231(8)
10.3 Converse Consistency
239(2)
10.4 Other Logical Relations between Consistency, Its Converse, and Other Properties
241(8)
10.5 Lifting of Properties by Bilateral Consistency
249(6)
10.6 Characterizations
255(11)
10.7 Average Consistency
266(4)
11 Constructing Consistent Extensions of Two-Claimant Rules
270(38)
11.1 A General Extension Technique
271(6)
11.2 Consistent Extensions of Two-Claimant Rules Satisfying Equal Treatment of Equals
277(12)
11.2.1 Consistent Extension of Weighted Averages of the Two-Claimant Constrained Equal Awards and Constrained Equal Losses Rules
277(5)
11.2.2 Two-Claimant Rules that Have No Consistent Extension
282(1)
11.2.3 Consistent ICI and CIC Rules
283(5)
11.2.4 Other Consistent Families
288(1)
11.3 Consistent Extensions of Two-Claimant Rules that May Not Satisfy Equal Treatment of Equals
289(13)
11.3.1 Generalizing the Talmud Rule by Not Insisting on Equal Treatment of Equals
290(7)
11.3.2 Consistent Extensions of Two-Claimant Rules Satisfying Homogeneity, Composition Down, and Composition Up
297(5)
11.4 Further Characterizations Involving Consistency and Other Axioms but Not Equal Treatment of Equals
302(6)
12 Variable-Population Model: Other Properties
308(31)
12.1 Population Monotonicity and Related Properties
308(5)
12.2 Guarantee Structures
313(2)
12.3 Merging and Splitting Claims; Manipulation Issues and Extension Operators
315(9)
12.3.1 No Advantageous Merging or Splitting and Variants
316(4)
12.3.2 Extension Operators Based on the Merging of Claims
320(4)
12.4 Replication and Division: Invariance and Limit Results
324(10)
12.4.1 Convergence of Rules under Replication
330(4)
12.5 Balanced Impact and Potential
334(1)
12.6 Multiple Parameter Changes; Logical Relations and Characterizations
335(4)
13 Ranking Awards Vectors and Ranking Rules
339(20)
13.1 Orders Based on the Lorenz Criterion
340(8)
13.1.1 Maximality and Minimality Results
340(2)
13.1.2 A Criterion for Lorenz-Domination within the ICI Family
342(6)
13.2 Preservation of Orders by Operators
348(3)
13.3 Lifting of Orders by Bilateral Consistency
351(1)
13.4 Other Properties of Rules Pertaining to Orders
352(2)
13.5 Orders Based on Gap and Variance
354(5)
14 Modeling Claims Problems as Games
359(31)
14.1 Modeling Claims Problems as Cooperative Games
359(21)
14.1.1 Bargaining Games
359(8)
14.1.2 Coalitional Games
367(13)
14.2 Modeling Claims Problems as Strategic Games
380(10)
14.2.1 Game of Stakes
380(3)
14.2.2 Game of Rules
383(5)
14.2.3 Sequential Game of Offers
388(2)
15 Variants and Generalizations of the Base Model
390(18)
15.1 Claims Problems in Which No Claim Exceeds the Endowment
390(1)
15.2 Claims Problems in Which the Data Are Natural Numbers
391(2)
15.3 Claims Problems with a Large Number of Claimants
393(2)
15.4 Surplus-Sharing Problems
395(1)
15.5 Generalizing the Notion of a Rule
396(1)
15.6 Computational Issues
397(1)
15.7 Incorporating Additional Information into the Model
397(8)
15.8 Experimental Testing
405(1)
15.9 A Concluding Comment
406(2)
16 Summary Graphs and Tables
408(8)
17 Appendices
416(40)
17.1 Deriving a Formula for the Minimal Overlap Rule
416(1)
17.2 More about the CIC Rules
417(3)
17.3 Paths of Awards of the DT Rule
420(2)
17.4 Neither Claim Monotonicity Nor No-Transfer Paradox Is Preserved under the Duality Operator
422(4)
17.5 Claim Monotonicity Is Not Preserved under the Attribution of Minimal Rights Operator
426(2)
17.6 Lifting of Properties by Bilateral Consistency
428(1)
17.7 Characterizing the Family of Equal-Sacrifice Rules
429(3)
17.8 On the Existence and Uniqueness of Average Consistent Extensions
432(2)
17.9 Constructing Consistent Extensions
434(2)
17.10 On the Consistent Members of the CIC Family
436(2)
17.11 Characterizing a Family of Sequential Talmud Rules
438(2)
17.12 Completion of the Proof of the Characterization of Family M
440(4)
17.13 Population Monotonicity Is Not Preserved under Duality
444(3)
17.14 Characterization of the Constrained Equal Awards Rule as Offering Maximal Group Guarantees
447(2)
17.15 Under Replication, the Random Arrival Rule Converges to the Proportional Rule
449(3)
17.16 Convexity of the TU Coalitional Game Associated with a Claims Problem
452(1)
17.17 Proof of the Correspondence between the Talmud Rule and the Nucleolus, and of the Constrained Equal Awards Rule and the Dutta-Ray Solution
453(3)
References 456(16)
Index 472
William Thomson is the Elmer Milliman Professor of Economics at the University of Rochester, New York. He is the author of several books including A Guide for the Young Economist (2011) which has appeared in four translations, and over one hundred articles. In 2001, he won the University Award for Excellence in Graduate Teaching at the University of Rochester. He is a Fellow of the Econometric Society, the Society for Economic Theory, and the Game Theory Society.
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