Managerial Logic

Managerial Logic

By: Kenneth J. Arrow (author), Harve Raynaud (author)Hardback

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Description

The publication of the first book by Kenneth Arrow and Herve Raynaud, in 1986, led to an important wave of research in the field of axiomatic approach applied to managerial logic. Managerial Logic summarizes the prospective results of this research and offers consultants, researchers, and decision makers a unified framework for handling the difficult decisions they face. Based on confirmed results of experimental psychology, this book places the problem in a phenomenological framework and shows how the influence of traditional methods has slowed the effective resolution of these problems. It provides a panorama of principal concepts and theorems demonstrated on axiomatized methods to guide readers in choosing the best alternatives and rejecting the worst ones. Finally, it describes the obtained extensions, often paradoxical, reached when these results are extended to classification problems. The objective of this book is also to allow the decision maker to find his way through the plethora of multicriterion methods promoted by council organizations. The meta-method it proposes will allow him to distinguish the wheat from the chaff. The collaboration with Kenneth Arrow comes essentially from the fact that his work influenced all subsequent works quoted in this book. His famous impossibility theorem, his gem of a PhD thesis, and his various other works resulted in him receiving the Nobel Prize for economy just before meeting Herve Raynaud who was at that time a visiting professor at Berkeley University in California. Their mutual publications serve as the basis for the axiomatic approach in multicriterion decision-making.

About Author

Herv Raynaud, a former student of the cole Polytechnique and an honorary emeritus professor of Mathematics, has worked with about 20 academic organizations around the world. A former psychoanalyst, researcher, and international consultant, he is now teaching at the Sigmund Freud University of Vienna, in its Paris branch, and at the Conservatoire National de la Villette in France. Kenneth J. Arrow is an American economist and a joint winner of the Nobel Memorial Prize in Economics with John Hicks in 1972. His most significant works deal with social choice theory, notably "Arrow's impossibility theorem" and his research on general equilibrium analysis. He is currently the Joan Kenney Professor of Economics and Professor of Operations Research, Emeritus at Stanford University.

Contents

General Introduction xi PART 1. A PARADOXICAL RESEARCH FIELD 1 Chapter 1. The Initial Problem 5 1.1. Introduction 5 1.2. The decision makers and their consultants usual work11 1.3. Toward a paradigm for managerial decision-making 21 1.4. Exercises 28 1.5. Corrected exercises 32 Chapter 2. Paradoxes 35 2.1. Arrow s axiomatic system 36 2.2. May s axiomatic system 43 2.3. Strategic majority voting 44 2.4. Exercises 47 2.5. Corrected exercises 53 PART 2. A CENTRAL CASE: THE MAJORITY METHOD 57 Chapter 3. Majority Method and Limited Domain 61 3.1. Sen s lemma [SEN 66] 62 3.2. Coombs condition 63 3.3. Black s unimodality condition [BLA 48, BLA 58] 66 3.4. Romero s arboricity 67 3.5. Romero s quasi-unimodality 69 3.6. Arrow Black s single-peakedness 72 3.7. The Cij s 74 3.8. Exercises 78 3.9. Corrected exercises 80 Chapter 4. Intuition Can Easily Suggest Errors 87 4.1. Inada s conditions 87 4.2. Is the bipartition the same as the NITM condition? 88 4.3. Diversity of the NIMT condition 92 4.4. Exercises 94 4.5. Corrected exercises 94 Chapter 5. Would Transitivity be a Prohibitive Luxury? 97 5.1. Star-shapedness 98 5.2. Ward s condition 101 5.3. The failure of the majority method 104 5.4. Exercises 106 5.5. Corrected exercises 106 Conclusion of the Second Part 109 PART 3. AXIOMATIZING CHOICE FUNCTIONS 111 Chapter 6. Helpful Tools for the Sensible Decision Maker 117 6.1. The habitual decision maker and his/her traditional means 117 6.2. The habitual decision maker 124 6.3. A sensible decision maker confronted with a difficult decision 137 6.4. The urgency of raising the moral standard of the market 138 6.5. Conclusion 141 6.6. Exercises 146 6.7. Corrected exercises 149 Chapter 7. An Important Class of Choice Functions 153 7.1. Introduction 153 7.2. The problem: various definitions 154 7.3. Natural properties of the E-matrices and B-F-matrices 156 7.4. Choice functions that depend only on the E-matrix or on the B-F-matrix 158 7.5. Characterization of the choice functions that depend only on the E-matrix (respectively, B-F-matrix) 161 7.6. Conclusion 163 7.7. Exercises 165 7.8. Corrected exercises 167 Chapter 8. Prudent Choice Functions 171 8.1. Introduction 171 8.2. Toward the prudence axiom 172 8.3. Properties related to prudence for choice functions 179 8.4. Exercises 182 8.5. Corrected exercises 186 Chapter 9. Often Implicit Axioms: Sovereignty, Homogeneity, Decision by Rejection or Selection, Prudence and Violence 191 9.1. Introduction 191 9.2. Sovereignty 193 9.3. Homogeneous choice 195 9.4. Choice by selection and choice by rejection 198 9.5. Violent choice and prudent choice 202 9.6. Exercises 205 9.7. Corrected exercises 207 Chapter 10. Coherent Choice Functions 211 10.1. Introduction 211 10.2. Characterization of the Borda method 211 10.3. Coherence and the other axioms 218 10.4. Exercises 223 10.5. Corrected exercises 224 Chapter 11. Rationality and Independence 227 11.1. Introduction 227 11.2. Rationalities 228 11.3. Axioms of independence 237 11.4. The inclusive iteration principle 242 11.5. Conclusion 243 11.6. Exercises 245 11.7. Corrected exercises 246 Chapter 12. Monotonic Choice Functions 251 12.1. Introduction 251 12.2. Monotonicity defined 252 12.3. Prudence and monotonicity 258 12.4. Prudence and binary monotonic independence 260 12.5. Strong monotonicity 262 12.6. Exercises 263 12.7. Corrected exercises 264 PART 4. MULTICRITERION RANKING FUNCTIONS 267 Chapter 13. Sequentially Independent Rankings 275 13.1. Introduction 275 13.2. The sequential independence axioms 277 13.3. Sequential independence with current choice and rejection functions 281 13.4. Exercises 287 13.5. Corrected exercises 290 Chapter 14. Prudent Rankings 293 14.1. Introduction 293 14.2. Some unexpected theorems 294 14.3. Prudent rankings 297 14.4. Prudence in preorders and iterated prudent choice 300 14.5. Exercises 305 14.6. Corrected exercises 307 Chapter 15. Coherent Condorcet Rankings 313 15.1. Introduction 313 15.2. What does one call Kemeny s method or second Condorcet method? 313 15.3. Young and Levenglick s theorem 319 15.4. Exercises 322 15.5. Corrected exercises 326 Chapter 16. Monotonic Rankings 333 16.1. Definitions of monotonicity for ranking functions 333 16.2. Monotonicity of the most ordinary non-sequential multicriterion ranking function 339 16.3. Various remarks 346 16.4. Exercises 348 16.5. Corrected exercises 350 Concluding Remarks 355 Bibliography 367 APPENDICES 377 Appendix 1. Benjamin Franklin s Letter 379 Appendix 2. Pyramids and Snakes: Romero s Algorithm 381 Appendix 3. A Few Widespread Commercial Multicriterion Decision Techniques 387 Index 405

Product Details

  • ISBN13: 9781848212978
  • Format: Hardback
  • Number Of Pages: 410
  • ID: 9781848212978
  • weight: 766
  • ISBN10: 1848212976

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