Managerial Logic

Hervé Raynaud, a former student of the école 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.

• General Introduction xiPART 1. A PARADOXICAL RESEARCH FIELD 1Chapter 1. The Initial Problem 51.1. Introduction 51.2. The decision makers and their consultants’ usual work111.3. Toward a paradigm for managerial decision-making 211.4. Exercises 281.5. Corrected exercises 32Chapter 2. Paradoxes 352.1. Arrow’s axiomatic system 362.2. May’s axiomatic system 432.3. Strategic majority voting 442.4. Exercises 472.5. Corrected exercises 53PART 2. A CENTRAL CASE: THE MAJORITY METHOD 57Chapter 3. Majority Method and Limited Domain 613.1. Sen’s lemma [SEN 66] 623.2. Coombs’ condition 633.3. Black’s unimodality condition [BLA 48, BLA 58] 663.4. Romero’s arboricity 673.5. Romero’s quasi-unimodality 693.6. Arrow–Black’s single-peakedness 723.7. The Cij’s 743.8. Exercises 783.9. Corrected exercises 80Chapter 4. Intuition Can Easily Suggest Errors 874.1. Inada’s conditions 874.2. Is the bipartition the same as the NITM condition? 884.3. Diversity of the NIMT condition 924.4. Exercises 944.5. Corrected exercises 94Chapter 5. Would Transitivity be a Prohibitive Luxury? 975.1. Star-shapedness 985.2. Ward’s condition 1015.3. The failure of the majority method 1045.4. Exercises 1065.5. Corrected exercises 106Conclusion of the Second Part 109PART 3. AXIOMATIZING CHOICE FUNCTIONS 111Chapter 6. Helpful Tools for the Sensible Decision Maker 1176.1. The “habitual” decision maker and his/her traditional means 1176.2. The habitual decision maker 1246.3. A “sensible” decision maker confronted with a difficult decision 1376.4. The urgency of raising the moral standard of the market 1386.5. Conclusion 1416.6. Exercises 1466.7. Corrected exercises 149Chapter 7. An Important Class of Choice Functions 1537.1. Introduction 1537.2. The problem: various definitions 1547.3. Natural properties of the E-matrices and B-F-matrices 1567.4. Choice functions that depend only on the E-matrix or on the B-F-matrix 1587.5. Characterization of the choice functions that depend only on the E-matrix (respectively, B-F-matrix) 1617.6. Conclusion 1637.7. Exercises 1657.8. Corrected exercises 167Chapter 8. Prudent Choice Functions 1718.1. Introduction 1718.2. Toward the prudence axiom 1728.3. Properties related to prudence for choice functions 1798.4. Exercises 1828.5. Corrected exercises 186Chapter 9. Often Implicit Axioms: Sovereignty, Homogeneity, Decision by Rejection or Selection, Prudence and Violence 1919.1. Introduction 1919.2. Sovereignty 1939.3. Homogeneous choice 1959.4. Choice by selection and choice by rejection 1989.5. Violent choice and prudent choice 2029.6. Exercises 2059.7. Corrected exercises 207Chapter 10. Coherent Choice Functions 21110.1. Introduction 21110.2. Characterization of the Borda method 21110.3. Coherence and the other axioms 21810.4. Exercises 22310.5. Corrected exercises 224Chapter 11. Rationality and Independence 22711.1. Introduction 22711.2. Rationalities 22811.3. Axioms of independence 23711.4. The inclusive iteration principle 24211.5. Conclusion 24311.6. Exercises 24511.7. Corrected exercises 246Chapter 12. Monotonic Choice Functions 25112.1. Introduction 25112.2. Monotonicity defined 25212.3. Prudence and monotonicity 25812.4. Prudence and binary monotonic independence 26012.5. Strong monotonicity 26212.6. Exercises 26312.7. Corrected exercises 264PART 4. MULTICRITERION RANKING FUNCTIONS 267Chapter 13. Sequentially Independent Rankings 27513.1. Introduction 27513.2. The sequential independence axioms 27713.3. Sequential independence with current choice and rejection functions 28113.4. Exercises 28713.5. Corrected exercises 290Chapter 14. Prudent Rankings 29314.1. Introduction 29314.2. Some unexpected theorems 29414.3. Prudent rankings 29714.4. Prudence in preorders and iterated prudent choice 30014.5. Exercises 30514.6. Corrected exercises 307Chapter 15. Coherent Condorcet Rankings 31315.1. Introduction 31315.2. What does one call Kemeny’s method or second Condorcet method? 31315.3. Young and Levenglick’s theorem 31915.4. Exercises 32215.5. Corrected exercises 326Chapter 16. Monotonic Rankings 33316.1. Definitions of monotonicity for ranking functions 33316.2. Monotonicity of the most ordinary non-sequential multicriterion ranking function 33916.3. Various remarks 34616.4. Exercises 34816.5. Corrected exercises 350Concluding Remarks 355Bibliography 367APPENDICES 377Appendix 1. Benjamin Franklin’s Letter 379Appendix 2. Pyramids and Snakes: Romero’s Algorithm 381Appendix 3. A Few Widespread Commercial Multicriterion Decision Techniques 387Index 405