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 consultantsâ 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. Arrowâs axiomatic system 36
2.2. Mayâs 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. Senâs lemma [SEN 66] 62
3.2. Coombsâ condition 63
3.3. Blackâs unimodality condition [BLA 48, BLA 58] 66
3.4. Romeroâs arboricity 67
3.5. Romeroâs quasi-unimodality 69
3.6. Arrowâ"Blackâs single-peakedness 72
3.7. The Cijâs 74
3.8. Exercises 78
3.9. Corrected exercises 80
Chapter 4. Intuition Can Easily Suggest Errors 87
4.1. Inadaâs 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. Wardâs 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 âhabitualâ decision maker and his/her traditional means 117
6.2. The habitual decision maker 124
6.3. A âsensibleâ 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 Kemenyâs method or second Condorcet method? 313
15.3. Young and Levenglickâs 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 Franklinâs Letter 379
Appendix 2. Pyramids and Snakes: Romeroâs Algorithm 381
Appendix 3. A Few Widespread Commercial Multicriterion Decision Techniques 387
Index 405
