Cover -- Title Page -- Copyright Page -- Table of Contents -- General Introduction -- PART 1. A PARADOXICAL RESEARCH FIELD -- Chapter 1. The Initial Problem -- 1.1. Introduction -- 1.2. The decision makers and their consultants' usual work -- 1.2.1. Identifying the admissible alternatives -- 1.2.2. Identifying the criteria -- 1.2.3. Evaluating alternatives -- 1.2.4. Synthesizing the "data" -- 1.2.5. Interpreting the results of the calculation -- 1.3. Toward a paradigm for managerial decision-making -- 1.3.1. Criteria only in the form of preorderings? -- 1.3.2. Synthesis of data: choosing the method -- 1.4. Exercises -- 1.5. Corrected exercises -- Chapter 2. Paradoxes -- 2.1. Arrow's axiomatic system -- 2.2. May's axiomatic system -- 2.3. Strategic majority voting -- 2.3.1. The cake -- 2.3.2. A miser, a drunkard, and a health freak -- 2.4. Exercises -- 2.5. Corrected exercises -- PART 2. A CENTRAL CASE: THE MAJORITY METHOD -- Chapter 3. Majority Method and Limited Domain -- 3.1. Sen's lemma [SEN 66] -- 3.2. Coombs' condition -- 3.3. Black's unimodality condition [BLA 48, BLA 58] -- 3.4. Romero's arboricity -- 3.5. Romero's quasi-unimodality -- 3.6. Arrow-Black's single-peakedness -- 3.7. The Cij's -- 3.8. Exercises -- 3.9. Corrected exercises -- Chapter 4. Intuition Can Easily Suggest Errors -- 4.1. Inada's conditions -- 4.2. Is the bipartition the same as the NITM condition? -- 4.3. Diversity of the NIMT condition -- 4.4. Exercises -- 4.5. Corrected exercises -- Chapter 5. Would Transitivity be a Prohibitive Luxury? -- 5.1. Star-shapedness -- 5.2. Ward's condition -- 5.2.1. In search of reasonable axiomatic limitations on the feasible domain for the criteria -- 5.2.2. A fundamental result -- 5.3. The failure of the majority method -- 5.4. Exercises -- 5.5. Corrected exercises -- Conclusion of the Second Part.

PART 3. AXIOMATIZING CHOICE FUNCTIONS -- Chapter 6. Helpful Tools for the Sensible Decision Maker -- 6.1. The "habitual" decision maker and his/her traditional means -- 6.1.1. Decision makers' reluctance in the face of the consultants' "knowledge" -- 6.1.2. The "habitual" decision maker and the framing of Kahneman and Tversky -- 6.2. The habitual decision maker -- 6.2.1. A small history of utilitarianism -- 6.2.2. How can one explain utilitarianism's success? -- 6.2.3. What remains of utilitarianism if it wants to support a well-founded decision-making theory? -- 6.3. A "sensible" decision maker confronted with a difficult decision -- 6.4. The urgency of raising the moral standard of the market -- 6.5. Conclusion -- 6.6. Exercises -- 6.7. Corrected exercises -- Chapter 7. An Important Class of Choice Functions -- 7.1. Introduction -- 7.2. The problem: various definitions -- 7.3. Natural properties of the E-matrices and B-F-matrices -- 7.4. Choice functions that depend only on the E-matrix or on the B-F-matrix -- 7.5. Characterization of the choice functions that depend only on the E-matrix (respectively, B-F-matrix) -- 7.6. Conclusion -- 7.7. Exercises -- 7.8. Corrected exercises -- Chapter 8. Prudent Choice Functions -- 8.1. Introduction -- 8.2. Toward the prudence axiom -- 8.2.1. The Condorcet principle -- 8.2.2. The mindominance principle -- 8.2.3. The maxdomination principle -- 8.2.4. The prudence principle -- 8.3. Properties related to prudence for choice functions -- 8.4. Exercises -- 8.5. Corrected exercises -- Chapter 9. Often Implicit Axioms: Sovereignty, Homogeneity, Decision by Rejection or Selection, Prudence and Violence -- 9.1. Introduction -- 9.2. Sovereignty -- 9.2.1. About the definition domain of the criteria -- 9.2.2. About the image of the choice function -- 9.3. Homogeneous choice.

9.4. Choice by selection and choice by rejection -- 9.5. Violent choice and prudent choice -- 9.6. Exercises -- 9.7. Corrected exercises -- Chapter 10. Coherent Choice Functions -- 10.1. Introduction -- 10.2. Characterization of the Borda method -- 10.3. Coherence and the other axioms -- 10.3.1. Coherence and Condorcet choice function -- 10.3.2. Coherence and prudence -- 10.4. Exercises -- 10.5. Corrected exercises -- Chapter 11. Rationality and Independence -- 11.1. Introduction -- 11.2. Rationalities -- 11.3. Axioms of independence -- 11.4. The inclusive iteration principle -- 11.5. Conclusion -- 11.6. Exercises -- 11.7. Corrected exercises -- Chapter 12. Monotonic Choice Functions -- 12.1. Introduction -- 12.2. Monotonicity defined -- 12.3. Prudence and monotonicity -- 12.4. Prudence and binary monotonic independence -- 12.5. Strong monotonicity -- 12.6. Exercises -- 12.7. Corrected exercises -- PART 4. MULTICRITERION RANKING FUNCTIONS -- Chapter 13. Sequentially Independent Rankings -- 13.1. Introduction -- 13.2. The sequential independence axioms -- 13.3. Sequential independence with current choice and rejection functions -- 13.4. Exercises -- 13.5. Corrected exercises -- Chapter 14. Prudent Rankings -- 14.1. Introduction -- 14.2. Some unexpected theorems -- 14.3. Prudent rankings -- 14.4. Prudence in preorders and iterated prudent choice -- 14.5. Exercises -- 14.6. Corrected exercises -- Chapter 15. Coherent Condorcet Rankings -- 15.1. Introduction -- 15.2. What does one call Kemeny's method or second Condorcet method? -- 15.2.1. Sources of the method -- 15.2.2. Properties of Kemeny's multifunction -- 15.2.3. Values of Kemeny's function on some particular profiles -- 15.3. Young and Levenglick's theorem -- 15.4. Exercises -- 15.5. Corrected exercises -- Chapter 16. Monotonic Rankings -- 16.1. Definitions of monotonicity for ranking functions.

16.1.1. Preliminary definitions -- 16.1.2. Monotonicity axioms for ranking functions -- 16.1.3. Relations between these definitions -- 16.2. Monotonicity of the most ordinary non-sequential multicriterion ranking function -- 16.2.1. Monotonicities and ordinary non-sequential ranking functions -- 16.2.2. With the sequential versions? -- 16.3. Various remarks -- 16.3.1. The bonds between monotonicity and independence are particularly strong: is monotonicity really as "expensive"as it seems to be? -- 16.3.2. Durand's paradoxal theorem (iterated strongly monotonic and symmetrical choice function) -- 16.4. Exercises -- 16.5. Corrected exercises -- Concluding Remarks -- Bibliography -- APPENDICES -- Appendix 1. Benjamin Franklin's Letter -- Appendix 2. Pyramids and Snakes: Romero's Algorithm -- Appendix 3. A Few Widespread Commercial Multicriterion Decision Techniques -- Index.