Acknowledgments vii; Preface ix; 1 Preliminaries 1; 1.1 Review 1; 1.2 Decision theory 8; 1.3 Discussion 17; 1.4 Exercises 17; 1.5 Further reading 18; 2 Strategy-Proof Collective Choice 19; 2.1 Strategy- proofness on finite sets 20; 2.2 Application: The amendment rule 29; 2.3 Strategy-proofness and Arrovian aggregation 30; 2.