ABSTRACT
CONTENTS 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.2 Some Solutions to Electing a Single Winner . . . . . . . . . . . . . . . . . . . . . . . . 79 4.3 Some Solutions to Electing Multiple Winners . . . . . . . . . . . . . . . . . . . . . . . 82 4.4 Blending Systems Together . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.5 Other Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 4.6 Which Systems Are Good? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.6.1 A Theorist’s Point of View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.6.1.1 Majority Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.6.1.2 Bad News Begins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.6.1.3 Arrow’s Impossibility Theorem . . . . . . . . . . . . . . . . . 93 4.6.1.4 Gibbard-Satterthwaite Impossibility Theorem . . . 94 4.6.1.5 Systems with Respect to Criteria . . . . . . . . . . . . . . . . 95
4.6.2 A Practitioner’s Point of View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
An electoral system, or simply a voting method, defines the rules by which the choices or preferences of voters are collected, tallied, aggregated and collectively interpreted to obtain the results of an election [249, 489].
