Mathematics to the Rescue of Democracy: What Does Voting Mean and How Can It Be Improved?

Abstract

Intro -- Preface -- Acknowledgements -- Contents -- About the Author -- 1 Introduction -- 2 Voting -- 3 Aggregating Different Evaluations into One Unique Evaluation -- 4 Condorcet -- 4.1 Majority Principle -- 4.2 Condorcet's Principle -- 4.3 Condorcet Cycles -- 4.4 Principle of Independence of Irrelevant Alternatives -- 4.5 Choice Among Many Motions -- 5 Borda -- 5.1 Rankings and Points -- 5.2 Difficulties in Borda's Method -- 5.3 Difficulties in Range Voting -- 6 Simple Majority and Run-Off Voting -- 6.1 Problems with Simple Majority -- 6.2 Run-Off Voting -- 6.3 Instant Run-Off Voting -- 7 Impossible Wishes -- 7.1 Arrow's Impossibility Theorem -- 7.2 Single Vote and Arrow -- 7.3 Condorcet and Arrow -- 7.4 Approval Voting and Arrow -- 7.5 Only Two Alternatives -- 7.6 Non-manipulability of an Electoral System -- 7.7 Participation Criterion -- 7.8 Choice and Rank Monotonicity -- 8 Majority Judgement -- 8.1 The Median and the Majority Grade -- 8.2 Grade Language -- 8.3 Collective Ranking -- 8.4 Domination in Majority Judgement -- 8.5 The 2012 French Presidential Elections -- 8.6 Majority Judgement and Condorcet -- 8.7 Majority Judgement and the Impossible Wishes -- 8.8 Possible Future Developments -- 9 Legislative Territorial Representation -- 9.1 General Criteria -- 9.2 Largest Remainder Method -- 9.3 Paradoxes -- 9.4 Divisor Methods -- 9.5 Seats of the European Parliament -- 10 The United States Congress -- 11 Legislative Political Representation -- 11.1 Foreword -- 11.2 Choice of the Candidates -- 12 Biproportional Representation -- 12.1 Biproportional Apportionments -- 12.2 A Simple Case: One Seat per District and Two Parties -- 12.3 The Italian Electoral `Bug' -- 13 Political Districting -- 13.1 Territory Subdivision -- 13.2 Equity of a Subdivision -- 13.3 Criteria for Fair Political Districting -- 14 One Person-One Vote -- 14.1 Voting Power.

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Mathematics to the rescue of democracy: what does voting mean and how can it be improved?

Serafini, Paolo

Serafini, Paolo

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