## A Mathematical Approach to Proportional Representation: Duncan Black on Lewis Carroll`This is a book about a well-known writer, Lewis Carroll, and about a little-known subject, the theory of voting' (from the Editors' Introduction). This book has been edited from the manuscripts of the late Scottish economist Duncan Black. Shortly after the publication of The Theory of Committees and Elections Black started to collect material for papers and a book on Lewis Carroll's theory of proportional representation. Black's chapter plans made it clear that the book was to be in three parts, written by himself, followed by a reprint of Carroll's Principles of Parliamentary Representation and its main sources. Part I is biographical, introducing Lewis Carroll and giving relevant details of his life. Part II is Black's already published work on Lewis Carroll. Part III comprises the more detailed arguments about Carroll's reasoning, and Part IV contains reprints of rare original material on proportional representation by Carroll, James Garth Marshall, and Walter Baily. Taken together, the editors have provided a complete reference source for the theory of voting and proportional representation. |

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### Contents

The Life and Logic of Lewis Carroll | 1 |

The Principles of Parliamentary Representation | 45 |

An Analysis of Carrolls Argument | 91 |

Copyright | |

2 other sections not shown

### Common terms and phrases

A-candidate able to fill Alice Liddell argument Arthur Cohen belfry Cambridge Carroll's Carroll's theory choice Christ Church coalition Cohen Common Room complete Droop quotas Condorcet Cumulative Vote curve d'Hondt method Diaries distribution District Dodgson Droop quota Duncan Black Edith Denman elector is allowed electoral system electors unrepresented fill one seat fill two seats Goschen Governing Body Hartington integer letter Lewis Carroll Logic London lowest row majority Marshall's mathematical maximin criterion method minority number of candidates number of Electors number of Members number of seats number of supporters number of votes optimum strategy Oxford pamphlet Parliamentary Representation party payoff matrix percentage political possible preference Principles of Parliamentary problem procedure Proportional Representation represented Roger Lancelyn Green seats available single transferable vote single vote Snark suppose theorem theory of committees three seats total number two-party system two-person zero-sum game upper m rows voters Walter Baily