The Theory of Committees and Elections
THIS book or some related work has occupied me spasmodically over rather a long period, in fact ever since I listened to the class lectures of Professor A. K. White on the possibility of forming a pure science of Politics. Mter an earlier version of Part
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The Theory of Committees and Elections by
Duncan Black, M.A., Ph.D. Emeritus Professor of Economics University College of North Wales
...
K1uwer Academic Publishers
Boston/Dordecht/Lancaster
Distributors for North America: Kluwer Academic Publishers 101 Philip Drive Assinippi Park Norwell, MA 02061, USA Distributors for the UK and Ireland: Kluwer Academic Publishers MTP Press Limited Falcon House, Queen Square Lancaster LAI IRN, UNITED KINGDOM Distributors for all other countries: Kluwer Academic Publishers Group Distribution Centre Post Office Box 322 3300 AH Dordrecht THE NETHERLANDS
Library of Congress Cataloging in Publication Data Black, Duncan. The theory of committees and elections. Bibliography: p. Includes index. 1. Voting. 2. Social choice. I. Title. JF100I.B49 1986 328'.2 86-22452 ISBN-I 3:978-94-0 10-8375-1 DOl: 10.1 007/978-94-009-4225-7
elSBN-13:978-94-009-4225-7
Copyright © 1987 by Kluwer Academic Publishers First published in 1958 by Cambridge University Press. Reprinted in 1963, 1968 and 1971. This reprinting made by arrangement with the author. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, Kluwer Academic Publishers, 101 Philip Drive, Assinippi Park, Norwell, Massachusetts 02061.
IN MEMORIAM M.B.
CONTENTS
page xi
Preface Acknowledgements
xiii
PART I THE THEORY OF COMMITTEES AND ELECTIONS I. A Committee and Motions II. Independent Valuation
1 4
III. Can a Motion be Represented by the same Symbol on Different Schedules 1
11
IV. A Committee using a Simple Majority: Singlepeaked Preference Curves
14
V. A Committee using a Simple Majority: other Shapes of Preference Curves
25
1. Curves either single-peaked or single-peaked with a plateau on top
2. Other classes of curves
VI. A Committee using a Simple Majority: any Shapes of Preference Curves, Number of Motions Finite VII. Cyclical Majorities VIII. When the Ordinary Committee Procedure is in use the Members' Scales of Valuation may be Incomplete IX. Which Candidate O'U{/ht to be Elected 1 X. Examination of some Methods of Election in Single-member Constituencies XI. Proportional Representation
35 46
51 55 66 75 [ vii ]
XII. The Decisions of a Committee using a Special Majority page 84 1. When the members' preference curves are single-
peaked 2. When the members' preference curves are subject to no restriction
XIII. The Elasticity of Committee Decisions with an Altering Size of Majority
99
1. When the members' preference curves are single-
peaked 2. When the members' preference curves are subject to no restriction
XIV. The Elasticity of Committee Decisions with alterations in the Members' Preference Schedules
109
1. When the members' preference curves are singlepeaked
2. When the members' preference curves are subject to no restriction
XV. The Converse Problem: the Group of Schedules to Correspond to a Given Votin
