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 I had failed to obtain publication in 1947, some chapters appeared as articles, and I am obliged to the editors of the journals mentioned below for permission to reprint this material, sometimes in a modified form. When I first attempted publication I was unacquainted with the earlier history of the theory, and, indeed, did not even know that it had a history; and the later additions to the book have largely been by way of writing the present Part II. This historical section does not include the important recent work, Social Ohoice and Individual Values (1951), of Professor Kenneth J. Arrow; but it does include all the mathematical work on committees and elections appearing before the middle of this century which has come to my notice, although the last item in it is dated 1907. No doubt there is much important material which I have failed to see. The theorizing of the book grew out of a reading of the English political philosophers and of the Italian writers on Public Finance. At a very early stage I was helped to find the general lines of development by discussion with my colleague Professor Ronald H.

I The Theory of Committees and Elections. - I. A Committee and Motions. - II. Independent Valuation. - III. Can a Motion be Represented by the same Symbol on Different Schedules? . - IV. A Committee using a Simple Majority: Single-peaked Preference Curves. - V. A Committee using a Simple Majority: other Shapes of Preference 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 ought to be Elected? . - X. Examination of some Methods of Election in Single-member Constituencies. - XI. Proportional Representation. - XII. The Decisions of a Committee using a Special Majority. - XIII. The Elasticity of Committee Decisions with an Altering Size of Majority. - XIV. The Elasticity of Committee Decisions with Alterations in the Members Preference Schedules. - XV. The Converse Problem: the Group of Schedules to Correspond to a Given Voting Matrix. - XVI. A Committee using a Simple Majority: Complementary Motions. - XVII. International Agreements, Sovereignty and the Cabinet. - II History of the Mathematical Theory of Committees and Elections (Excluding Proportional Representation). - XVIII. Borda, Condorcet and Laplace. - XIX. E. J. Nanson and Francis Galton. - XX. The Circumstances in which Rev. C. L. Dodgson (Lewis Carroll) wrote his Three Pamphlets. - Appendix. Text of Dodgson s Three Pamphlets and of `The Cyclostyled Sheet . - A Discussion of the Various Methods of Procedure in Conducting Elections (1873). - Suggestions as to the Best Method of Taking Votes, Where More than Two Issues are to be Voted on (1874). - A Method of Taking Votes on More than Two Issues (1876) `TheCyclostyled Sheet (7 Dec. 1877). - Notes on Dodgson s Third Pamphlet `A Method (1876).