In this book, first published in 1958, the social choice theorist and economist Duncan Black aims to formulate a pure science of politics. Focusing on the mathematics of committees and, accordingly, of elections, Black's writing engages with the theories of Condorcet, Borda and Laplace in order to describe the ways in which different systems of voting will yield different results. This can, as Black discusses in detail, influence whether the chosen candidate or motion is relatively agreeable to all, or only suited to the majority group of voters. Black also presents a history of the political science of elections, placing his own work within the context of earlier research and thought on this subject. Professor Black ensures that only a basic knowledge of arithmetic is needed to understand his arguments, although his methods of reasoning will be more familiar to those readers who have previously studied mathematics and economics.
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.- 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 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.- 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.- 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.- 1. When the members' preference curves are single-peaked.- 2. When the members' preference curves are subject to no restriction.- 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.- 1. Jean-Charles de Borda (1733-1799).- 2. Marie Jean Antoine Nicolas Caritat, Marquis de Condorcet (1743-1794).- 3. Pierre-Simon, Marquis de Laplace (1749-1827).- 4. Conclusions.- 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) 'The Cyclostyled Sheet' (7 Dec. 1877).- Notes on Dodgson's Third Pamphlet 'A Method...' (1876).
Number Of Pages: 242
Published: 5th March 1999
Publisher: Kluwer Academic Publishers
Country of Publication: US
Dimensions (cm): 24.13 x 15.88
Weight (kg): 0.45
Edition Type: New edition