Comparing Voting Systems: (3 Theory and Decision Library A:)

In many contexts of everyday life we find ourselves faced with the problem of reconciling the views of several persons. These problems are usually solved by resorting to some opinion aggre­ gating procedure, like voting. Very often the problem is thought of as being solved after the decision to take a vote has been made and the ballots have been counted. Most official decision making bodies have formally instituted procedures of voting but in informal groups such procedures are typically chosen in casu. Curiously enough people do not seem to pay much attention to which particular procedure is being resorted to as long as some kind of voting takes place. As we shall see shortly the procedure being used often makes a great difference to the voting outcomes. Thus, the Question arises as to which voting procedure is best. This book is devoted to a discussion of this problem in the light of various criteria of optimality. We shall deal with a number of procedures that have been proposed foruse or are actually in use in voting contexts. The aim of this book is to give an evaluation of the virtues and shortcomings of these procedures. On the basis of this evaluation the reader will hopefully be able to determine which procedure is optimal for the decision setting that he or she has in mind.

Table of Contents:
1. Introduction.- 2. Preliminaries.- 3. Social Welfare Function, Social Choice Function and Voting Procedures.- 4. First Problem: Cyclic Majorities.- 4.1. The Condorcet paradox.- 4.2. How to conceal the problem: the amendment procedure.- 4.3. How common are the cycles.- 4.4. Solutions based on ordinal preferences.- 4.5. Solution based on scoring function: the Borda count.- 4.6. More general majority cycles.- 5. Second Problem: How to Satisfy the Condorcet Criteria.- 5.1. Condorcet criteria.- 5.2. Some complete successes.- 5.3. Some partial successes.- 5.4. Complete failures.- 5.5. Some probability considerations and the plausibility of the Condorcet criteria.- 5.6. The majority winning criterion.- 6. Third Problem: How the Avoid Perverse Response to Changes in Individual Opinions.- 6.1. Monotonicity and related concepts.- 6.2. Successes.- 6.3. Failures.- 6.4. The relevance of the monotonicity criteria.- 7. Fourth Problem: How to Honour Unanimous Preferences.- 7.1. Unanimity and Paretoconditions.- 7.2. Successes.- 7.3. A partial failure and a total failure.- 7.4 Relevance and compatibility with other criteria.- 8. Fifth Problem: How to Make Consistent Choices.- 8.1. Choice set invariance criteria.- 8.2. Performances with respect to consistency.- 8.3. Performances with respect to WARP and PI.- 8.4. The relevance of the criteria.- 9. Sixth Problem: How to Encourage the Sincere Revelation of Preferences.- 9.1. Manipulability.- 9.2. Performance with respect to manipulability.- 9.3. The difficulty of manipulation.- 9.4. Agenda-manipulability.- 9.5. Sincere truncation of preferences.- 10. Social Choice Methods Based on More detailed information about Individual Preferences.- 10.1. The von Neumann-Morgenstern utility and classes of interpersonal comparability.- 10.2. Old and new methods.- 10.3. An assessment.- 11. Asking for Less Than Individual Preference Orderings.- 11.1. Constructing a social preference order for a subset of alternatives.- 11.2. Results based on individual choice functions.- 12. Why Is There So Much Stability and How Can We Get More of It?.- 12.1. Explanations of stability.- 12.2. Improving the performance of the voting procedures.- 13. From Committees to Elections.- 13.1. Proportional and majoritarian systems.- 13.2. Criteria for proportional systems.- 13.3. Voting power.- 14. Conclusions.- Name Index.