Voting Procedures under Uncertainty

We live in an uncertain world, is a truism most of us hear more often than we would like. What one usually means to say by this is that we do not know what will happen in the future. Since changes, even major ones, have occurred in the past, it is possible that they will occur again in the future. In politics institutions are ways of coping with continuity and change. In democratic systems the electoral institutions provide ways of peaceful adjustment to changes in popular opinions. This book is about uncertainty as it pertains to electoral institutions. We shall deal with the ways in which analytic models are capable of taking into account voter uncertainty, ignorance and incompetence. We shall also discuss how uncertainty pertains to electoral outcomes. Given voter opinions, there is often a wide variation in the possible electoral outcomes. This could be called procedure-dependence of outcomes. Its existence shows that uncertainty is not something that can characterize only future events. It can pertain to past ones as well. This work is part of the Democracy and Constitution Project of Center for Business and Policy Studies (SNS). The idea of writing a book on the performance of voting procedures under uncertain cir­ cumstances came up in my correspondence with Dr. Per Molander of SNS a few years ago.

Table of Contents:
1. Choice Theory and Constitutional Design.- 1.1 Theories and Models.- 1.2 Applying Social Choice Theory.- 1.3 Varying Assumptions.- 2. Chaotic Behavior of Models.- 2.1 The U.S. Presidential Elections.- 2.2 Referendum Paradox and the Properties of Majority Rule.- 2.3 How Chaotic Can It Get?.- 3. Results Based on Standard Model.- 3.1 Voting Procedures.- 3.2 Performance Criteria.- 3.3 Chaos, Strategy and Self Correction.- 4. Aggregating Voting Probabilities and Judgments.- 4.1 Avoiding Arrow’s Theorem via Average Rule.- 4.2 Condorcet’s Jury Theorem.- 4.3 Relaxing the Independence Assumption.- 4.4 Optimal Jury Decision Making.- 4.5 Thought Experiment: Council of Ministers as a Jury.- 5. Condorcet’s Rule and Preference Proximity.- 5.1 Condorcet’s Rule.- 5.2 Measuring Preference Similarity.- 5.3 Preference Proximity and Other Desiderata.- 5.4 Ranking and Choice Rules.- 5.5 Kemeny, Dodgson and Slater.- 6. Responses to Changes in Voter Opinions.- 6.1 Monotonicity, Maskin-Monotonicity and No-Show Paradox 92.- 6.2 The Strong No-Show Paradox.- 6.3 Qualified Majorities and No-Show Paradox.- 6.4 Monotonicity Violations of Voting Systems.- 6.5 Preference Truncation Paradox.- 6.6 Preference Misrepresentation.- 7. Mos Docendi Geometricus.- 7.1 The British Parliamentary Elections of 2001.- 7.2 Critique of Condorcet’s Intuition.- 7.3 Profile Decomposition.- 7.4 Berlin vs. Bonn Vote Revisited.- 8. Conclusions.- List of Figures 139 List of Tables.- Author Index.

Review :
From the reviews: "The main objective of Voting Procedures under Uncertainty is to clarify how uncertainty pertains to the performance of voting procedures. This significant task is successfully undertaken … . this book is a useful, refreshing and challenging reading for students and researchers of collective decision making." (S. Nitzan, Journal of Economics, Vol. 80 (3), 2003) "For the person interested in a ‘reader friendly’ introduction to the mathematics of voting theory, an outline of some of the more recent contributions to this area, or a reference book with references to the main results, I highly recommend Nurmi’s book." (Donald G. Saari, Mathematical Reviews, 2004 d) "The author considers the impact of various types of uncertainty on social choice theory, and especially voting theory. … The explanations are clear and accompanied by either simple theoretical examples or ones drawn from recent political experience. The book contains a wealth of information for the interested reader." (Duncan J. Melville, Zentralblatt MATH, Vol. 1018, 2003)