Elections, Voting Rules and Paradoxical Outcomes

1. Front Matter

   Pages i-xiv

   PDF

2. Elections and Voting Paradoxes

   • William V. Gehrlein, Dominique Lepelley

   Pages 1-25

3. Probabilities of Voting Paradoxes

   • William V. Gehrlein, Dominique Lepelley

   Pages 27-57

4. Measures of Agreement in Voters’ Preferences

   • William V. Gehrlein, Dominique Lepelley

   Pages 59-83

5. Single-Stage Election Procedures

   • William V. Gehrlein, Dominique Lepelley

   Pages 85-115

6. Two-Stage Election Procedures

   • William V. Gehrlein, Dominique Lepelley

   Pages 117-140

7. The Impact of Voter Indifference

   • William V. Gehrlein, Dominique Lepelley

   Pages 141-160

8. Other Voting Rules and Considerations

   • William V. Gehrlein, Dominique Lepelley

   Pages 161-183

This monograph studies voting procedures based on the probability that paradoxical outcomes like the famous Condorcet Paradox might exist. It is well known that hypothetical examples of many different paradoxical election outcomes can be developed, but this analysis examines factors that are related to the process by which voters form their preferences on candidates that will significantly reduce the likelihood that such voting paradoxes will ever actually be observed. It is found that extreme forms of voting paradoxes should be uncommon events with a small number of candidates. Another consideration is the propensity of common voting rules to elect the Condorcet Winner, which is widely accepted as the best choice as the winner, when it exists. All common voting rules are found to have identifiable scenarios for which they perform well on the basis of this criterion. But, Borda Rule is found to consistently work well at electing the Condorcet Winner, while the other voting rules have scenarios where they work poorly or have a very small likelihood of electing a different candidate than Borda Rule. The conclusions of previous theoretical work are presented in an expository format and they are validated with empirically-based evidence. Practical implications of earlier studies are also developed.

• Voting
• Voting rules
• Elections
• Election procedures
• Social choice
• Condorcet's Paradox
• Voting paradox
• Voting rules

“This book should be of interest to any mathematically inclined reader who is interested in the mathematics of voting, and this book is especially timely since it arrives at a time when some cities and states in the United States are considering switching their voting rules from plurality to methods such as instant runoff voting.” (David McCune, Mathematical Reviews, March 2, 2020)

• Department of Business Administration, University of Delaware, Newark, USA

  William V. Gehrlein

• University of La Réunion, Saint-Denis, Ile de La Réunion, France

  Dominique Lepelley

Dr. William V. Gehrlein is currently Professor Emeritus at University of Delaware (US), which he has been affiliated with since 1978.  He has received a number of grants and awards, and has served on two journal editorial boards. His research interests have spanned the topics of statistics, operations management, and graph theory; with a primary focus on social choice theory.  He has authored more than 150 publications, along with several books and edited volumes.

Dr. Dominique Lepelley received his Ph.D in Economics from the University of Caen. He is currently Professor at the University of La Réunion (France). He is primarily interested in social choice theory. More specifically, his work examines the properties of voting procedures and electoral systems. He served as a member of the editorial board of the journal Social Choice and Welfare and has authored more than 80 publications, including two books and one edited volume.

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