Voting Procedures and Their Properties
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Critical Strategies Under Approval Voting: Who Gets Ruled in and Ruled Out
Critical Strategies Under Approval Voting: Who Gets Ruled In And Ruled Out Steven J. Brams Department of Politics New York University New York, NY 10003 USA [email protected] M. Remzi Sanver Department of Economics Istanbul Bilgi University 80310, Kustepe, Istanbul TURKEY [email protected] January 2005 2 Abstract We introduce the notion of a “critical strategy profile” under approval voting (AV), which facilitates the identification of all possible outcomes that can occur under AV. Included among AV outcomes are those given by scoring rules, single transferable vote, the majoritarian compromise, Condorcet systems, and others as well. Under each of these systems, a Condorcet winner may be upset through manipulation by individual voters or coalitions of voters, whereas AV ensures the election of a Condorcet winner as a strong Nash equilibrium wherein voters use sincere strategies. To be sure, AV may also elect Condorcet losers and other lesser candidates, sometimes in equilibrium. This multiplicity of (equilibrium) outcomes is the product of a social-choice framework that is more general than the standard preference-based one. From a normative perspective, we argue that voter judgments about candidate acceptability should take precedence over the usual social-choice criteria, such as electing a Condorcet or Borda winner. Keywords: approval voting; elections; Condorcet winner/loser; voting games; Nash equilibrium. Acknowledgments. We thank Eyal Baharad, Dan S. Felsenthal, Peter C. Fishburn, Shmuel Nitzan, Richard F. Potthoff, and Ismail Saglam for valuable suggestions. 3 1. Introduction Our thesis in this paper is that several outcomes of single-winner elections may be socially acceptable, depending on voters’ individual views on the acceptability of the candidates. -
A Generalization of the Minisum and Minimax Voting Methods
A Generalization of the Minisum and Minimax Voting Methods Shankar N. Sivarajan Undergraduate, Department of Physics Indian Institute of Science Bangalore 560 012, India [email protected] Faculty Advisor: Prof. Y. Narahari Deparment of Computer Science and Automation Revised Version: December 4, 2017 Abstract In this paper, we propose a family of approval voting-schemes for electing committees based on the preferences of voters. In our schemes, we calcu- late the vector of distances of the possible committees from each of the ballots and, for a given p-norm, choose the one that minimizes the magni- tude of the distance vector under that norm. The minisum and minimax methods suggested by previous authors and analyzed extensively in the literature naturally appear as special cases corresponding to p = 1 and p = 1; respectively. Supported by examples, we suggest that using a small value of p; such as 2 or 3, provides a good compromise between the minisum and minimax voting methods with regard to the weightage given to approvals and disapprovals. For large but finite p; our method reduces to finding the committee that covers the maximum number of voters, and this is far superior to the minimax method which is prone to ties. We also discuss extensions of our methods to ternary voting. 1 Introduction In this paper, we consider the problem of selecting a committee of k members out of n candidates based on preferences expressed by m voters. The most common way of conducting this election is to allow each voter to select his favorite candidate and vote for him/her, and we select the k candidates with the most number of votes. -
THE SINGLE-MEMBER PLURALITY and MIXED-MEMBER PROPORTIONAL ELECTORAL SYSTEMS : Different Concepts of an Election
THE SINGLE-MEMBER PLURALITY AND MIXED-MEMBER PROPORTIONAL ELECTORAL SYSTEMS : Different Concepts of an Election by James C. Anderson A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Master of Arts in Political Science Waterloo, Ontario, Canada, 2006 © James C. Anderson 2006 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Library and Bibliotheque et Archives Canada Archives Canada Published Heritage Direction du Branch Patrimoine de I'edition 395 Wellington Street 395, rue Wellington Ottawa ON K1A 0N4 Ottawa ON K1A 0N4 Canada Canada Your file Votre reference ISBN: 978-0-494-23700-7 Our file Notre reference ISBN: 978-0-494-23700-7 NOTICE: AVIS: The author has granted a non L'auteur a accorde une licence non exclusive exclusive license allowing Library permettant a la Bibliotheque et Archives and Archives Canada to reproduce,Canada de reproduire, publier, archiver, publish, archive, preserve, conserve,sauvegarder, conserver, transmettre au public communicate to the public by par telecommunication ou par I'lnternet, preter, telecommunication or on the Internet,distribuer et vendre des theses partout dans loan, distribute and sell theses le monde, a des fins commerciales ou autres, worldwide, for commercial or non sur support microforme, papier, electronique commercial purposes, in microform,et/ou autres formats. paper, electronic and/or any other formats. The author retains copyright L'auteur conserve la propriete du droit d'auteur ownership and moral rights in et des droits moraux qui protege cette these. this thesis. Neither the thesis Ni la these ni des extraits substantiels de nor substantial extracts from it celle-ci ne doivent etre imprimes ou autrement may be printed or otherwise reproduits sans son autorisation. -
Responsiveness, Capture and Efficient Policymaking
CENTRO DE INVESTIGACIÓN Y DOCENCIA ECONÓMICAS, A.C. ELECTIONS AND LOTTERIES: RESPONSIVENESS, CAPTURE AND EFFICIENT POLICYMAKING TESINA QUE PARA OBTENER EL GRADO DE MAESTRO EN CIENCIA POLÍTICA PRESENTA JORGE OLMOS CAMARILLO DIRECTOR DE LA TESINA: DR. CLAUDIO LÓPEZ-GUERRA CIUDAD DE MÉXICO SEPTIEMBRE, 2018 CONTENTS I. Introduction .............................................................................................................. 1 II. Literature Review ..................................................................................................... 6 1. Political Ambition .............................................................................................. 6 2. Electoral Systems and Policymaking ................................................................. 7 3. The Revival of Democracy by Lot ..................................................................... 8 III. Lottocracy in Theory .............................................................................................. 12 IV. Elections and Lotteries ........................................................................................... 14 1. Responsiveness ................................................................................................. 14 2. Legislative Capture ........................................................................................... 16 3. Efficiency.......................................................................................................... 18 V. A Formal Model of Legislator’s Incentives .......................................................... -
Are Condorcet and Minimax Voting Systems the Best?1
1 Are Condorcet and Minimax Voting Systems the Best?1 Richard B. Darlington Cornell University Abstract For decades, the minimax voting system was well known to experts on voting systems, but was not widely considered to be one of the best systems. But in recent years, two important experts, Nicolaus Tideman and Andrew Myers, have both recognized minimax as one of the best systems. I agree with that. This paper presents my own reasons for preferring minimax. The paper explicitly discusses about 20 systems. Comments invited. [email protected] Copyright Richard B. Darlington May be distributed free for non-commercial purposes Keywords Voting system Condorcet Minimax 1. Many thanks to Nicolaus Tideman, Andrew Myers, Sharon Weinberg, Eduardo Marchena, my wife Betsy Darlington, and my daughter Lois Darlington, all of whom contributed many valuable suggestions. 2 Table of Contents 1. Introduction and summary 3 2. The variety of voting systems 4 3. Some electoral criteria violated by minimax’s competitors 6 Monotonicity 7 Strategic voting 7 Completeness 7 Simplicity 8 Ease of voting 8 Resistance to vote-splitting and spoiling 8 Straddling 8 Condorcet consistency (CC) 8 4. Dismissing eight criteria violated by minimax 9 4.1 The absolute loser, Condorcet loser, and preference inversion criteria 9 4.2 Three anti-manipulation criteria 10 4.3 SCC/IIA 11 4.4 Multiple districts 12 5. Simulation studies on voting systems 13 5.1. Why our computer simulations use spatial models of voter behavior 13 5.2 Four computer simulations 15 5.2.1 Features and purposes of the studies 15 5.2.2 Further description of the studies 16 5.2.3 Results and discussion 18 6. -
MGF 1107 FINAL EXAM REVIEW CHAPTER 9 1. Amy (A), Betsy
MGF 1107 FINAL EXAM REVIEW CHAPTER 9 1. Amy (A), Betsy (B), Carla (C), Doris (D), and Emilia (E) are candidates for an open Student Government seat. There are 110 voters with the preference lists below. 36 24 20 18 8 4 A E D B C C B C E D E D C B C C B B D D B E D E E A A A A A Who wins the election if the method used is: a) plurality? b) plurality with runoff? c) sequential pairwise voting with agenda ABEDC? d) Hare system? e) Borda count? 2. What is the minimum number of votes needed for a majority if the number of votes cast is: a) 120? b) 141? 3. Consider the following preference lists: 1 1 1 A C B B A D D B C C D A If sequential pairwise voting and the agenda BACD is used, then D wins the election. Suppose the middle voter changes his mind and reverses his ranking of A and B. If the other two voters have unchanged preferences, B now wins using the same agenda BACD. This example shows that sequential pairwise voting fails to satisfy what desirable property of a voting system? 4. Consider the following preference lists held by 5 voters: 2 2 1 A B C C C B B A A First, note that if the plurality with runoff method is used, B wins. Next, note that C defeats both A and B in head-to-head matchups. This example shows that the plurality with runoff method fails to satisfy which desirable property of a voting system? 5. -
On the Distortion of Voting with Multiple Representative Candidates∗
The Thirty-Second AAAI Conference on Artificial Intelligence (AAAI-18) On the Distortion of Voting with Multiple Representative Candidates∗ Yu Cheng Shaddin Dughmi David Kempe Duke University University of Southern California University of Southern California Abstract voters and the chosen candidate in a suitable metric space (Anshelevich 2016; Anshelevich, Bhardwaj, and Postl 2015; We study positional voting rules when candidates and voters Anshelevich and Postl 2016; Goel, Krishnaswamy, and Mu- are embedded in a common metric space, and cardinal pref- erences are naturally given by distances in the metric space. nagala 2017). The underlying assumption is that the closer In a positional voting rule, each candidate receives a score a candidate is to a voter, the more similar their positions on from each ballot based on the ballot’s rank order; the candi- key questions are. Because proximity implies that the voter date with the highest total score wins the election. The cost would benefit from the candidate’s election, voters will rank of a candidate is his sum of distances to all voters, and the candidates by increasing distance, a model known as single- distortion of an election is the ratio between the cost of the peaked preferences (Black 1948; Downs 1957; Black 1958; elected candidate and the cost of the optimum candidate. We Moulin 1980; Merrill and Grofman 1999; Barbera,` Gul, consider the case when candidates are representative of the and Stacchetti 1993; Richards, Richards, and McKay 1998; population, in the sense that they are drawn i.i.d. from the Barbera` 2001). population of the voters, and analyze the expected distortion Even in the absence of strategic voting, voting systems of positional voting rules. -
Single-Winner Voting Method Comparison Chart
Single-winner Voting Method Comparison Chart This chart compares the most widely discussed voting methods for electing a single winner (and thus does not deal with multi-seat or proportional representation methods). There are countless possible evaluation criteria. The Criteria at the top of the list are those we believe are most important to U.S. voters. Plurality Two- Instant Approval4 Range5 Condorcet Borda (FPTP)1 Round Runoff methods6 Count7 Runoff2 (IRV)3 resistance to low9 medium high11 medium12 medium high14 low15 spoilers8 10 13 later-no-harm yes17 yes18 yes19 no20 no21 no22 no23 criterion16 resistance to low25 high26 high27 low28 low29 high30 low31 strategic voting24 majority-favorite yes33 yes34 yes35 no36 no37 yes38 no39 criterion32 mutual-majority no41 no42 yes43 no44 no45 yes/no 46 no47 criterion40 prospects for high49 high50 high51 medium52 low53 low54 low55 U.S. adoption48 Condorcet-loser no57 yes58 yes59 no60 no61 yes/no 62 yes63 criterion56 Condorcet- no65 no66 no67 no68 no69 yes70 no71 winner criterion64 independence of no73 no74 yes75 yes/no 76 yes/no 77 yes/no 78 no79 clones criterion72 81 82 83 84 85 86 87 monotonicity yes no no yes yes yes/no yes criterion80 prepared by FairVote: The Center for voting and Democracy (April 2009). References Austen-Smith, David, and Jeffrey Banks (1991). “Monotonicity in Electoral Systems”. American Political Science Review, Vol. 85, No. 2 (June): 531-537. Brewer, Albert P. (1993). “First- and Secon-Choice Votes in Alabama”. The Alabama Review, A Quarterly Review of Alabama History, Vol. ?? (April): ?? - ?? Burgin, Maggie (1931). The Direct Primary System in Alabama. -
Plurality Voting Under Uncertainty
Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence (IJCAI 2015) Plurality Voting under Uncertainty Reshef Meir Harvard University Abstract vote. Moreover, even for a given belief there may be sev- eral different actions that can be justified as rational. Hence Understanding the nature of strategic voting is the holy grail any model of voting behavior and equilibrium must state ex- of social choice theory, where game-theory, social science plicitly its epistemic and behavioral assumptions. and recently computational approaches are all applied in or- der to model the incentives and behavior of voters. In a recent A simple starting point would be to apply some “stan- paper, Meir et al. (2014) made another step in this direction, dard” assumptions from game-theory, for example that vot- by suggesting a behavioral game-theoretic model for voters ers play a Nash equilibrium of the game induced by their under uncertainty. For a specific variation of best-response preferences. However, such a prediction turns out to be very heuristics, they proved initial existence and convergence re- uninformative: a single voter can rarely affect the outcome, sults in the Plurality voting system. and thus almost any way the voters vote is a Nash equilib- This paper extends the model in multiple directions, consid- rium (including, for example, when all voters vote for their ering voters with different uncertainty levels, simultaneous least preferred candidate). It is therefore natural to consider strategic decisions, and a more permissive notion of best- the role of uncertainty in voters’ decisions. response. It is proved that a voting equilibrium exists even in the most general case. -
A Canadian Model of Proportional Representation by Robert S. Ring A
Proportional-first-past-the-post: A Canadian model of Proportional Representation by Robert S. Ring A thesis submitted to the School of Graduate Studies in partial fulfilment of the requirements for the degree of Master of Arts Department of Political Science Memorial University St. John’s, Newfoundland and Labrador May 2014 ii Abstract For more than a decade a majority of Canadians have consistently supported the idea of proportional representation when asked, yet all attempts at electoral reform thus far have failed. Even though a majority of Canadians support proportional representation, a majority also report they are satisfied with the current electoral system (even indicating support for both in the same survey). The author seeks to reconcile these potentially conflicting desires by designing a uniquely Canadian electoral system that keeps the positive and familiar features of first-past-the- post while creating a proportional election result. The author touches on the theory of representative democracy and its relationship with proportional representation before delving into the mechanics of electoral systems. He surveys some of the major electoral system proposals and options for Canada before finally presenting his made-in-Canada solution that he believes stands a better chance at gaining approval from Canadians than past proposals. iii Acknowledgements First of foremost, I would like to express my sincerest gratitude to my brilliant supervisor, Dr. Amanda Bittner, whose continuous guidance, support, and advice over the past few years has been invaluable. I am especially grateful to you for encouraging me to pursue my Master’s and write about my electoral system idea. -
Legislature by Lot: Envisioning Sortition Within a Bicameral System
PASXXX10.1177/0032329218789886Politics & SocietyGastil and Wright 789886research-article2018 Special Issue Article Politics & Society 2018, Vol. 46(3) 303 –330 Legislature by Lot: Envisioning © The Author(s) 2018 Article reuse guidelines: Sortition within a Bicameral sagepub.com/journals-permissions https://doi.org/10.1177/0032329218789886DOI: 10.1177/0032329218789886 System* journals.sagepub.com/home/pas John Gastil Pennsylvania State University Erik Olin Wright University of Wisconsin–Madison Abstract In this article, we review the intrinsic democratic flaws in electoral representation, lay out a set of principles that should guide the construction of a sortition chamber, and argue for the virtue of a bicameral system that combines sortition and elections. We show how sortition could prove inclusive, give citizens greater control of the political agenda, and make their participation more deliberative and influential. We consider various design challenges, such as the sampling method, legislative training, and deliberative procedures. We explain why pairing sortition with an elected chamber could enhance its virtues while dampening its potential vices. In our conclusion, we identify ideal settings for experimenting with sortition. Keywords bicameral legislatures, deliberation, democratic theory, elections, minipublics, participation, political equality, sortition Corresponding Author: John Gastil, Department of Communication Arts & Sciences, Pennsylvania State University, 232 Sparks Bldg., University Park, PA 16802, USA. Email: [email protected] *This special issue of Politics & Society titled “Legislature by Lot: Transformative Designs for Deliberative Governance” features a preface, an introductory anchor essay and postscript, and six articles that were presented as part of a workshop held at the University of Wisconsin–Madison, September 2017, organized by John Gastil and Erik Olin Wright. -
Application for Absentee Ballot
Application for Absentee Ballot Including Absentee List Request, Election Specific Absentee Ballot Request, Request for Absentee Ballot Due to Illness or Health Emergency or to be removed from receiving an Absentee Ballot. Fields marked with an asterisk (*) are required fields. Please type or use black or blue pen only and print clearly. COMPLETE FORM AND SUBMIT TO COUNTY ELECTION OFFICE BY NOON THE DAY BEFORE ELECTION DAY APPLICANT IDENTIFYING AND CONTACT INFORMATION Last Name* First Name* Middle Name (Optional) Birthdate* (MM/DD/YYYY) Phone Number (Optional) Email Address (Optional) County where you reside and are registered to vote* Montana Residence Address* City* Zip Code* Mailing Address (required if differs from residence address*) City and State Zip Code Check if the mailing address listed above is for part of the year only and if so, complete the information below (for absentee ballot list only). Clearly print the complete mailing address(es) and specify the applicable time periods for address (add more addresses as necessary). Seasonal Mailing Address (Optional) City and State Zip Code Period (mm/dd/yyyy-mm/dd/yyyy) BALLOT REQUEST OPTIONS AND VOTER AFFIRMATION Yes, I request an absentee ballot to be mailed to me for ALL elections in which I am eligible to vote as long as I reside at the address listed on this application. I understand that if I file a change of address with the U.S. postal service, I must complete, sign, and return a confirmation notice mailed to me by the county election office; OR I hereby request an absentee ballot for the upcoming election (check only one): Primary General Municipal Other election to be held on By signing below, I understand that I am officially requesting an absentee ballot and affirm that I will have met the 30-day Montana residency requirement before voting my absentee ballot.