Geometric Ways of Understanding Voting Problems
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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. -
Crowdsourcing Applications of Voting Theory Daniel Hughart
Crowdsourcing Applications of Voting Theory Daniel Hughart 5/17/2013 Most large scale marketing campaigns which involve consumer participation through voting makes use of plurality voting. In this work, it is questioned whether firms may have incentive to utilize alternative voting systems. Through an analysis of voting criteria, as well as a series of voting systems themselves, it is suggested that though there are no necessarily superior voting systems there are likely enough benefits to alternative systems to encourage their use over plurality voting. Contents Introduction .................................................................................................................................... 3 Assumptions ............................................................................................................................... 6 Voting Criteria .............................................................................................................................. 10 Condorcet ................................................................................................................................. 11 Smith ......................................................................................................................................... 14 Condorcet Loser ........................................................................................................................ 15 Majority ................................................................................................................................... -
Approval Voting a Characterization and a Compilation of Advantages and Drawbacks in Respect of Other Voting Procedures
Die approbierte Originalversion dieser Diplom-/Masterarbeit ist an der Hauptbibliothek der Technischen Universität Wien aufgestellt (http://www.ub.tuwien.ac.at). The approved original version of this diploma or master thesis is available at the main library of the Vienna University of Technology (http://www.ub.tuwien.ac.at/englweb/). Ao.Univ.Prof. Dipl.-Ing. Dr.techn. Alexander Mehlmann DIPLOMARBEIT Approval Voting A characterization and a compilation of advantages and drawbacks in respect of other voting procedures ausgef¨uhrtam Institut f¨ur Wirtschaftsmathematik der Technischen Universit¨atWien unter Anleitung von Ao.Univ.Prof. Dipl.-Ing. Dr.techn. Alexander Mehlmann durch Michael Maurer Guglgasse 6/2/268 1110 Wien Wien, am 16. Oktober 2007 Michael Maurer Abstract This diploma thesis gives a characterization and a compilation of advantages and drawbacks of approval voting in respect of other voting procedures. Approval voting is a voting procedure, where voters can approve of as many candidates as they like, therefore casting a vote for every candidate they approve of. After a short introduc- tion into voting and social choice theory, and the presentation of two discouraging results (Arrow's theorem and the Gibbard-Satterthwaite theorem), the present work evaluates approval voting by some standard social choice criteria. Then, it character- izes approval voting among ballot aggregation functions, it characterizes candidates who can win approval voting elections, and provides advice to voters on what strate- gies they should employ according to their preference ranking. The main part of this work compiles advantages and disadvantages of approval voting as far as dichoto- mous, trichotomous and multichotomous preferences, strategy-proofness, election of Pareto and Condorcet candidates, stability of outcomes, Condorcet efficiency, comparison of outcomes to other voting procedures, computational manipulation, vulnerability to majority decisiveness and to the erosion of the majority principle, and subset election outcomes are concerned. -
Consistent Approval-Based Multi-Winner Rules
Consistent Approval-Based Multi-Winner Rules Martin Lackner Piotr Skowron TU Wien University of Warsaw Vienna, Austria Warsaw, Poland Abstract This paper is an axiomatic study of consistent approval-based multi-winner rules, i.e., voting rules that select a fixed-size group of candidates based on approval bal- lots. We introduce the class of counting rules, provide an axiomatic characterization of this class and, in particular, show that counting rules are consistent. Building upon this result, we axiomatically characterize three important consistent multi- winner rules: Proportional Approval Voting, Multi-Winner Approval Voting and the Approval Chamberlin–Courant rule. Our results demonstrate the variety of multi- winner rules and illustrate three different, orthogonal principles that multi-winner voting rules may represent: individual excellence, diversity, and proportionality. Keywords: voting, axiomatic characterizations, approval voting, multi-winner elections, dichotomous preferences, apportionment 1 Introduction In Arrow’s foundational book “Social Choice and Individual Values” [5], voting rules rank candidates according to their social merit and, if desired, this ranking can be used to select the best candidate(s). As these rules are concerned with “mutually exclusive” candidates, they can be seen as single-winner rules. In contrast, the goal of multi-winner rules is to select the best group of candidates of a given size; we call such a fixed-size set of candidates a committee. Multi-winner elections are of importance in a wide range of scenarios, which often fit in, but are not limited to, one of the following three categories [25, 29]. The first category contains multi-winner elections aiming for proportional representation. -
General Conference, Universität Hamburg, 22 – 25 August 2018
NEW OPEN POLITICAL ACCESS JOURNAL RESEARCH FOR 2018 ECPR General Conference, Universität Hamburg, 22 – 25 August 2018 EXCHANGE EDITORS-IN-CHIEF Alexandra Segerberg, Stockholm University, Sweden Simona Guerra, University of Leicester, UK Published in partnership with ECPR, PRX is a gold open access journal seeking to advance research, innovation and debate PRX across the breadth of political science. NO ARTICLE PUBLISHING CHARGES THROUGHOUT 2018–2019 General Conference bit.ly/introducing-PRX 22 – 25 August 2018 General Conference Universität Hamburg, 22 – 25 August 2018 Contents Welcome from the local organisers ........................................................................................ 2 Mayor’s welcome ..................................................................................................................... 3 Welcome from the Academic Convenors ............................................................................ 4 The European Consortium for Political Research ................................................................... 5 ECPR governance ..................................................................................................................... 6 ECPR Council .............................................................................................................................. 6 Executive Committee ................................................................................................................ 7 ECPR staff attending ................................................................................................................. -
Electoral Institutions, Party Strategies, Candidate Attributes, and the Incumbency Advantage
Electoral Institutions, Party Strategies, Candidate Attributes, and the Incumbency Advantage The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Llaudet, Elena. 2014. Electoral Institutions, Party Strategies, Candidate Attributes, and the Incumbency Advantage. Doctoral dissertation, Harvard University. Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:12274468 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA Electoral Institutions, Party Strategies, Candidate Attributes, and the Incumbency Advantage A dissertation presented by Elena Llaudet to the Department of Government in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of Political Science Harvard University Cambridge, Massachusetts April 2014 ⃝c 2014 - Elena Llaudet All rights reserved. Dissertation Advisor: Professor Stephen Ansolabehere Elena Llaudet Electoral Institutions, Party Strategies, Candidate Attributes, and the Incumbency Advantage Abstract In developed democracies, incumbents are consistently found to have an electoral advantage over their challengers. The normative implications of this phenomenon depend on its sources. Despite a large existing literature, there is little consensus on what the sources are. In this three-paper dissertation, I find that both electoral institutions and the parties behind the incumbents appear to have a larger role than the literature has given them credit for, and that in the U.S. context, between 30 and 40 percent of the incumbents' advantage is driven by their \scaring off” serious opposition. -
Perspective Chaos, but in Voting and Apportionments?
Proc. Natl. Acad. Sci. USA Vol. 96, pp. 10568–10571, September 1999 Perspective Chaos, but in voting and apportionments? Donald G. Saari* Department of Mathematics, Northwestern University, Evanston, IL 60208-2730 Mathematical chaos and related concepts are used to explain and resolve issues ranging from voting paradoxes to the apportioning of congressional seats. Although the phrase ‘‘chaos in voting’’ may suggest the complex- A wins with the plurality vote (1, 0, 0, 0), B wins by voting ity of political interactions, here I indicate how ‘‘mathematical for two candidates, that is, with (1, 1, 0, 0), C wins by voting chaos’’ helps resolve perplexing theoretical issues identified as for three candidates, and D wins with the method proposed by early as 1770, when J. C. Borda (1) worried whether the way the Borda, now called the Borda Count (BC), where the weights French Academy of Sciences elected members caused inappro- are (3, 2, 1, 0). Namely, election outcomes can more accurately priate outcomes. The procedure used by the academy was the reflect the choice of a procedure rather than the voters’ widely used plurality system, where each voter votes for one preferences. This aberration raises the realistic worry that candidate. To illustrate the kind of difficulties that can arise in this inadvertently we may not select whom we really want. system, suppose 30 voters rank the alternatives A, B, C, and D as ‘‘Bad decisions’’ extend into, say, engineering, where one follows (where ‘‘՝’’ means ‘‘strictly preferred’’): way to decide among design (material, etc.) alternatives is to assign points to alternatives based on how they rank over Table 1. -
Universidade Federal De Pernambuco Centro De Tecnologia E Geociências Departamento De Engenharia De Produção Programa De Pós-Graduação Em Engenharia De Produção
UNIVERSIDADE FEDERAL DE PERNAMBUCO CENTRO DE TECNOLOGIA E GEOCIÊNCIAS DEPARTAMENTO DE ENGENHARIA DE PRODUÇÃO PROGRAMA DE PÓS-GRADUAÇÃO EM ENGENHARIA DE PRODUÇÃO GUILHERME BARROS CORRÊA DE AMORIM RANDOM-SUBSET VOTING Recife 2020 GUILHERME BARROS CORRÊA DE AMORIM RANDOM-SUBSET VOTING Doctoral thesis presented to the Production Engineering Postgraduation Program of the Universidade Federal de Pernambuco in partial fulfillment of the requirements for the degree of Doctor of Science in Production Engineering. Concentration area: Operational Research. Supervisor: Prof. Dr. Ana Paula Cabral Seixas Costa. Co-supervisor: Prof. Dr. Danielle Costa Morais. Recife 2020 Catalogação na fonte Bibliotecária Margareth Malta, CRB-4 / 1198 A524p Amorim, Guilherme Barros Corrêa de. Random-subset voting / Guilherme Barros Corrêa de Amorim. - 2020. 152 folhas, il., gráfs., tabs. Orientadora: Profa. Dra. Ana Paula Cabral Seixas Costa. Coorientadora: Profa. Dra. Danielle Costa Morais. Tese (Doutorado) – Universidade Federal de Pernambuco. CTG. Programa de Pós-Graduação em Engenharia de Produção, 2020. Inclui Referências e Apêndices. 1. Engenharia de Produção. 2. Métodos de votação. 3. Votação probabilística. 4. Racionalidade limitada. 5. Teoria da decisão. I. Costa, Ana Paula Cabral Seixas (Orientadora). II. Morais, Danielle Costa (Coorientadora). III. Título. UFPE 658.5 CDD (22. ed.) BCTG/2020-184 GUILHERME BARROS CORRÊA DE AMORIM RANDOM-SUBSET VOTING Tese apresentada ao Programa de Pós- Graduação em Engenharia de Produção da Universidade Federal de Pernambuco, como requisito parcial para a obtenção do título de Doutor em Engenharia de Produção. Aprovada em: 05 / 05 / 2020. BANCA EXAMINADORA ___________________________________ Profa. Dra. Ana Paula Cabral Seixas Costa (Orientadora) Universidade Federal de Pernambuco ___________________________________ Prof. Leandro Chaves Rêgo, PhD (Examinador interno) Universidade Federal do Ceará ___________________________________ Profa. -
Voting Systems: from Method to Algorithm
Voting Systems: From Method to Algorithm A Thesis Presented to The Faculty of the Com puter Science Department California State University Channel Islands In (Partial) Fulfillment of the Requirements for the Degree M asters of Science in Com puter Science b y Christopher R . Devlin Advisor: Michael Soltys December 2019 © 2019 Christopher R. Devlin ALL RIGHTS RESERVED APPROVED FOR MS IN COMPUTER SCIENCE Advisor: Dr. Michael Soltys Date Name: Dr. Bahareh Abbasi Date Name: Dr. Vida Vakilian Date APPROVED FOR THE UNIVERITY Name Date Acknowledgements I’d like to thank my wife, Eden Byrne for her patience and support while I completed this Masters Degree. I’d also like to thank Dr. Michael Soltys for his guidance and mentorship. Additionally I’d like to thank the faculty and my fellow students at CSUCI who have given nothing but assistance and encouragement during my time here. Voting Systems: From Method to Algorithm Christopher R. Devlin December 18, 2019 Abstract Voting and choice aggregation are used widely not just in poli tics but in business decision making processes and other areas such as competitive bidding procurement. Stakeholders and others who rely on these systems require them to be fast, efficient, and, most impor tantly, fair. The focus of this thesis is to illustrate the complexities inherent in voting systems. The algorithms intrinsic in several voting systems are made explicit as a way to simplify choices among these systems. The systematic evaluation of the algorithms associated with choice aggregation will provide a groundwork for future research and the implementation of these tools across public and private spheres. -
POLYTECHNICAL UNIVERSITY of MADRID Identification of Voting
POLYTECHNICAL UNIVERSITY OF MADRID Identification of voting systems for the identification of preferences in public participation. Case Study: application of the Borda Count system for collective decision making at the Salonga National Park in the Democratic Republic of Congo. FINAL MASTERS THESIS Pitshu Mulomba Mukadi Bachelor’s degree in Chemistry Democratic Republic of Congo Madrid, 2013 RURAL DEVELOPMENT & SUSTAINABLE MANAGEMENT PROJECT PLANNING UPM MASTERS DEGREE 1 POLYTECHNICAL UNIVERSIY OF MADRID Rural Development and Sustainable Management Project Planning Masters Degree Identification of voting systems for the identification of preferences in public participation. Case Study: application of the Borda Count system for collective decision making at the Salonga National Park in the Democratic Republic of Congo. FINAL MASTERS THESIS Pitshu Mulomba Mukadi Bachelor’s degree in Chemistry Democratic Republic of Congo Madrid, 2013 2 3 Masters Degree in Rural Development and Sustainable Management Project Planning Higher Technical School of Agronomy Engineers POLYTECHICAL UNIVERSITY OF MADRID Identification of voting systems for the identification of preferences in public participation. Case Study: application of the Borda Count system for collective decision making at the Salonga National Park in the Democratic Republic of Congo. Pitshu Mulomba Mukadi Bachelor of Sciences in Chemistry [email protected] Director: Ph.D Susan Martín [email protected] Madrid, 2013 4 Identification of voting systems for the identification of preferences in public participation. Case Study: application of the Borda Count system for collective decision making at the Salonga National Park in the Democratic Republic of Congo. Abstract: The aim of this paper is to review the literature on voting systems based on Condorcet and Borda. -
The Dinner Meeting Will Be Held at the Mcminnville Civic Hall and Will Begin at 6:00 P.M
CITY COUNCIL MEETING McMinnville, Oregon AGENDA McMINNVILLE CIVIC HALL December 8, 2015 200 NE SECOND STREET 6:00 p.m. – Informal Dinner Meeting 7:00 p.m. – Regular Council Meeting Welcome! All persons addressing the Council will please use the table at the front of the Board Room. All testimony is electronically recorded. Public participation is encouraged. If you desire to speak on any agenda item, please raise your hand to be recognized after the Mayor calls the item. If you wish to address Council on any item not on the agenda, you may respond as the Mayor calls for “Invitation to Citizens for Public Comment.” NOTE: The Dinner Meeting will be held at the McMinnville Civic Hall and will begin at 6:00 p.m. CITY MANAGER'S SUMMARY MEMO a. City Manager's Summary Memorandum CALL TO ORDER PLEDGE OF ALLEGIANCE INVITATION TO CITIZENS FOR PUBLIC COMMENT – The Mayor will announce that any interested audience members are invited to provide comments. Anyone may speak on any topic other than: 1) a topic already on the agenda; 2) a matter in litigation, 3) a quasi judicial land use matter; or, 4) a matter scheduled for public hearing at some future date. The Mayor may limit the duration of these comments. 1. INTERVIEW AND APPOINTMENT OF MEMBER TO THE BUDGET COMMITTEE 2. INTERVIEW AND APPOINTMENT OF MEMBER TO THE McMINNVILLE HISTORIC LANDMARKS COMMITTEE 3. OLD BUSINESS a. Update from Zero Waste Regarding Fundraising Efforts to Meet Matching Funds b. Approval of Visit McMinnville Business Plan c. Consideration of a Roundabout for the Intersection of Johnson and 5th Streets 4. -
On the Distortion of Voting with Multiple Representative Candidates
On the Distortion of Voting with Multiple Representative Candidates Yu Cheng Shaddin Dughmi Duke University University of Southern California David Kempe University of Southern California Abstract We study positional voting rules when candidates and voters are embedded in a common metric space, and cardinal preferences are naturally given by distances in the metric space. In a positional voting rule, each candidate receives a score from each ballot based on the ballot’s rank order; the candidate with the highest total score wins the election. The cost of a candidate is his sum of distances to all voters, and the distortion of an election is the ratio between the cost of the elected candidate and the cost of the optimum candidate. We consider the case when candidates are representative of the population, in the sense that they are drawn i.i.d. from the population of the voters, and analyze the expected distortion of positional voting rules. Our main result is a clean and tight characterization of positional voting rules that have constant expected distortion (independent of the number of candidates and the metric space). Our characterization result immediately implies constant expected distortion for Borda Count and elections in which each voter approves a constant fraction of all candidates. On the other hand, we obtain super-constant expected distortion for Plurality, Veto, and approving a con- stant number of candidates. These results contrast with previous results on voting with metric preferences: When the candidates are chosen adversarially, all of the preceding voting rules have distortion linear in the number of candidates or voters.