Voting System: Elections
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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. -
Automated Verification for Functional and Relational Properties of Voting
Automated Verification for Functional and Relational Properties of Voting Rules Bernhard Beckert, Thorsten Bormer, Michael Kirsten, Till Neuber, and Mattias Ulbrich Abstract In this paper, we formalise classes of axiomatic properties for voting rules, discuss their characteristics, and show how symmetry properties can be exploited in the verification of other properties. Following that, we describe how automated verification methods such as software bounded model checking and deductive verification can be used to verify implementations of voting rules. We present a case study, where we use and compare different approaches to verify that plurality voting satisfies the majority and the anonymity property. 1 Introduction Axiomatic definitions of characteristic properties for voting rules are important both for understanding existing voting rules and for designing new ones. For the trustworthiness of elections, it is also important to analyse the algorithmic descriptions of voting rules and to prove that they have the desired properties, i.e., they satisfy the declarative description. There are two classes of voting rule properties, namely (a) functional (absolute) properties, such as the majority criterion, which refer to single voting results, and (b) relational properties, such as anonymity, which are defined by comparing two (or more) results. In this paper, we first formally define these two classes of properties and discuss their characteristics (Section 2). We then show how symmetry properties { which are a particular kind of relational properties { can be exploited to more efficiently verify voting rules w.r.t. other (functional) properties (Section 3). Proving properties of voting rules by hand is tedious and error-prone { in particular, if the rules and properties evolve during design and various versions have to be verified. -
Voting Systems∗
Voting Systems∗ Paul E. Johnson May 27, 2005 Contents 1 Introduction 3 2 Mathematical concepts 4 2.1 Transitivity. 4 2.2 Ordinal versus Cardinal Preferences . 5 3 The Plurality Problem 7 3.1 Two Candidates? No Problem! . 7 3.2 Shortcomings of Plurality Rule With More than Two Candidates . 9 4 Rank-order voting: The Borda Count 14 4.1 The Borda Count . 15 4.2 A Paradox in the Borda Procedure . 17 4.3 Another Paradox: The Borda Winner Is A Loser? . 20 4.4 Inside the Guts of the Borda Count . 21 ∗This is a chapter prepared for educational usage by undergraduates at the University of Kansas and for eventual inclusion in a mathematics textbook that is being written with Saul Stahl of the University of Kansas Department of Mathematics. Revisions will be ongoing, so comments & corrections are especially welcome. Please contact Paul Johnson <[email protected]>. 1 4.5 Digression on the Use of Cardinal Preferences . 25 5 Sequential Pairwise Comparisons 28 5.1 A Single Elimination Tournament . 28 5.2 Dominated Winner Paradox . 30 5.3 The Intransitivity of Majority Rule . 30 6 Condorcet Methods: The Round Robin Tournament 35 6.1 Searching for an Unbeatable Set of Alternatives . 36 6.2 The Win-Loss Record . 37 6.3 Aggregated Pairwise Voting: The Borda Count Strikes Back! . 38 6.4 The Schulze Method . 43 7 Single Vote Systems: Cousins of Plurality and Majority Rule 57 8 Conclusion 63 List of Figures 1 Hypothetical Football Tournament . 29 2 Tournament Structure for the Dominated Winner Paradox . 31 3 The Smith Set . -
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 ................................................................................................................................... -
The Space of All Proportional Voting Systems and the Most Majoritarian Among Them
Social Choice and Welfare https://doi.org/10.1007/s00355-018-1166-9 ORIGINAL PAPER The space of all proportional voting systems and the most majoritarian among them Pietro Speroni di Fenizio1 · Daniele A. Gewurz2 Received: 10 July 2017 / Accepted: 30 November 2018 © The Author(s) 2018 Abstract We present an alternative voting system that aims at bridging the gap between pro- portional representative systems and majoritarian electoral systems. The system lets people vote for multiple party-lists, but then assigns each ballot paper to a single party. This opens a whole range of possible parliaments, all proportionally representative. We show theoretically that this space is convex. Then among the possible parliaments we present an algorithm to produce the most majoritarian result. We then test the system and compare the results with a pure proportional and a majoritarian voting system showing how the results are comparable with the majoritarian system. Then we simulate the system and show how it tends to produce parties of exponentially decreasing size with always a first, major party with about half of the seats. Finally we describe how the system can be used in the context of a parliament made up of two separate houses. 1 Introduction One of the main difficulties in choosing an electoral systems is how to approach the dichotomy between governability and representativeness. The general consensus is that it is impossible to have a system that is both proportionally representative and that assures a sufficient concentration of power in few parties to give them the possibility to efficiently govern a country. -
The Expanding Approvals Rule: Improving Proportional Representation and Monotonicity 3
Working Paper The Expanding Approvals Rule: Improving Proportional Representation and Monotonicity Haris Aziz · Barton E. Lee Abstract Proportional representation (PR) is often discussed in voting settings as a major desideratum. For the past century or so, it is common both in practice and in the academic literature to jump to single transferable vote (STV) as the solution for achieving PR. Some of the most prominent electoral reform movements around the globe are pushing for the adoption of STV. It has been termed a major open prob- lem to design a voting rule that satisfies the same PR properties as STV and better monotonicity properties. In this paper, we first present a taxonomy of proportional representation axioms for general weak order preferences, some of which generalise and strengthen previously introduced concepts. We then present a rule called Expand- ing Approvals Rule (EAR) that satisfies properties stronger than the central PR axiom satisfied by STV, can handle indifferences in a convenient and computationally effi- cient manner, and also satisfies better candidate monotonicity properties. In view of this, our proposed rule seems to be a compelling solution for achieving proportional representation in voting settings. Keywords committee selection · multiwinner voting · proportional representation · single transferable vote. JEL Classification: C70 · D61 · D71 1 Introduction Of all modes in which a national representation can possibly be constituted, this one [STV] affords the best security for the intellectual qualifications de- sirable in the representatives—John Stuart Mill (Considerations on Represen- tative Government, 1861). arXiv:1708.07580v2 [cs.GT] 4 Jun 2018 H. Aziz · B. E. Lee Data61, CSIRO and UNSW, Sydney 2052 , Australia Tel.: +61-2-8306 0490 Fax: +61-2-8306 0405 E-mail: [email protected], [email protected] 2 Haris Aziz, Barton E. -
Selecting the Runoff Pair
Selecting the runoff pair James Green-Armytage New Jersey State Treasury Trenton, NJ 08625 [email protected] T. Nicolaus Tideman Department of Economics, Virginia Polytechnic Institute and State University Blacksburg, VA 24061 [email protected] This version: May 9, 2019 Accepted for publication in Public Choice on May 27, 2019 Abstract: Although two-round voting procedures are common, the theoretical voting literature rarely discusses any such rules beyond the traditional plurality runoff rule. Therefore, using four criteria in conjunction with two data-generating processes, we define and evaluate nine “runoff pair selection rules” that comprise two rounds of voting, two candidates in the second round, and a single final winner. The four criteria are: social utility from the expected runoff winner (UEW), social utility from the expected runoff loser (UEL), representativeness of the runoff pair (Rep), and resistance to strategy (RS). We examine three rules from each of three categories: plurality rules, utilitarian rules and Condorcet rules. We find that the utilitarian rules provide relatively high UEW and UEL, but low Rep and RS. Conversely, the plurality rules provide high Rep and RS, but low UEW and UEL. Finally, the Condorcet rules provide high UEW, high RS, and a combination of UEL and Rep that depends which Condorcet rule is used. JEL Classification Codes: D71, D72 Keywords: Runoff election, two-round system, Condorcet, Hare, Borda, approval voting, single transferable vote, CPO-STV. We are grateful to those who commented on an earlier draft of this paper at the 2018 Public Choice Society conference. 2 1. Introduction Voting theory is concerned primarily with evaluating rules for choosing a single winner, based on a single round of voting. -
10. Dalton Et Al. Pp.124-38.Pmd
ADVANCED DEMOCRACIES AND THE NEW POLITICS Russell J. Dalton, Susan E. Scarrow, and Bruce E. Cain Russell J. Dalton is director of the Center for the Study of Democracy at the University of California, Irvine. Susan E. Scarrow is associate professor of political science at the University of Houston. Bruce E. Cain is Robson Professor of Political Science at the University of California, Berkeley, and director of the Institute of Governmental Studies. This essay is adapted from their edited volume, Democracy Transformed? Expanding Political Opportunities in Advanced Indus- trial Democracies (2003). Over the past quarter-century in advanced industrial democracies, citi- zens, public interest groups, and political elites have shown decreasing confidence in the institutions and processes of representative govern- ment. In most of these nations, electoral turnout and party membership have declined, and citizens are increasingly skeptical of politicians and political institutions.1 Along with these trends often go louder demands to expand citizen and interest-group access to politics, and to restructure democratic deci- sion-making processes. Fewer people may be voting, but more are signing petitions, joining lobby groups, and engaging in unconventional forms of political action.2 Referenda and ballot initiatives are growing in popu- larity; there is growing interest in processes of deliberative or consultative democracy;3 and there are regular calls for more reliance on citizen advi- sory committees for policy formation and administration—especially at the local level, where direct involvement is most feasible. Contempo- rary democracies are facing popular pressures to grant more access, increase the transparency of governance, and make government more accountable. -
Chapter 3 Voting Systems
Chapter 3 Voting Systems 3.1 Introduction We rank everything. We rank movies, bands, songs, racing cars, politicians, professors, sports teams, the plays of the day. We want to know “who’s number one?” and who isn't. As a lo- cal sports writer put it, “Rankings don't mean anything. Coaches continually stress that fact. They're right, of course, but nobody listens. You know why, don't you? People love polls. They absolutely love ’em” (Woodling, December 24, 2004, p. 3C). Some rankings are just for fun, but people at the top sometimes stand to make a lot of money. A study of films released in the late 1970s and 1980s found that, if a film is one of the 5 finalists for the Best Picture Oscar at the Academy Awards, the publicity generated (on average) generates about $5.5 mil- lion in additional box office revenue. Winners make, on average, $14.7 million in additional revenue (Nelson et al., 2001). In today's inflated dollars, the figures would no doubt be higher. Actors and directors who are nominated (and who win) should expect to reap rewards as well, since the producers of new films are eager to hire Oscar-winners. This chapter is about the procedures that are used to decide who wins and who loses. De- veloping a ranking can be a tricky business. Political scientists have, for centuries, wrestled with the problem of collecting votes and moulding an overall ranking. To the surprise of un- 1 CHAPTER 3. VOTING SYSTEMS 2 dergraduate students in both mathematics and political science, mathematical concepts are at the forefront in the political analysis of voting procedures. -
Minimax Is the Best Electoral System After All
1 Minimax Is the Best Electoral System After All Richard B. Darlington Department of Psychology, Cornell University Abstract When each voter rates or ranks several candidates for a single office, a strong Condorcet winner (SCW) is one who beats all others in two-way races. Among 21 electoral systems examined, 18 will sometimes make candidate X the winner even if thousands of voters would need to change their votes to make X a SCW while another candidate Y could become a SCW with only one such change. Analysis supports the intuitive conclusion that these 18 systems are unacceptable. The well-known minimax system survives this test. It fails 10 others, but there are good reasons to ignore all 10. Minimax-T adds a new tie-breaker. It surpasses competing systems on a combination of simplicity, transparency, voter privacy, input flexibility, resistance to strategic voting, and rarity of ties. It allows write-ins, machine counting except for write-ins, voters who don’t rate or rank every candidate, and tied ratings or ranks. Eleven computer simulation studies used 6 different definitions (one at a time) of the “best” candidate, and found that minimax-T always soundly beat all other tested systems at picking that candidate. A new maximum-likelihood electoral system named CMO is the theoretically optimum system under reasonable conditions, but is too complex for use in real-world elections. In computer simulations, minimax and minimax-T nearly always pick the same winners as CMO. Comments invited [email protected] Copyright Richard B. Darlington May be distributed free for non-commercial purposes 2 1. -
Political Institutions and Their Effect on Democracy in the Dominican Republic
CORE Metadata, citation and similar papers at core.ac.uk Provided by NORA - Norwegian Open Research Archives Political institutions and their effect on democracy in the Dominican Republic -A critical assessment Leiv Marsteintredet Thesis Submitted for the Degree Candidatus Rerum Politicarum February 2004 The University of Bergen Department of Comparative Politics To Dixie Acknowledgments At the Department of Comparative Politics, I must thank my supervisor Einar Berntzen. His comments, critique, keen eye for details and advices have constantly pushed me forward in writing and improving this thesis. I must also thank Einar for opening my eyes for conceptual issues, and especially for making me look into the details of radial concepts. Mike Alvarez also deserves mentioning. His positive comments gave me the necessary confidence when Einar was far away, and his tips on relevant literature have been an important contribution. Financially, I should thank the Meltzer foundation for financing my research trip to the Dominican Republic. In particular I want to thank my parents (and the rest of the family in Ulvik and Oslo), without my parents’ support and extra funding, this project would not have been possible to finish. I also want to thank my family for their general support throughout my years at the University. Thank you for never doubting me. In the Dominican Republic, Jacqueline Jiménez Polanco was of tremendous help. She helped me understand the inner life and thoughts of the political parties in the Dominican Republic. I also appreciate the help I got from Carlos Pimentel at OECI. I also should thank all my friends in the Dominican Republic for not getting tired of my eternal need to discuss politics when I had taken a couple of Presidentes too many. -
Which Voting System Is Best for Canada?
Electoral Reform: Which Voting System is Best For Canada? By David Piepgrass While watching the election coverage last Monday night, I was disconcerted by claims from party leaders and even journalists, suggesting that Canadians had “asked” for various things by their voting: “Canadians have asked our party to take the lead” “Canadians have selected a new government.” “Although Canadians have voted for change, they have not given any one party a majority in the House of Commons. They have asked us to cooperate, to work together, and to get on with tackling the real issues that matter to ordinary working people and their families.” - Stephen Harper “Canadians have asked the Conservatives to form a government – in a minority Parliament” “while the people of Canada asked Mr. Harper to form a minority government, the people of Canada also asked New Democrats to balance that government...” - Jack Layton But I voted in the election, and guess what I didn't see on the ballot? I wonder what they based their statements on. Votes vs. Seats (Federal Election 2006) Probably, it was either the popular vote or the Conservatives makeup of the government, but isn't it odd that the Liberals two are different? You can see the dichotomy NDP Percent of vote between the popular vote and the seat allocation Bloc Percent of on the right. It looks like the NDP and Bloc have Other seats somehow confused each other's seats, but actually, 0 5 10 15 20 25 30 35 40 45 as Canadian elections go, this one isn't too bad.