DOCSLIB.ORG

Proportionality and Strategyproofness in Multiwinner Elections

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Proportionality and Strategyproofness in Multiwinner Elections Proportionality and Strategyproofness in Multiwinner Elections Dominik Peters University of Oxford Oxford, UK [email protected] ABSTRACT for applications in areas outside the political sphere, such as in Multiwinner voting rules can be used to select a fixed-size com- group recommendation systems. mittee from a larger set of candidates. We consider approval-based To formalise the requirement of proportionality in this party-free committee rules, which allow voters to approve or disapprove can- setting, it is convenient to consider the case where input preferences didates. In this setting, several voting rules such as Proportional are given as approval ballots: each voter reports a set of candidates Approval Voting (PAV) and Phragmén’s rules have been shown to that they find acceptable. Even for this simple setting, there isa produce committees that are proportional, in the sense that they rich variety of rules that exhibit different behaviour [31], and this proportionally represent voters’ preferences; all of these rules are setting gives rise to a rich variety of axioms. strategically manipulable by voters. On the other hand, a generalisa- One natural way of selecting a committee of : candidates when tion of Approval Voting gives a non-proportional but strategyproof given approval ballots is to extend Approval Voting (AV): for each voting rule. We show that there is a fundamental tradeoff between of the < candidates, count how many voters approve them (their these two properties: we prove that no multiwinner voting rule can approval score), and then return the committee consisting of the : simultaneously satisfy a weak form of proportionality (a weakening candidates whose approval score is highest. Notably, this rule can of justified representation) and a weak form of strategyproofness. produce committees that fail to represent large groups of voters. Our impossibility is obtained using a formulation of the problem Consider, for example, an instance where : = 3, and where 5 voters in propositional logic and applying SAT solvers; a human-readable approve candidates 0, 1 and 2, while 4 other voters approve only the version of the computer-generated proof is obtained by extracting candidate 3. Then AV would select the committee f0,1, 2g, leaving a minimal unsatisfiable set (MUS). We also discuss several related almost half of the electorate unrepresented. Intuitively, the latter axiomatic questions in the domain of committee elections. group of 4 voters, consisting of more than a third of the electorate, should be represented by at least 1 of the 3 committee members. KEYWORDS Aziz et al. [3] introduce an axiom called justified representation (JR) which formalises this intuition that a group of =/: voters should computational social choice; multiwinner elections; proportionality; not be left without any representation; a stronger version of this strategyproofness; computer-aided methods; SAT solving axiom called proportional justified representation (PJR) has also been introduced and studied [39]. While AV fails these axioms, there Note. [September 2020] This version is a slight revision of the are appealing rules which satisfy them. An example is Proportional paper that appeared in the conference proceedings. The conference Approval Voting (PAV), first proposed by Thiele [46]. The intuition version contained a gap in the proof of Lemma 5.5. To fix this gap, it behind this rule is that voters prefer committees which contain was necessary to introduce an additional axiom, weak efficiency, to more of their approved candidates, but that there are decreasing the impossibility theorems; see Section 3.3. I thank Boas Kluiving, marginal returns; specifically, let us presume that voters gain 1 ‘util’ 1 Adriaan de Vries, Pepijn Vrijbergen for pointing out the error. in committees that contain exactly 1 approved candidates, 1¸ 2 utils 1 1 with 2 approved candidates, and in general 1 ¸ 2 ¸ · · · ¸ A utils with 1 INTRODUCTION A approved candidates. PAV returns the committee that maximises The theory of multiwinner elections is concerned with designing utilitarian social welfare with this choice of utility function. PAV and analysing procedures that, given preference information from satisfies a strong form of justified representation [3]. arXiv:2104.08594v1 [cs.GT] 17 Apr 2021 a collection of voters, select a fixed-size committee consisting of : When voters are strategic, PAV has the drawback that it can often members, drawn from a larger set of < candidates. Often, we will be manipulated. Indeed, suppose a voter 8 approves candidates 0 be interested in picking a representative committee whose members and 1. If 0 is also approved by many other voters, PAV is likely to together cover the diverse interests of the voters. We may also aim include 0 in its selected committee anyway, but it might not include for this representation to be proportional; for example, if a group 1 because voter 8 is already happy enough due to the inclusion of 0. of 20% of the voters have similar interests, then about 20% of the However, if voter 8 pretends not to approve 0, then it may be utility- members of the committee should represent those voters’ interests. maximising for PAV to include both 0 and 1, so that 8 successfully Historically, much work in mathematical social science has tried manipulated the election.∗ Besides PAV, there exist several other to formalise the latter type of proportionality requirement, in the proportional rules, such as rules proposed by Phragmén [14, 30], form of finding solutions to the apportionment problem, which arises but all of them can be manipulated using a similar strategy. in settings where voters express preferences over parties which are comprised of many candidates [5]. More recently, theorists have ∗For a specific example, consider % = ¹012,012,012,013,013º for which 012 is the focussed on cases where there are no parties, and preferences are unique PAV-committee for : = 3. If the last voter instead reports to approve 3 only, expressed directly over the candidates [23]. The latter setting allows then the unique PAV-committee is 013. , Dominik Peters That voting rules are manipulable is very familiar to voting 퐴8 of 퐶, so that ; < 퐴8 ( 퐶; let B denote the set of all ballots. For theorists; indeed the Gibbard–Satterthwaite theorem shows that brevity, when writing ballots, we often omit braces and commas, so for single-winner voting rules and strict preferences, every non- that the ballot f0,1g is written 01. An (approval) profile is a function trivial voting rule is manipulable. However, in the approval-based % : # !B assigning every voter an approval ballot. For brevity, multiwinner election setting, we have the tantalising example of we write a profile % as an =-tuple, so that % = ¹% ¹1º,...,% ¹=ºº. For Approval Voting (AV): this rule is strategyproof in the sense that example, in the profile ¹01, 012,3º, voter 1 approves candidates 0 voters cannot induce AV to return a committee including more and 1, voter 2 approves 0, 1, and 2, and voter 3 approves 3 only. approved candidates by misrepresenting their approval set. This Let : be a fixed integer with 1 6 : 6 <.A committee is a subset raises the natural question of whether there exist committee rules of 퐶 of cardinality :. We write C: for the set of committees, and that combine the benefits of AV and PAV: are there rules that are again for brevity, the committee f0,1g is written as 01. An (approval- # simultaneously proportional and strategyproof? based) committee rule is a function 5 : B !C: , assigning to The contribution of this paper is to show that these two demands each approval profile a unique winning committee. Note that this are incompatible. No approval-based multiwinner rule satisfies both definition assumes that 5 is resolute, so that for every possible requirements. This impossibility holds even for very weak versions profile, it returns exactly one committee. In our proofs, wewill Ð of proportionality and of strategyproofness. The version of propor- implicitly restrict the domain of 5 to profiles % with j 8 2# % ¹8ºj > tionality we use is much weaker than JR. It requires that if there is :, so that it is possible to fill the committee with candidates who a group of at least =/: voters who all approve a certain candidate 2, are each approved by at least one voter. Since we are aiming for and none of them approve any other candidate, and no other voters a negative result, this domain restriction only makes the result approve 2, then 2 should be part of the committee. Strategyproof- stronger. ness requires that a voter cannot manipulate the committee rule Let us define two specific committee rules which will be useful by dropping candidates from their approval ballot; a manipulation examples throughout. would be deemed successful if the voter ends up with a committee Approval Voting (AV) is the rule that selects the : candidates that contains additional approved candidates. In particular, our no- with highest approval score, that is, the : candidates 2 for which tion of strategyproofness only requires that the committee rule be jf8 2 # : 2 2 % ¹8ºgj is highest. Ties are broken lexicographically. robust to dropping candidates; we do not require robustness against Proportional Approval Voting (PAV) is the rule that returns the arbitrary manipulations that both add and remove candidates. Ad- set , ⊆ 퐶 with j, j = : which maximises ditionally, we impose a mild efficiency axiom requiring that the ∑︁ 1 1 rule not elect candidates who are approved by none of the voters. 1 ¸ ¸ · · · ¸ . 2 j% ¹8º \ , j The impossibility theorem is obtained using computer-aided 8 2# techniques that have recently found success in many areas of social choice theory [27]. We encode the problem of finding a committee In case of ties, PAV returns the lexicographically first optimum. rule satisfying our axioms into propositional logic, and then use Other important examples that we occasionally mention are a SAT solver to check whether the formula is satisfiable.
Load more

Recommended publications
  • California Institute of Technology
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Caltech Authors - Main DIVISION OF THE HUM ANITIES AND SO CI AL SCIENCES CALIFORNIA INSTITUTE OF TECHNOLOGY PASADENA, CALIFORNIA 91125 IMPLEMENTATION THEORY Thomas R. Palfrey � < a: 0 1891 u. "')/,.. () SOCIAL SCIENCE WORKING PAPER 912 September 1995 Implementation Theory Thomas R. Palfrey Abstract This surveys the branch of implementation theory initiated by Maskin (1977). Results for both complete and incomplete information environments are covered. JEL classification numbers: 025, 026 Key words: Implementation Theory, Mechanism Design, Game Theory, Social Choice Implementation Theory* Thomas R. Palfrey 1 Introduction Implementation theory is an area of research in economic theory that rigorously investi­ gates the correspondence between normative goals and institutions designed to achieve {implement) those goals. More precisely, given a normative goal or welfare criterion for a particular class of allocation pro blems (or domain of environments) it formally char­ acterizes organizational mechanisms that will guarantee outcomes consistent with that goal, assuming the outcomes of any such mechanism arise from some specification of equilibrium behavior. The approaches to this problem to date lie in the general domain of game theory because, as a matter of definition in the implementation theory litera­ ture, an institution is modelled as a mechanism, which is essentially a non-cooperative game. Moreover, the specific models of equilibrium behavior
    [Show full text]
  • Game Theory 2021
    More Mechanism Design Game Theory 2021 Game Theory 2021 Ulle Endriss Institute for Logic, Language and Computation University of Amsterdam Ulle Endriss 1 More Mechanism Design Game Theory 2021 Plan for Today In this second lecture on mechanism design we are going to generalise beyond the basic scenario of auctions|as much as we can manage: • Revelation Principle: can focus on direct-revelation mechanisms • formal model of direct-revelation mechanisms with money • incentive compatibility of the Vickrey-Clarke-Groves mechanism • other properties of VCG for special case of combinatorial auctions • impossibility of achieving incentive compatibility more generally Much of this is also (somewhat differently) covered by Nisan (2007). N. Nisan. Introduction to Mechanism Design (for Computer Scientists). In N. Nisan et al. (eds.), Algorithmic Game Theory. Cambridge University Press, 2007. Ulle Endriss 2 More Mechanism Design Game Theory 2021 Reminder Last time we saw four auction mechanisms for selling a single item: English, Dutch, first-price sealed-bid, Vickrey. The Vickrey auction was particularly interesting: • each bidder submits a bid in a sealed envelope • the bidder with the highest bid wins, but pays the price of the second highest bid (unless it's below the reservation price) It is a direct-revelation mechanism (unlike English and Dutch auctions) and it is incentive-compatible, i.e., truth-telling is a dominant strategy (unlike for Dutch and FPSB auctions). Ulle Endriss 3 More Mechanism Design Game Theory 2021 The Revelation Principle Revelation Principle: Any outcome that is implementable in dominant strategies via some mechanism can also be implemented by means of a direct-revelation mechanism making truth-telling a dominant strategy.
    [Show full text]
  • Designing Mechanisms to Make Welfare- Improving Strategies Focal∗
    Designing Mechanisms to Make Welfare- Improving Strategies Focal∗ Daniel E. Fragiadakis Peter Troyan Texas A&M University University of Virginia Abstract Many institutions use matching algorithms to make assignments. Examples include the allocation of doctors, students and military cadets to hospitals, schools and branches, respec- tively. Most of the market design literature either imposes strong incentive constraints (such as strategyproofness) or builds mechanisms that, while more efficient than strongly incentive compatible alternatives, require agents to play potentially complex equilibria for the efficiency gains to be realized in practice. Understanding that the effectiveness of welfare-improving strategies relies on the ease with which real-world participants can find them, we carefully design an algorithm that we hypothesize will make such strategies focal. Using a lab experiment, we show that agents do indeed play the intended focal strategies, and doing so yields higher overall welfare than a common alternative mechanism that gives agents dominant strategies of stating their preferences truthfully. Furthermore, we test a mech- anism from the field that is similar to ours and find that while both yield comparable levels of average welfare, our algorithm performs significantly better on an individual level. Thus, we show that, if done carefully, this type of behavioral market design is a worthy endeavor that can most promisingly be pursued by a collaboration between institutions, matching theorists, and behavioral and experimental economists. JEL Classification: C78, C91, C92, D61, D63, Keywords: dictatorship, indifference, matching, welfare, efficiency, experiments ∗We are deeply indebted to our graduate school advisors Fuhito Kojima, Muriel Niederle and Al Roth for count- less conversations and encouragement while advising us on this project.
    [Show full text]
  • 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.
    [Show full text]
  • Strategyproof Exchange with Multiple Private Endowments
    Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence Strategyproof Exchange with Multiple Private Endowments Taiki Todo, Haixin Sun, Makoto Yokoo Dept. of Informatics Kyushu University Motooka 744, Fukuoka, JAPAN ftodo, sunhaixin, [email protected] Abstract efficient and individually rational. Moreover, it is the only We study a mechanism design problem for exchange rule that satisfies those three properties (Ma 1994). Due to economies where each agent is initially endowed with these advantages, TTC has been attracting much attention a set of indivisible goods and side payments are not al- from both economists and computer scientists. lowed. We assume each agent can withhold some en- In this paper we consider exchange economies where each dowments, as well as misreport her preference. Under this assumption, strategyproofness requires that for each agent is endowed with a set of multiple goods, instead of agent, reporting her true preference with revealing all a single good. Under that model, Pareto efficiency, indi- her endowments is a dominant strategy, and thus implies vidual rationality, and strategyproofness cannot be simulta- individual rationality. Our objective in this paper is to neously satisfied (Sonmez¨ 1999). Therefore, one main re- analyze the effect of such private ownership in exchange search direction on exchanges with multiple endowments is economies with multiple endowments. As fundamental to achieve strategyproof rules that guarantee a limited notion results, we first show that the revelation principle holds of efficiency. In particular, Papai´ (2003) defined a class of under a natural assumption and that strategyproofness exchange rules and gave a characterization by strategyproof- and Pareto efficiency are incompatible even under the ness and individual rationality with some other weak effi- lexicographic preference domain.
    [Show full text]
  • Proportionality and Strategyproofness in Multiwinner Elections
    Session 43: Social Choice Theory 3 AAMAS 2018, July 10-15, 2018, Stockholm, Sweden Proportionality and Strategyproofness in Multiwinner Elections Dominik Peters University of Oxford Oxford, UK [email protected] ABSTRACT focussed on cases where there are no parties, and preferences are Multiwinner voting rules can be used to select a fixed-size com- expressed directly over the candidates [23]. The latter setting allows mittee from a larger set of candidates. We consider approval-based for applications in areas outside the political sphere, such as in committee rules, which allow voters to approve or disapprove can- group recommendation systems. didates. In this setting, several voting rules such as Proportional To formalise the requirement of proportionality in this party-free Approval Voting (PAV) and Phragmén’s rules have been shown to setting, it is convenient to consider the case where input preferences produce committees that are proportional, in the sense that they are given as approval ballots: each voter reports a set of candidates proportionally represent voters’ preferences; all of these rules are that they find acceptable. Even for this simple setting, there isa strategically manipulable by voters. On the other hand, a generalisa- rich variety of rules that exhibit different behaviour [31], and this tion of Approval Voting gives a non-proportional but strategyproof setting gives rise to a rich variety of axioms. voting rule. We show that there is a fundamental tradeoff between One natural way of selecting a committee of k candidates when these two properties: we prove that no multiwinner voting rule can given approval ballots is to extend Approval Voting (AV): for each simultaneously satisfy a weak form of proportionality (a weakening of the m candidates, count how many voters approve them (their of justified representation) and a weak form of strategyproofness.
    [Show full text]
  • Utilitarian Welfare and Representation Guarantees of Approval-Based Multiwinner Rules
    Utilitarian Welfare and Representation Guarantees of Approval-Based Multiwinner Rules Martin Lackner Piotr Skowron TU Wien University of Warsaw Vienna, Austria Warsaw, Poland [email protected] [email protected] Abstract To choose a suitable multiwinner voting rule is a hard and ambiguous task. Depending on the context, it varies widely what constitutes the choice of an “optimal” subset of alternatives. In this paper, we provide a quantitative analysis of multiwinner voting rules using methods from the theory of approximation algorithms—we estimate how well multiwinner rules approximate two extreme objectives: a representation criterion defined via the Approval Chamberlin–Courant rule and a utilitarian criterion defined via Multiwinner Approval Voting. With both theoretical and experimental methods, we classify multiwinner rules in terms of their quantitative alignment with these two opposing objectives. Our results provide fundamental information about the nature of multiwinner rules and, in particular, about the necessary tradeoffs when choosing such a rule. 1 Introduction A multiwinner rule is a voting method for selecting a fixed-size subset of alternatives, a so-called committee. More formally, it is a function that—given (i) a set of candidates, (ii) preferences of a population of voters over these candidates, and (iii) an integer k—returns a subset of exactly k candidates. Multiwinner rules are applicable to problems from and beyond the political arXiv:1801.01527v4 [cs.MA] 31 Aug 2020 domain, for instance for selecting a representative body such as a parliament or university senate [Chamberlin and Courant, 1983, Faliszewski et al., 2017], shortlisting candidates (e.g., in a competition) [Barbera` and Coelho, 2008], designing search engines [Dwork et al., 2001, Skowron et al., 2017], building recommender systems [Skowron et al., 2016], and as mechanisms for locating facilities [Feldman et al., 2016].
    [Show full text]
  • Relaxing Strategyproofness in One-Sided Matching
    Relaxing Strategyproofness in One-sided Matching TIMO MENNLE and SVEN SEUKEN University of Zurich We consider the one-sided matching problem, where agents must be matched to indivisible ob- jects. Our first result is a novel characterization of strategyproof mechanisms by three intuitive axioms. Furthermore, we introduce partial strategyproofness, a new relaxation of strategyproof- ness that bridges the gap between full and weak strategyproofness. Partial strategyproofness finds application in the incentive analysis of non-strategyproof mechanisms, such as Probabilistic Serial, different variants of the Boston mechanism, and hybrid mechanisms. In this letter, we summarize the main results from [Mennle and Seuken 2014a] and demonstrate how they can be used for the design and analysis of matching mechanisms.1 Categories and Subject Descriptors: J.4.a [Social and Behavioral Sciences]: Economics General Terms: Economics; Theory Additional Key Words and Phrases: Matching, Mechanism Design, Strategyproofness 1. INTRODUCTION The (probabilistic) one-sided matching problem is concerned with the allocation of indivisible goods to self-interested agents with privately known preferences in domains where monetary transfers are not permitted. Such problems often arise in situations that are of great importance to peoples' lives. For example, students must be matched to schools, teachers to training programs, or tenants to houses. Strategyproof mechanisms, such as Random Serial Dictatorship (RSD), are ap- pealing because they make truthful reporting a dominant strategy for all agents. Participation in the mechanism becomes an easy task as there is no need for delib- eration about the best response, thus reducing cognitive costs for the agents and (likely) endowing the mechanism with correct information about agents' preferences.
    [Show full text]
  • Specification Faithfulness in Networks with Rational Nodes
    Specification Faithfulness in Networks with Rational Nodes Jeffrey Shneidman, David C. Parkes Division of Engineering and Applied Sciences, Harvard University, 33 Oxford Street, Cambridge MA 02138 {jeffsh, parkes}@eecs.harvard.edu ABSTRACT drive up their “contributed computation” credit [15]. There It is useful to prove that an implementation correctly follows is interesting work documenting the “free rider” problem [1] a specification. But even with a provably correct implemen- and the “tragedy of the commons” [12] in a data centric peer tation, given a choice, would a node choose to follow it? This to peer setting. paper explores how to create distributed system specifica- This behavior can be classified as a type of failure, which tions that will be faithfully implemented in networks with should stand independently from other types of failures in rational nodes, so that no node will choose to deviate. Given distributed systems and is indicative of an underlying in- a strategyproof centralized mechanism, and given a network centive problem in a system’s design when run on a network of nodes modeled as having rational-manipulation faults, with rational nodes. Whereas traditional failure models are we provide a proof technique to establish the incentive-, overcome by relying on redundancy, rational manipulation communication-, and algorithm-compatibility properties that can also be overcome with design techniques such as prob- guarantee that participating nodes are faithful to a sug- lem partitioning, catch-and-punish, and incentives. In such gested specification. As a case study, we apply our methods a network one can state a strong claim about the faithfulness to extend the strategyproof interdomain routing mechanism of each node’s implementation.
    [Show full text]
  • Approximate Strategyproofness
    Approximate Strategyproofness The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Benjamin Lubin and David C. Parkes. 2012. Approximate strategyproofness. Current Science 103, no. 9: 1021-1032. Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:11879945 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#OAP Approximate Strategyproofness Benjamin Lubin David C. Parkes School of Management School of Engineering and Applied Sciences Boston University Harvard University [email protected] [email protected] July 24, 2012 Abstract The standard approach of mechanism design theory insists on equilibrium behavior by par- ticipants. This assumption is captured by imposing incentive constraints on the design space. But in bridging from theory to practice, it often becomes necessary to relax incentive constraints in order to allow tradeo↵s with other desirable properties. This paper surveys a number of dif- ferent options that can be adopted in relaxing incentive constraints, providing a current view of the state-of-the-art. 1 Introduction Mechanism design theory formally characterizes institutions for the purpose of establishing rules that engender desirable outcomes in settings with multiple, self-interested agents each with private information about their preferences. In the context of mechanism design, an institution is formalized as a framework wherein messages are received from agents and outcomes selected on the basis of these messages.
    [Show full text]
  • Proportionality and Strategyproofness in Multiwinner Elections
    Proportionality and Strategyproofness in Multiwinner Elections Dominik Peters Abstract Multiwinner voting rules can be used to select a fixed-size committee from a larger set of candidates. We consider approval-based committee rules, which allow vot- ers to approve or disapprove candidates. In this setting, several voting rules such as Proportional Approval Voting (PAV) and Phragm´en'srules have been shown to produce committees that are proportional, in the sense that they proportionally rep- resent voters' preferences; all of these rules are strategically manipulable by voters. On the other hand, a generalisation of Approval Voting gives a non-proportional but strategyproof voting rule. We show that there is a fundamental tradeoff between these two properties: we prove that no multiwinner voting rule can simultaneously satisfy a weak form of proportionality (a weakening of justified representation) and a weak form of strategyproofness. Our impossibility is obtained using a formulation of the problem in propositional logic and applying SAT solvers; a human-readable version of the computer-generated proof is obtained by extracting a minimal unsat- isfiable set (MUS). We also discuss several related axiomatic questions in the domain of committee elections. 1 Introduction The theory of multiwinner elections is concerned with designing and analysing procedures that, given preference information from a collection of voters, select a fixed-size committee consisting of k members, drawn from a larger set of m candidates. Often, we will be interested in picking a representative committee whose members together cover the diverse interests of the voters. We may also aim for this representation to be proportional; for example, if a group of 20% of the voters have similar interests, then about 20% of the members of the committee should represent those voters' interests.
    [Show full text]
  • Voting Rules for Expressing Conditional Preferences in Multiwinner Elections
    Voting Rules for Expressing Conditional Preferences in Multiwinner Elections Papasotiropoulos Giorgos A.0020 Examination Committee: Fotakis Dimitris, School of Electrical and Computer Engineering, National Technical University of Athens. Leonardos Nikos, Department of Informatics and Telecommunications, co-Supervisors: National and Kapodistrian University of Athens. Markakis Evangelos, asst prof Markakis Evangelos, Pagourtzis Aris, assoc prof Department of Informatics, Athens University of Economics and Business. Pagourtzis Aris, School of Electrical and Computer Engineering, National Technical University of Athens. April, ’19 ABSTRACT Computational Social Choice studies the aggregation of individual prefer- ences toward a collective decision from an algorithmic point of view. Various problems in multiagent systems, decision making technologies, network de- sign, policy making, recommendation systems and so on, require the design and theoretical evaluation of a wide range of voting rules. In the first chapter we present the origins, possible applications, some of the subtopics of Computational Social Choice as well as a historical overview of the field. In the second chapter we introduce the reader to election scenarios with more than a single winner by describing some commonly desired prop- erties of multi-winner voting rules and defining the most widely used rules together with a glance at algorithmic and computational aspects. Since in many voting settings, voters wish to be allowed to express preferential dependencies, in the third chapter we focus on elections on combinatorial domains by presenting some specific applications along with some solutions which have been proposed in order to deal with combinatorial votes. Ulti- mately, in the fourth chapter we describe the recently proposed model for handling conditional approval preferences on multiple binary issues followed by new contributions which mainly concerns optimum and approximate re- sults for minisum and minimax conditional approval voting rule.
    [Show full text]