Computational Aspects of Multi-Winner Approval Voting

We study computational aspects of three prominent voting rules that use approval ballots to elect multiple winners. These rules are satisfaction approval voting, proportional approval voting, and reweighted approval voting. We first show that computing the winner for proportional approval voting is NP-hard, closing a long standing open problem. As none of the rules are strategyproof, even for dichotomous preferences, we study various strategic aspects of the rules. In particular, we examine the computational complexity of computing a best response for both a single agent and a group of agents. In many settings, we show that it is NP-hard for an agent or agents to compute how best to vote given a fixed set of approval ballots from the other agents

Parameterized Complexity of Multi-winner Determination: More Effort Towards Fixed-Parameter Tractability

We study the parameterized complexity of Winners Determination for three prevalent $k$-committee selection rules, namely the minimax approval voting (MAV), the proportional approval voting (PAV), and the Chamberlin-Courant's approval voting (CCAV). It is known that Winners Determination for these rules is NP-hard. Moreover, these problems have been studied from the parameterized complexity point of view with respect to some natural parameters recently. However, many results turned out to be W[1]-hard or W[2]-hard. Aiming at deriving more fixed-parameter algorithms, we revisit these problems by considering more natural and important single parameters, combined parameters, and structural parameters.Comment: 31 pages, 2 figures, AAMAS 201

Finding a Collective Set of Items: From Proportional Multirepresentation to Group Recommendation

We consider the following problem: There is a set of items (e.g., movies) and a group of agents (e.g., passengers on a plane); each agent has some intrinsic utility for each of the items. Our goal is to pick a set of $K$ items that maximize the total derived utility of all the agents (i.e., in our example we are to pick $K$ movies that we put on the plane's entertainment system). However, the actual utility that an agent derives from a given item is only a fraction of its intrinsic one, and this fraction depends on how the agent ranks the item among the chosen, available, ones. We provide a formal specification of the model and provide concrete examples and settings where it is applicable. We show that the problem is hard in general, but we show a number of tractability results for its natural special cases

Multi-Winner Voting with Approval Preferences

Approval-based committee (ABC) rules are voting rules that output a fixed-size subset of candidates, a so-called committee. ABC rules select committees based on dichotomous preferences, i.e., a voter either approves or disapproves a candidate. This simple type of preferences makes ABC rules widely suitable for practical use. In this book, we summarize the current understanding of ABC rules from the viewpoint of computational social choice. The main focus is on axiomatic analysis, algorithmic results, and relevant applications.Comment: This is a draft of the upcoming book "Multi-Winner Voting with Approval Preferences

Multi-Winner Voting with Approval Preferences

From fundamental concepts and results to recent advances in computational social choice, this open access book provides a thorough and in-depth look at multi-winner voting based on approval preferences. The main focus is on axiomatic analysis, algorithmic results and several applications that are relevant in artificial intelligence, computer science and elections of any kind. What is the best way to select a set of candidates for a shortlist, for an executive committee, or for product recommendations? Multi-winner voting is the process of selecting a fixed-size set of candidates based on the preferences expressed by the voters. A wide variety of decision processes in settings ranging from politics (parliamentary elections) to the design of modern computer applications (collaborative filtering, dynamic Q&A platforms, diversity in search results, etc.) share the problem of identifying a representative subset of alternatives. The study of multi-winner voting provides the principled analysis of this task. Approval-based committee voting rules (in short: ABC rules) are multi-winner voting rules particularly suitable for practical use. Their usability is founded on the straightforward form in which the voters can express preferences: voters simply have to differentiate between approved and disapproved candidates. Proposals for ABC rules are numerous, some dating back to the late 19th century while others have been introduced only very recently. This book explains and discusses these rules, highlighting their individual strengths and weaknesses. With the help of this book, the reader will be able to choose a suitable ABC voting rule in a principled fashion, participate in, and be up to date with the ongoing research on this topic

Complexity of Manipulating and Controlling Approval-Based Multiwinner Voting

We investigate the complexity of several manipulation and control problems under numerous prevalent approval-based multiwinner voting rules. Particularly, the rules we study include approval voting (AV), satisfaction approval voting (SAV), net-satisfaction approval voting (NSAV), proportional approval voting (PAV), approval-based Chamberlin-Courant voting (ABCCV), minimax approval voting (MAV), etc. We show that these rules generally resist the strategic types scrutinized in the paper, with only a few exceptions. In addition, we also obtain many fixed-parameter tractability results for these problems with respect to several natural parameters, and derive polynomial-time algorithms for certain special cases.Comment: 45pages, 1figure, full version of a paper at IJCAI 201

Structure in Dichotomous Preferences

Many hard computational social choice problems are known to become tractable when voters' preferences belong to a restricted domain, such as those of single-peaked or single-crossing preferences. However, to date, all algorithmic results of this type have been obtained for the setting where each voter's preference list is a total order of candidates. The goal of this paper is to extend this line of research to the setting where voters' preferences are dichotomous, i.e., each voter approves a subset of candidates and disapproves the remaining candidates. We propose several analogues of the notions of single-peaked and single-crossing preferences for dichotomous profiles and investigate the relationships among them. We then demonstrate that for some of these notions the respective restricted domains admit efficient algorithms for computationally hard approval-based multi-winner rules.Comment: A preliminary version appeared in the proceedings of IJCAI 2015, the International Joint Conference on Artificial Intelligenc

Voting Rules for Expressing Conditional Preferences in Multiwinner Elections

Ο τομέας της Υπολογιστικής Θεωρίας Κοινωνικής Επιλογής μελετά, από αλγοριθμική σκοπιά, την αποτίμηση των προσωπικών προτιμήσεων προς μια συλλογική απόφαση. Πληθώρα προβλημάτων σε πολυπρακτορικά συστήματα, τεχνολογίες λήψης αποφάσεων, σχεδιασμό δικτύων, πολιτικό σχεδιασμό, συστήματα συστάσεων και άλλα, απαιτούν το σχεδιασμό και τη θεωρητική αξιολόγηση κανόνων ψηφοφορίας. Στο πρώτο κεφάλαιο παρουσιάζουμε την προέλευση, ορισμένες εφαρμογές και υποπεριοχές μαζί με μία ιστορική επισκόπηση του αντικειμένου. Στο δεύτερο κεφάλαιο, εισάγουμε τον αναγνώστη σε εκλογικά σενάρια με περισσότερους από έναν νικητές, περιγράφοντας κάποιες επιθυμητές ιδιότητες των σχετικών κανόνων ψηφοφοριών και ορίζοντας τους πιο συχνά χρησιμοποιούμενους κανόνες μαζί με μία ματιά στα γνωστά αλγοριθμικά και υπολογιστικά τους αποτελέσματα. Μιας και σε πολλές περιπτώσεις, οι ψηφοφόροι επιθυμούν να τους επιτραπεί να εκφράσουν εξαρτήσεις μεταξύ των θεμάτων, όταν καλούνται να αποφασίσουν για περισσότερα από ένα θέματα, στο τρίτο κεφάλαιο εστιάζουμε σε εκλογές συνδυαστικής φύσεως, παρουσιάζοντας ορισμένες σχετικές εφαρμογές μαζί με λύσεις που έχουν προταθεί για την αντιμετώπιση αυτών των περιστάσεων. Τέλος, στο τέταρτο κεφάλαιο, περιγράφουμε ένα μοντέλο για χειρισμό ψήφων αποδοχής υπό συνθήκες σε πολλαπλά δυαδικά ζητήματα, ακολουθούμενο από ορισμένα νέα αποτελέσματα που αφορούν κυρίως βέλτιστους και προσεγγιστικούς αλγορίθμους για τον minisum και τον minimax κανόνα.Computational Social Choice studies the aggregation of individual preferences toward a collective decision from an algorithmic point of view. Various problems in multiagent systems, decision making technologies, network design, 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 properties 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. Ultimately, 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 results for minisum and minimax conditional approval voting rule