Approval Voting Research Articles (Page 1)

On the complexity of winner determination and strategic control in conditional approval voting

A variety of constructive manipulation, control, and bribery problems for approval-based multiwinner voting have been extensively studied recently. However, their destructive counterparts seem to be less explored. This paper investigates the complexity of several destructive bribery problems under five prestigious approval-based multiwinner voting rules—approval voting, satisfaction approval voting, net-satisfaction approval voting, Chamberlin-Courant approval voting, and proportional approval voting. Broadly, these problems aim to determine if a number of given candidates can be excluded from any winning committees by performing a limited number of modification operations. We offer a complete landscape of the complexity of the problems. For NP -hard problems, we study their parameterized complexity with respect to meaningful parameters.

We prove that, for any given set of networks satisfying suitable conditions, the net-oudegree network solution, the net-indegree network solution, and the total network solution are the unique network solutions on that set satisfying neutrality, consistency and cancellation. The generality of the result obtained allows to get an analogous result for social choice correspondences: for any given set of preference profiles satisfying suitable conditions, the net-oudegree social choice correspondence, the net-indegree social choice correspondence and the total social choice correspondence are the unique social choice correspondences on that set satisfying neutrality, consistency and cancellation. Using the notable fact that several well-known voting rules coincide with the restriction of the net-outdegree social choice correspondence to appropriate sets of preference profiles, we are able to deduce a variety of new and known characterization theorems for the Borda rule, the Partial Borda rule, the Averaged Borda rule, the Approval Voting, the Plurality rule and the anti-Plurality rule, among which Young’s characterization of the Borda rule and Fishburn’s characterization of the Approval Voting.

In perpetual voting, multiple decisions are made at different moments in time. Taking the history of previous decisions into account allows us to satisfy properties such as proportionality over periods of time. In this paper, we consider the following question: is there a perpetual approval voting method that guarantees that no voter is dissatisfied too many times? We identify a sufficient condition on voter behavior ---which we call 'bounded conflicts' condition---under which a sublinear growth of dissatisfaction is possible. We provide a tight upper bound on the growth of dissatisfaction under bounded conflicts, using techniques from Kolmogorov complexity. We also observe that the approval voting with binary choices mimics the machine learning setting of prediction with expert advice. This allows us to present a voting method with sublinear guarantees on dissatisfaction under bounded conflicts, based on the standard techniques from prediction with expert advice.

Participatory Budgeting (PB) has evolved into a key democratic instrument for resource allocation in cities. Enabled by digital platforms, cities now have the opportunity to let citizens directly propose and vote on urban projects, using different voting input and aggregation rules. However, the choices cities make in terms of the rules of their PB have often not been informed by academic studies on voter behaviour and preferences. Therefore, this work presents the results of behavioural experiments where participants were asked to vote in a fictional PB setting. We identified approaches to designing PB voting that minimise cognitive load and enhance the perceived fairness and legitimacy of the digital process from the citizens’ perspective. In our study, participants preferred voting input formats that are more expressive (like rankings and distributing points) over simpler formats (like approval voting). Participants also indicated a desire for the budget to be fairly distributed across city districts and project categories. Participants found the Method of Equal Shares voting rule to be fairer than the conventional Greedy voting rule. These findings offer actionable insights for digital governance, contributing to the development of fairer and more transparent digital systems and collective decision-making processes for citizens.

In multiwinner approval voting, the goal is to select a k -member committee based on voters’ approval ballots. A well-studied concept of proportionality in this context is the justified representation (JR) axiom, which demands that no large cohesive group of voters remains unrepresented. However, the JR axiom may conflict with other desiderata, such as social welfare (the number of approvals obtained by committee members) or coverage (the number of voters who approve at least one committee member). In this article, we investigate the price of imposing the JR axiom (as well as the more demanding extended justified representation axiom) on social welfare and coverage. Our approach is twofold: We derive worst-case bounds on the loss of welfare/coverage caused by imposing JR and study the computational complexity of finding committees with high welfare that provide JR (obtaining hardness results, approximation algorithms, and an exact algorithm for one-dimensional preferences).

Recent attempts to provide a viable account of decision making under normative uncertainty through the use of voting procedures seem promising, but incomparable options pose a challenge. This paper focuses on the so-called Borda approach to decision making under normative uncertainty (MacAskill, Mind 125(500):967–1004, 2016; MacAskill et al., Moral uncertainty, Oxford University Press, 2020) and illustrates how an extended version of it aimed at accommodating incomplete preference orderings associated with normative theories fails. I propose a different account for proponents fond of the voter-theoretic approach that is grounded by approval voting, which sufficiently addresses the problem of option incomparability and is pragmatically compelling due to its simpler structure.

Collective action is essential for addressing the grand challenges of our time. However, for such action to be successful, decision-making processes must be perceived as legitimate. In this study, we investigate the legitimacy of different voting methods. Using a pre-registered human subject experiment, 120 participants cast their votes using four voting methods: majority voting, combined approval voting, range voting, and the modified Borda count. These methods represent a range of preference elicitation designs, from low to high complexity and flexibility. Furthermore, we developed a legitimacy scale upon which the participants rate the voting methods. The experiment was conducted in a non-political setting (voting on color preferences) and a political context (voting on COVID-19-related questions). Our findings suggest that the perceived legitimacy of a voting method is context-dependent. Specifically, preferential voting methods are seen as more legitimate than majority voting in a political decision-making situation, but only for individuals with well-defined preferences. Furthermore, preferential voting methods are more legitimate than majority voting in a highly polarized situation.

We study how voting rules shape voter coordination in large three-candidate elections. We consider three rules, that differ on the number of candidates that voters can support: Plurality (one), Anti-Plurality (two) and Approval Voting (one or two). We show that the Condorcet winner is always elected at some equilibrium under Approval Voting, and that this rule provides better welfare guarantees than Plurality. We then numerically study a dynamic process of political tâtonnement which delivers rich insights. The Condorcet winner is virtually always elected under Approval Voting, but not under the other rules. The dominance of Approval Voting is robust to several alternative welfare criteria and the introduction of expressive voters.

The article proposes a solution to the scientific-applied problem of automating decision support regarding the review of criteria and indicators used in the evaluation of state-supported scientific institutions. This topic is highly relevant for scientific and technical activities both in the conditions of martial law and during the restoration of the country in peacetime. To address this issue, an information technology for decision support by experts is proposed based on an integrative methodology that involves data structuring, support for expert judgments, and visualization of decision-making processes using methods such as approval voting, hierarchy analysis, analytical networks, computer ontologies, and elements of graph theory. A concise description of the integrative methodology and the cognitive process of solving unstructured multi-criteria problems supported by this methodology is provided. The functionality of the developed software toolkit is discussed using an illustrative example related to determining the criteria base for the evaluation of scientific institutions. Elements of the ontological evaluation framework, a hierarchical model for the decision-making task of selecting quantitative assessment alternatives, and the results of experts determining criteria weights for evaluating alternatives and conducting pairwise comparisons of alternatives are presented. The conducted research indicates that the developed methodology and software tools, which have previously been tested in law enforcement agencies, can also be applied in other structures of government administration. The obtained results, aimed at enhancing the efficiency of evaluating scientific institutions, can be utilized to support decision-making in various aspects of managing scientific and technical activities.

In approval-based committee (ABC) elections, the goal is to select a fixed-size subset of the candidates, a so-called committee, based on the voters' approval ballots over the candidates. One of the most popular classes of ABC voting rules are ABC scoring rules, for which voters give points to each committee and the committees with maximal total points are chosen. While the set of ABC scoring rules has recently been characterized in a model where the output is a ranking of all committees, no full characterization of these rules exists in the standard model where a set of winning committees is returned. We address this issue by characterizing two important subclasses of ABC scoring rules in the standard ABC election model, thereby both extending the result for ABC ranking rules to the standard setting and refining it to subclasses. In more detail, by relying on a consistency axiom for variable electorates, we characterize (i) the prominent class of Thiele rules and (ii) a new class of ABC voting rules called ballot size weighted approval voting. Based on these theorems, we also infer characterizations of three well-known ABC voting rules, namely multi-winner approval voting, proportional approval voting, and satisfaction approval voting.

We consider spatial voting where candidates are located in the Euclidean d-dimensional space, and each voter ranks candidates based on their distance from the voter's ideal point. We explore the case where information about the location of voters' ideal points is incomplete: for each dimension, we are given an interval of possible values. We study the computational complexity of finding the possible and necessary winners for positional scoring rules. Our results show that we retain tractable cases of the classic model where voters have partial-order preferences. Moreover, we show that there are positional scoring rules under which the possible-winner problem is intractable for partial orders, but tractable in the one-dimensional spatial setting. We also consider approval voting in this setting. We show that for up to two dimensions, the necessary-winner problem is tractable, while the possible-winner problem is hard for any number of dimensions.

We study the problem of fair sequential decision making given voter preferences. In each round, a decision rule must choose a decision from a set of alternatives where each voter reports which of these alternatives they approve. Instead of going with the most popular choice in each round, we aim for proportional representation, using axioms inspired by the multi-winner voting literature. The axioms require that every group of α% of the voters, if it agrees in every round (i.e., approves a common alternative), then those voters must approve at least α% of the decisions. A stronger version of the axioms requires that every group of α% of the voters that agrees in a β fraction of rounds must approve β⋅α% of the decisions. We show that three attractive voting rules satisfy axioms of this style. One of them (Sequential Phragmén) makes its decisions online, and the other two satisfy strengthened versions of the axioms but make decisions semi-online (Method of Equal Shares) or fully offline (Proportional Approval Voting). We present empirical results for these rules based on synthetic data and U.S. political elections. We also run experiments using the moral machine dataset about ethical dilemmas. We train preference models on user responses from different countries and let the models cast votes. We find that aggregating these votes using our rules leads to a more equal utility distribution across demographics than making decisions using a single global preference model.

Approval Voting offers advantages over other voting systems for single-winner elections. This manuscript analyzes three unique virtues of Approval Voting. First, the procedure does not violate the independence of irrelevant alternatives criterion for rational choice. Second, it prevents manipulation of outcomes through agenda setting. Third, it avoids intransitive majority preference cycles like Condorcet paradoxes and so escapes Arrow’s Impossibility Theorem constraints. As a result of these virtues, which are generally not shared by its best-known competitors, Approval Voting emerges as a strong option for realizing majoritarian democratic will.

We consider a voting scenario in which the resource to be voted upon may consist of both indivisible and divisible goods. This setting generalizes both the well-studied model of multiwinner voting and the recently introduced model of cake sharing. Under approval votes, we propose two variants of the extended justified representation (EJR) notion from multiwinner voting, a stronger one called EJR for mixed goods (EJR-M) and a weaker one called EJR up to 1 (EJR-1). We extend three multiwinner voting rules to our setting—GreedyEJR, the method of equal shares (MES), and proportional approval voting (PAV)—and show that while all three generalizations satisfy EJR-1, only the first one provides EJR-M. In addition, we derive tight bounds on the proportionality degree implied by EJR-M and EJR-1, and investigate the proportionality degree of our proposed rules.

Quantification of the Effects of Voter Protocols on the Outcome of Approval Voting

In the high-stakes race for scalability, some blockchains have turned to committee-based consensus (CBC), whereby the chain’s recordkeeping rights are entrusted to a committee of block producers elected via approval voting. Smaller committees boost speed and scalability but can compromise security when voters have limited information. In this environment, voting strategies are naturally nonlinear, and equilibria can become intractable. Despite this, we show that elections converge to optimality asymptotically (in voter numbers), exponentially quickly, and under relatively weak informational requirements. Compared to popular stake-weighted lottery and single-vote protocols used in practice, we find that CBC, when paired with approval voting, can offer meaningful efficiency and robustness gains if enough voters are engaged. This paper was accepted by Will Cong, Special Section of Management Science: Blockchains and Crypto Economics. Funding: This work was funded by The Hogeg Blockchain Research Institute. Supplemental Material: The data files and online appendix are available at https://doi.org/10.1287/mnsc.2022.03177 .

Preference-approval structures combine preference rankings and approval voting for declaring opinions over a set of alternatives. In this paper, we propose a new procedure for clustering alternatives in order to reduce the complexity of the preference-approval space and provide a more accessible interpretation of data. To that end, we present a new family of pseudometrics on the set of alternatives that take into account voters’ preferences via preference-approvals. To obtain clusters, we use the Ranked k-medoids (RKM) partitioning algorithm, which takes as input the similarities between pairs of alternatives based on the proposed pseudometrics. Finally, using non-metric multidimensional scaling, clusters are represented in 2-dimensional space.

Abstract Survey experiments that investigate how voting procedures affect voting behavior and election outcomes use hypothetical questions and non-representative samples. We present here the results of a novel survey experiment that addresses both concerns. First, the winning party in our experiment receives a donation to its campaign funds inducing real consequences for voting. Second, we run an online experiment with a Dutch national representative sample (N = 1240). Our results validate previous findings using a representative sample, in particular that approval voting leads to a higher concentration in votes for smaller parties and strengthens centrist parties in comparison to plurality voting. Importantly, our results suggest that voting behavior is not affected by voting incentives and can be equally reliably elicited with hypothetical questions.

We study the parameterized complexity of winner determination problems 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 these problems are computationally hard. Although they have been studied from the parameterized complexity point of view with respect to several natural parameters, many of them turned out to be W[1]-hard or W[2]-hard. Aiming at obtaining plentiful fixed-parameter algorithms, we revisit these problems by considering more natural single parameters, combined parameters, and structural parameters.