Voting Rules Research Articles

Justifying political choice: from probability and institutions to communication

The article is devoted to the study of the dynamics of development of concepts that justify political choice. There is a general turn from the moral justification of political choice to ontological concepts based on the ideas of pragmatic and impartial behavior in the search for criteria for the “correct” decision, which includes the truth and the institutions that ensure it. The epistemic concept of democracy, based on Condorcet's jury theorem, defines the possibility of achieving the correct choice through majority rule voting, implies a competent, independent and sincere voter, which ensures an increase in the probability of the correct choice. The expansion of the composition of participants in political choice increased the role of diversity of knowledge and opinions in the justification, which led to the concept of the “smart plurality”, which ensures the correct choice is made by reducing its overall error through random mass participation. The development of social networks and their argumentative function in disputes have contributed to the transition to the concepts of argumentative networks that ensure the correct option is selected through communication. The identified dynamics allow us to conclude that the concept of politics is reviving its importance as a reasoning.

Approval-Based Committee Voting in Practice: A Case Study of (over-)Representation in the Polkadot Blockchain

We provide the first large-scale data collection of real-world approval-based committee elections. These elections have been conducted on the Polkadot blockchain as part of their Nominated Proof-of-Stake mechanism and contain around one thousand candidates and tens of thousands of (weighted) voters each. We conduct an in-depth study of application-relevant questions, including a quantitative and qualitative analysis of the outcomes returned by different voting rules. Besides considering proportionality measures that are standard in the multiwinner voting literature, we pay particular attention to less-studied measures of overrepresentation, as these are closely related to the security of the Polkadot network. We also analyze how different design decisions such as the committee size affect the examined measures.

Refined Characterizations of Approval-Based Committee Scoring Rules

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.

Participation Incentives in Approval-Based Committee Elections

In approval-based committee (ABC) voting, the goal is to choose a subset of predefined size of the candidates based on the voters’ approval preferences over the candidates. While this problem has attracted significant attention in recent years, the incentives for voters to participate in an election for a given ABC voting rule have been neglected so far. This paper is thus the first to explicitly study this property, typically called participation, for ABC voting rules. In particular, we show that all ABC scoring rules even satisfy group participation, whereas most sequential rules severely fail participation. We furthermore explore several escape routes to the impossibility for sequential ABC voting rules: we prove for many sequential rules that (i) they satisfy participation on laminar profiles, (ii) voters who approve none of the elected candidates cannot benefit by abstaining, and (iii) it is NP-hard for a voter to decide whether she benefits from abstaining

Temporal Fairness in Multiwinner Voting

Multiwinner voting captures a wide variety of settings, from parliamentary elections in democratic systems to product placement in online shopping platforms. There is a large body of work dealing with axiomatic characterizations, computational complexity, and algorithmic analysis of multiwinner voting rules. Although many challenges remain, significant progress has been made in showing existence of fair and representative outcomes as well as efficient algorithmic solutions for many commonly studied settings. However, much of this work focuses on single-shot elections, even though in numerous real-world settings elections are held periodically and repeatedly. Hence, it is imperative to extend the study of multiwinner voting to temporal settings. Recently, there have been several efforts to address this challenge. However, these works are difficult to compare, as they model multi-period voting in very different ways. We propose a unified framework for studying temporal fairness in this domain, drawing connections with various existing bodies of work, and consolidating them within a general framework. We also identify gaps in existing literature, outline multiple opportunities for future work, and put forward a vision for the future of multiwinner voting in temporal settings.

Proportional Aggregation of Preferences for Sequential Decision Making

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.

Welfare Maximization in Perpetual Voting (Student Abstract)

We study the computational problems associated with maximizing various welfare objectives—namely utilitarian welfare, egalitarian welfare, and Nash welfare—in perpetual voting, a sequential collective decision-making framework. Prior work look into notions of fairness over time and study extensions of single-round voting rules to the multi-round setting. We show that while a utilitarian-welfare maximizing outcome can be computed efficiently, an outcome that maximizes egalitarian or Nash welfare is computationally intractable, even in the case of two candidates. We complement this by showing that maximizing egalitarian welfare is fixed-parameter tractable in the number of agents, and maximizing egalitarian or Nash welfare is W[2]-hard and slicewise polynomial in the number of timesteps. We also provide an approximation algorithm for maximizing egalitarian welfare and study strategyproofness with respect to these welfare objectives. Finally, we show that a simple greedy algorithm can achieve approximate proportionality in this setting.

Optimizing decision-making in IoT through ensemble voting and dynamic group formation with DBSCAN

In the era of widespread connectivity, leveraging artificial intelligence models and analyzing the vast datasets generated by smart devices are central points in IoT research. While existing studies mainly focus on improving the decision-making prowess of central systems, the potential for local optimization remains largely unexplored. This paper presents an Ensemble Voting Scheme with Multilayer Dynamic Groups (EVMDS), which assigns decision weights to IoT devices based on their attribute data. By employing the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm, dynamic clusters among IoT devices can be identified, the application of ensemble voting rules at each stage of group formation, enabling layered computations to ease backend burden and achieve hierarchical decision-making capability, facilitating regional-level decision-making that strikes a balance between local and global optimization. Through simulated decision-making scenarios in a small-scale IoT environment, our experiments demonstrate the superior accuracy and reliability of the proposed approach compared to existing models.

Distributed Cooperative Driving Strategy for Connected Automated Vehicles at Unsignalized Intersections Based on Monte Carlo Method

One of the most important goals of cooperative driving is to control connected automated vehicles (CAVs) passing through conflict areas safely and efficiently without traffic signals. As a typical application scenario, allocating right-of-way reasonably at unsignalized intersections can effectively avoid collisions and reduce traffic delays. Proposed here is a new cooperative driving strategy for CAVs at unsignalized intersections based on distributed Monte Carlo tree search (MCTS). A task-area partition framework is also proposed to decompose the mission of cooperative driving into three main tasks: vehicle information sharing, passing order optimization, and trajectory control. Based on the schedule tree of the vehicle passing order, the root parallelization of MCTS combined with the majority voting rule is used to explore as many feasible passing orders (leaf nodes) as possible in a distributed way and find a nearly global-optimal passing order within the limited planning time. The aim is for CAVs to perform proper trajectory adjustments based on the obtained passing order to minimize traffic delays while making the slightest acceleration adjustments. A coupled simulation platform integrating SUMO and Python is developed to construct the unsignalized intersection scenarios and generate the proposed distributed cooperative driving strategy. Comparative analysis with conventional driving strategies demonstrates that the proposed strategy significantly enhances efficiency, safety, comfort, and emission, aligning well with innovative and environmentally friendly urban mobility aspirations.

Robustness of classifier systems using the optimal voting rule and neural network

In connection with the development of artificial neural network (ANN) technologies, it is of interest to compare the robustness of classifier systems using the optimal voting rule and ANN. Robust algorithms are required to have high (though not the highest) efficiency in the case of planned situations, and acceptable efficiency in case of predetermined deviations from the plan (model). The robustness of the optimal voting rule and the neural network to the inaccuracy of computing the posteriori probabilities of partial solutions of the combined classifiers was investigated. It was found that in calculating the posterior probabilities with the error the neural network has provided a better performance than the optimal voting rule, showing the property robustness to the inaccuracy of input data. The use of classifiers utilizing ANN allows to increase robustness of algorithms in the signal receivers.

Approval-based voting with mixed goods

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.

Polynomial Voting Rules

We propose and study a new class of polynomial voting rules for a general decentralized decision/consensus system, and more specifically for the proof-of-stake protocol. The main idea, inspired by the Penrose square-root law and the more recent quadratic voting rule, is to differentiate a voter’s voting power and the voter’s share (fraction of the total in the system). We show that, whereas voter shares form a martingale process that converges to a Dirichlet distribution, their voting powers follow a supermartingale process that decays to zero over time. This prevents any voter from controlling the voting process and, thus, enhances security. For both limiting results, we also provide explicit rates of convergence. When the initial total volume of votes (or stakes) is large, we show a phase transition in share stability (or the lack thereof), corresponding to the voter’s initial share relative to the total. We also study the scenario in which trading (of votes/stakes) among the voters is allowed and quantify the level of risk sensitivity (or risk aversion) in three categories, corresponding to the voter’s utility being a supermartingale, a submartingale, and a martingale. For each category, we identify the voter’s best strategy in terms of participation and trading. Funding: W. Tang gratefully acknowledges financial support through the National Science Foundation [Grants DMS-2113779 and DMS-2206038] and through a start-up grant at Columbia University. D. D. Yao’s work is part of a Columbia–City University/Hong Kong collaborative project that is supported by InnoHK Initiative, the Government of Hong Kong Special Administrative Region, and the Laboratory for AI-Powered Financial Technologies.

False-name-proof and strategy-proof voting rules under separable preferences

We consider the problem of a society that uses a voting rule to choose a subset from a given set of objects (candidates, binary issues, or alike). We assume that voters’ preferences over subsets of objects are separable: adding an object to a set leads to a better set if and only if the object is good (as a singleton set, the object is better than the empty set). A voting rule is strategy-proof if no voter benefits by not revealing its preferences truthfully and it is false-name-proof if no voter benefits by submitting several votes under other identities. We characterize all voting rules that satisfy false-name-proofness, strategy-proofness, and ontoness as the class of voting rules in which an object is chosen if it has either at least one vote in every society or a unanimous vote in every society. To do this, we first prove that if a voting rule is false-name-proof, strategy-proof, and onto, then the identities of the voters are not important.

Institutional Design and Rhetorical Spaces: China’s Human Rights Strategies in a Changing World Order

ABSTRACT This article underlines the need to pay attention to institutional design in the analysis of China’s stated aim of leading the reform of global governance. The argument made here is that institutional choice and institutional design matter in relation to the larger question of how Chinese objectives are translated into its desired outcomes. The process of translation is hindered or enabled not solely by the embeddedness of normative ideas but also by design features such as membership criteria, informal or formal voting and procedural rules, the relative power and status of various institutions, together with the relative power of China within these institutions. The ways in which institutional design affects what China is actually able to achieve is shown in reference to two UN-related and one Beijing-initiated international organization that deal with human rights, an issue area where China’s determination to effect reform or revision is largely agreed to be significant.

Symmetric reduced‐form voting

We study a model of voting with two alternatives in a symmetric environment. We characterize the interim allocation probabilities that can be implemented by a symmetric voting rule. We show that every such interim allocation probability can be implemented as a convex combination of two families of deterministic voting rules: qualified majority and qualified anti‐majority. We also provide analogous results by requiring implementation by a symmetric monotone (strategy‐proof) voting rule and by a symmetric unanimous voting rule. We apply our results to show that an ex ante Rawlsian rule is a convex combination of a pair of qualified majority rules.

A natural adaptive process for collective decision‐making

Consider an urn filled with balls, each labeled with one of several possible collective decisions. Now let a random voter draw two balls from the urn and pick her more preferred as the collective decision. Relabel the losing ball with the collective decision, put both balls back into the urn, and repeat. Once in a while, relabel a randomly drawn ball with a random collective decision. We prove that the empirical distribution of collective decisions produced by this process approximates a maximal lottery, a celebrated probabilistic voting rule proposed by Peter C. Fishburn. In fact, the probability that the collective decision in round n is made according to a maximal lottery increases exponentially in n. The proposed procedure is more flexible than traditional voting rules and bears strong similarities to natural processes studied in biology, physics, and chemistry as well as algorithms proposed in machine learning

Minimal Stable Voting Rules

Minimal Stable Voting Rules

Evaluating cognitive phenotypes and associations with neuroimaging biomarkers of dementia in a sample of aging individuals using unsupervised machine learning

AbstractBackgroundOtherwise cognitively normal individuals can experience age‐related cognitive dysfunction and may present with heterogenous patterns of cognitive impairment. There is limited knowledge regarding the presence and stability of cognitive subtypes observed in individuals with mild cognitive impairment and dementia (e.g., dysexecutive, non‐amnestic). Further, the extent to which cognitive subtypes related to age‐ and dementia‐related neuroimaging biomarkers is uncertain.MethodThis study sought to evaluate the presence and composition of cognitive subtypes in a large diverse community sample of aging individuals without dementia (NC; Baseline N = 337; Table 1). Participants enrolled in the Wake Forest ADRC and completed an annual battery of cognitive assessments (Uniform Data Set; NACC), the Mini‐Mental State Exam (MMSE), and Clinical Diagnostic Rating Scale (CDR). Unsupervised machine learning (e.g., clustering: hierarchical, k‐means, and k‐medoids algorithms; 1000 bootstrap iterations; majority voting rule) was applied to the battery of cognitive assessments. Demographic characteristics and neuroimaging measures of amyloid deposition (global PiB PET SUVr; Aβ‐PET), total brain volume (BVOL), diffusion‐weighted fractional anisotropy (FA), and NODDI freewater (FW) were compared across prospective clusters using general linear models. Highly correlated cognitive metrics (r>.85) were removed prior to analysis.ResultCluster analyses using baseline cognitive scores suggested NC participants could be partitioned into two to eight clusters; two primary clusters representing one large homogenous group of relatively unimpaired individuals and another heterogenous cluster composed of 4‐7 possible cognitive subgroups (Figure 1). The two‐cluster solution partitioned NC participants into higher and lower cognitive performers. Across cluster solutions, lower performing individuals were older, had higher Aβ‐PET, and lower total brain volume on average (p<.05; Figure 2).ConclusionWe did not observe well‐defined clusters representing distinct cognitive subtypes reported in previous studies (e.g., dysexecutive, amnestic, visuospatial). However, a heterogenous subset of NC participants exhibited substantial variability across assessments. Three‐ and four‐cluster solutions identified individuals with greater impairment in executive functioning, and verbal learning and memory respectively. Findings highlight the need to model complex patterns of cognitive abilities in otherwise healthy older adults. Future longitudinal work will assess how health information and neuroimaging biomarkers of dementia contribute to the composition and stability of cognitively defined subgroups.

Obvious manipulations of tops-only voting rules

In a voting problem with a finite set of alternatives to choose from, we study the manipulation of tops-only rules. Since all non-dictatorial (onto) voting rules are manipulable when there are more than two alternatives and all preferences are allowed, we look for rules in which manipulations are not obvious. First, we show that a rule does not have obvious manipulations if and only if when an agent vetoes an alternative it can do so with any preference that does not have such alternative in the top.Second, we focus on two classes of tops-only rules: (i) (generalized) median voter schemes, and (ii) voting by committees. For each class, we identify which rules do not have obvious manipulations on the universal domain of preferences.

China-US Trade War and the Dispute Settlement Mechanism of the WTO

This paper studies the hegemonism of the WTO dispute settlement mechanism and the severe damage to the free trade system exposed by the Sino-US trade war. The agency faces several problems. First, the WTO currently covers a wide range of areas, which makes it challenging to coordinate the interests of member states. Second, the WTO has adopted a decision-making mechanism by consensus. As long as no member objects, corresponding decisions can be adopted. From the historical development process of the decision-making mechanism, it is the first time that the consensus decision-making mechanism considers all members opinions in the decision-making process and tries to make overall considerations. Still, the consensus decision-making mechanism does not stipulate voting or specific decision-making rules. In addition, the paper proposes several potential solutions to modify the dispute settlement mechanism.