Voting Game Research Articles

Influence relation in two-output multichoice voting games

The influence relation, defined within the set of simple games, is identified as a preorder. Additionally, it is proved to be a subpreorder of the preorders induced by the Shapley–Shubik and Banzhaf–Coleman indices. When this relation extends to voting games with abstention, detailed in Tchantcho et al. (2008), and further to multichoice voting games as in Pongou et al. (2014), it is shown that these extensions aren't always preorders. Even when they are, they don't necessarily align with the preorders induced by the extended Banzhaf–Coleman and Shapley–Shubik power indices in Freixas (2005a) and Freixas (2005b). In this paper, we introduce extensions for two-output multichoice voting games that are both preorders and subpreorders of the Banzhaf–Coleman power index defined in Freixas (2005b). Further, we characterize the two-output multichoice voting games for which one of these new power theories agrees with the generalized Banzhaf–Coleman and Shapley–Shubik power indices in Freixas (2005a) and Freixas (2005b) respectively.

Multidimension: a dimensionality extension of simple games

In voting theory and social choice theory, decision systems can be represented as simple games, i.e., cooperative games defined through their players or voters and their set of winning coalitions. The weighted voting games form a well-known strict subclass of simple games, where each player has a voting weight so that a coalition wins if the sum of weights of their members exceeds a given quota. Since the number of winning coalitions can be exponential in the number of players, simple games can be represented much more compactly as intersections or unions of weighted voting games. A simple game’s dimension (codimension) is the minimum number of weighted voting games such that their intersection (union) is the given game. It is known there are voting systems with a high (co)dimension. This work introduces the multidimension as the minimum size of an expression with intersections and unions on weighted voting games necessary to obtain the considered simple game. We generalize this notion to subclasses of weighted voting games and analyze the generative properties of these subclasses. We also characterize the simple games with finite generalized multidimension over the set of weighted voting games without dummy players. We provide a comprehensive classification for simple games up to a certain number of players. These results complement similar classification results for generalized (co)dimensions. Our results show how generalized multidimension allows representing more simple games and more compactly, even for a small number of players and for subclasses.

The finagle point is close to the yolk

The yolk and the finagle point are two well-known solution concepts in spatial voting games without a core. No relationship between them has been rigorously established in the literature. We prove that every finagle point must be within 2.32472 yolk radii of every yolk center, in all dimensions. This result tightens and generalizes a claimed bound of 2.5 for two dimensions. The bound applies to all points with finagle radius less than the yolk radius. If the finagle radius is half the yolk radius, the bound decreases to 1.7607.

Controlling weighted voting games by deleting or adding players with or without changing the quota

Weighted voting games are a well-studied class of succinct simple games that can be used to model collective decision-making in, e.g., legislative bodies such as parliaments and shareholder voting. Power indices [1–4] are used to measure the influence of players in weighted voting games. In such games, it has been studied how a distinguished player’s power can be changed, e.g., by merging or splitting players (the latter is a.k.a. false-name manipulation) [5, 6], by changing the quota [7], or via structural control by adding or deleting players [8]. We continue the work on the structural control initiated by Rey and Rothe [8] by solving some of their open problems. In addition, we also modify their model to a more realistic setting in which the quota is indirectly changed during the addition or deletion of players (in a different sense than that of Zuckerman et al. [7] who manipulate the quota directly without changing the set of players), and we study the corresponding problems in terms of their computational complexity.

Banzhaf–Coleman–Dubey–Shapley sensitivity index for simple multichoice voting games

Banzhaf–Coleman–Dubey–Shapley sensitivity index for simple multichoice voting games

A Framework for Computing the Nucleolus via Dynamic Programming

This article defines a general class of cooperative games for which the nucleolus is efficiently computable. This class includes new members for which the complexity of computing their nucleolus was not previously known. We show that when the minimum excess coalition problem of a cooperative game can be formulated as a hypergraph dynamic program, its nucleolus is efficiently computable. This gives a general technique for designing efficient algorithms for computing the nucleolus of a cooperative game. This technique is inspired by a recent result of Pashkovich [ 27 ] on weighted voting games. However, our technique significantly extends beyond the capabilities of previous work. We demonstrate this by applying it to give an algorithm for computing the nucleolus of b -matching games in polynomial time on graphs of bounded treewidth.

Cooperative game theory methods for determining text complexity

We propose a method for estimating the complexity of texts based on the methods of cooperative game theory. The players in this game are the lengths of words in the text. The game itself is represented as a voting game in which the value of a player is determined by the number of coalitions in which the player is key. The ranks of the players are formed by computing the Shepley—Schubik value or the Banzaf index in a voting game with a given voting threshold. Thus, a vector of Shepley—Schubik or Banzaf values is assigned to each text. After that, the vector space is used to rank the texts in terms of complexity based on the expert evaluations obtained in this domain.

Discovery and Analysis of Control Associations in Shareholding Networks Based on the Voting Game Approach

Shareholding networks structured in a complex manner create complex control associations. The actual controllers, paths through which control is created between companies, and control scopes of specified companies are all hidden in shareholding networks. The discovery and analysis of these crucial control associations is essential for corporate governance. However, relative to ultimate shareholders’ control power, existing control studies based on the voting game ignore the critical role of intermediate companies in integrating outer shareholders’ votes and transferring control to the inner shareholders. Therefore, a foundation for discovering control associations within networks is lacking. We measure control by considering ultimate shareholders and intermediate companies based on the voting game approach and thus propose the Control Transfer Index ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Cti</i> ) to measure the strength of the control relationship between any two companies and corresponding Control Transfer Index Calculation (CTIC) algorithm to calculate <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Cti</i> precisely. Based on it, we propose the concept and algorithm of Crucial Control Path (CCP) to discover more essential control paths between companies. We also propose the concept and algorithm of the Company Control Community (CCC) to identify overlapping company communities that meet the control degree threshold. This study illustrates the effectiveness of these algorithms in identifying actual controllers, discovering control formation paths, and analyzing control scopes by analyzing the aforementioned crucial control associations in the context of control and risk cases.

Early warning indicators of epidemics on a coupled behaviour-disease model with vaccine hesitance and incomplete data

The ubiquity of hesitance sometimes defies social pressure, especially when individuals are required to make health-care decisions they deem momentous. In epidemiology, such intervention hesitance can both initiate and prolong infectious disease outbreaks, especially when paired with vaccine denial. Previous literature has yielded effective early warning signals (EWS) of disease outbreak and vaccine crisis for coupled behaviour-infection systems; these EWS arise from characteristic phenomena undergone by model dynamics during critical transition(s). In this study, we investigate the resilience of these EWS to the incorporation of a destructive delay to vaccination decisions. Simulations were conducted on a static small world network, using a model coupling an $ SIRV_p $ infection model with a social dynamic resembling a voting game with abstention. We find that some of the EWS tested retain their efficacy despite fundamental differences in model behaviour. We also find that these EWS (both pair- and cluster-based) can be reliably used while observing as little as $ 60\% $ of the total network with relatively small loss of accuracy. These findings not only show the resilience of these EWS, but also allow for potential expansion of use cases and reduction in computational resource requirements.

Collective Information Acquisition

Abstract We consider the problem faced by a group of players who bargain over what public signal to acquire before deciding on a collective action. The players differ in their privately known state-dependent payoffs from taking the action, and therefore differ also in their willingness to pay for the public signal. We take a mechanism design approach to characterizing the efficient frontier of outcomes achievable via bargaining over information. We identify novel distortions in the optimal information structure that arise from the information asymmetry and from the fact that after the signal is realized, the outcome is determined in equilibrium of a subsequent voting game.

A parametric worst-case approach to fairness in cooperative games with transferable utility

We study worst-case fairness in resource allocation and cooperative games with transferable utility, the stable division most dissimilar to a normative standard of fairness. Motivated by welfare economics, similarity is quantified using information-theoretic divergences. Worst-case fairness aims to parallel the spirit of the price of anarchy from noncooperative game theory, quantifying how much unfairness is compatible with coalitional rationality. Computing worst-case fairness is tractable in weighted voting games and classes of coalitional skill games, but NP-hard in highway allocation, induced-subgraph games and some task-count coalitional skill games. In these cases we show approximation algorithms that yield constant approximations. We also upper bound the performance of a Reverse Greedy algorithm on general convex games in terms of two game-specific constants.

The blocker postulates for measures of voting power

A proposed measure of voting power should satisfy two conditions to be plausible: first, it must be conceptually justified, capturing the intuitive meaning of what voting power is; second, it must satisfy reasonable postulates. This paper studies a set of postulates, appropriate for a priori voting power, concerning blockers (or vetoers) in a binary voting game. We specify and motivate five such postulates, namely, two subadditivity blocker postulates, two minimum-power blocker postulates, each in weak and strong versions, and the added-blocker postulate. We then test whether three measures of voting power, namely the classic Penrose–Banzhaf measure, the classic Shapley–Shubik index, and the newly proposed recursive measure, satisfy these postulates. We find that the first measure fails four of the postulates, the second fails two, while the third alone satisfies all five postulates. This work consequently adds to the plausibility of the recursive measure as a reasonable measure of voting power.

Measuring power in coalitional games with friends, enemies and allies

We extend the well-known model of graph-restricted games due to Myerson to signed graphs. In our model, it is possible to explicitly define not only that some players are friends (as in Myerson's model) but also that some other players are enemies. As such our games can express a wider range of situations, e.g., animosities between political parties. We define the value for signed graph games using the axiomatic approach that closely follows the celebrated characterization of the Myerson value. Furthermore, we propose an algorithm for computing an arbitrary semivalue, including the extension of the Myerson value proposed by us. We also develop a pseudo-polynomial algorithm for power indices in weighted voting games for signed graphs with bounded treewidth. Moreover, we consider signed graph games with a priori defined alliances (unions) between players and propose algorithms to compute the extension of the Owen value to this setting.

On the generalized dimension and codimension of simple games

Weighted voting games are simple games that can be represented by a collection of integer weights for each player so that a coalition wins if the sum of the player weights matches or exceeds a given quota. It is known that a simple game can be expressed as the intersection or the union of weighted voting games. The dimension (codimension) of a simple game is the minimum number of weighted voting games such that their intersection (union) is the given game. In this work, we analyze some subclasses of weighted voting games and their closure under intersection or union. We introduce generalized notions of dimension and codimension regarding some subclasses of weighted voting games. In particular, we show that not all simple games can be expressed as intersection (union) of pure weighted voting games (those in which dummy players are not allowed) and we provide a characterization of such simple games. Finally, we experimentally study the generalized dimension (codimension) for some subclasses defined by establishing restrictions on the representations of weighted voting games.

Improved U-Net Remote Sensing Classification Algorithm Based on Multi-Feature Fusion Perception

The selection and representation of remote sensing image classification features play crucial roles in image classification accuracy. To effectively improve the classification accuracy of features, an improved U-Net network framework based on multi-feature fusion perception is proposed in this paper. This framework adds the channel attention module (CAM-UNet) to the original U-Net framework and cascades the shallow features with the deep semantic features, replaces the classification layer in the original U-Net network with a support vector machine, and finally uses the majority voting game theory algorithm to fuse the multifeature classification results and obtain the final classification results. This study used the forest distribution in Xingbin District, Laibin City, Guangxi Zhuang Autonomous Region as the research object, which is based on Landsat 8 multispectral remote sensing images, and, by combining spectral features, spatial features, and advanced semantic features, overcame the influence of the reduction in spatial resolution that occurs with the deepening of the network on the classification results. The experimental results showed that the improved algorithm can improve classification accuracy. Before the improvement, the overall segmentation accuracy and segmentation accuracy of the forestland increased from 90.50% to 92.82% and from 95.66% to 97.16%, respectively. The forest cover results obtained by the algorithm proposed in this paper can be used as input data for regional ecological models, which is conducive to the development of accurate and real-time vegetation growth change models.

Inconsistent weighting in weighted voting games

In a weighted voting game, each voter has a given weight, and a coalition of voters is successful if the sum of their individual weights exceeds a given quota. Such voting systems translate the idea that voters are not all equal by assigning them different weights. In such a situation, two voters are symmetric in a game if interchanging the two voters leaves the outcome of the game unchanged. Two voters with the same weight are naturally symmetric in every weighted voting game, but the converse statement is not necessarily true. We call the latter scenario inconsistent weighting. We investigate herein the conditions that give rise to such a phenomenon within the class of weighted voting games, and we study how the choice of the quota, the total weight, and the number of voters can affect the probability of observing inconsistent weighting.

Squid Voting Game: Rational Indecisiveness in Sequential Voting

Squid Voting Game: Rational Indecisiveness in Sequential Voting

Shapley Value and Income Taxation

Income taxation is modeled as a spatial voting game where Shapley value leads to a simple linear tax function on gross income with a single marginal tax rate and a universal basic income subsidy. Shapley net income is not generally in the game core; therefore, it is inherently unstable and subject to relentless pressure from higher gross income individuals to reduce their taxes and increase their net incomes.

Dynamic Programming for Computing Power Indices for Weighted Voting Games with Precoalitions

We study the efficient computation of power indices for weighted voting games with precoalitions amongst subsets of players (reflecting, e.g., ideological proximity) using the paradigm of dynamic programming. Starting from the state-of-the-art algorithms for computing the Banzhaf and Shapley–Shubik indices for weighted voting games, we present a framework for fast algorithms for the three most common power indices with precoalitions, i.e., the Owen index, the Banzhaf–Owen index and the symmetric coalitional Banzhaf index, and point out why our new algorithms are applicable for large numbers of players. We discuss implementations of our algorithms for the three power indices with precoalitions in C++ and review computing times, as well as storage requirements.

Pseudo polynomial size LP formulation for calculating the least core value of weighted voting games

In this paper, we propose a pseudo polynomial size LP formulation for finding a payoff vector in the least core of a weighted voting game. The numbers of variables and constraints in our formulation are both bounded by O(nW+), where n is the number of players and W+ is the total sum of (integer) voting weights. When we employ our formulation, a commercial LP solver calculates a payoff vector in the least core of practical weighted voting games in a few seconds. We also extend our approach to vector weighted voting games.