scholarly journals The Power Index at Infinity: Weighted Voting in Sequential Infinite Anonymous Games

2021 ◽  
Author(s):  
Shereif Eid
Keyword(s):  
Power Index ◽  
Weighted Voting ◽  
Anonymous Games

scholarly journals Finding Optimal Solutions for Voting Game Design Problems

2014 ◽  
Vol 50 ◽  
pp. 105-140 ◽  
Author(s):  
B. De Keijzer ◽  
T. B. Klos ◽  
Y. Zhang
Keyword(s):  
Inverse Problem ◽  
Power Distribution ◽  
Game Design ◽  
Distance Measure ◽  
Power Index ◽  
Weighted Voting ◽  
Target Distribution ◽  
Voting Game ◽  
Distribution Of Power ◽  
Weighted Voting Game

In many circumstances where multiple agents need to make a joint decision, voting is used to aggregate the agents' preferences. Each agent's vote carries a weight, and if the sum of the weights of the agents in favor of some outcome is larger than or equal to a given quota, then this outcome is decided upon. The distribution of weights leads to a certain distribution of power. Several `power indices' have been proposed to measure such power. In the so-called inverse problem, we are given a target distribution of power, and are asked to come up with a game in the form of a quota, plus an assignment of weights to the players whose power distribution is as close as possible to the target distribution (according to some specied distance measure). Here we study solution approaches for the larger class of voting game design (VGD) problems, one of which is the inverse problem. In the general VGD problem, the goal is to find a voting game (with a given number of players) that optimizes some function over these games. In the inverse problem, for example, we look for a weighted voting game that minimizes the distance between the distribution of power among the players and a given target distribution of power (according to a given distance measure). Our goal is to find algorithms that solve voting game design problems exactly, and we approach this goal by enumerating all games in the class of games of interest. We first present a doubly exponential algorithm for enumerating the set of simple games. We then improve on this algorithm for the class of weighted voting games and obtain a quadratic exponential (i.e., 2^O(n^2)) algorithm for enumerating them. We show that this improved algorithm runs in output-polynomial time, making it the fastest possible enumeration algorithm up to a polynomial factor. Finally, we propose an exact anytime-algorithm that runs in exponential time for the power index weighted voting game design problem (the `inverse problem'). We implement this algorithm to find a weighted voting game with a normalized Banzhaf power distribution closest to a target power index, and perform experiments to obtain some insights about the set of weighted voting games. We remark that our algorithm is applicable to optimizing any exponential-time computable function, the distance of the normalized Banzhaf index to a target power index is merely taken as an example.

scholarly journals On the Complexity of the Inverse Semivalue Problem for Weighted Voting Games

2019 ◽  
Vol 33 ◽  
pp. 1869-1876 ◽  
Author(s):  
Ilias Diakonikolas ◽  
Chrystalla Pavlou
Keyword(s):  
Inverse Problem ◽  
Power Index ◽  
Power Indices ◽  
Weighted Voting ◽  
Weighted Voting Games ◽  
Voting Games ◽  
Shapley Values ◽  
Voting Game ◽  
Index Problem ◽  
Popular Power

Weighted voting games are a family of cooperative games, typically used to model voting situations where a number of agents (players) vote against or for a proposal. In such games, a proposal is accepted if an appropriately weighted sum of the votes exceeds a prespecified threshold. As the influence of a player over the voting outcome is not in general proportional to her assigned weight, various power indices have been proposed to measure each player’s influence. The inverse power index problem is the problem of designing a weighted voting game that achieves a set of target influences according to a predefined power index. In this work, we study the computational complexity of the inverse problem when the power index belongs to the class of semivalues. We prove that the inverse problem is computationally intractable for a broad family of semivalues, including all regular semivalues. As a special case of our general result, we establish computational hardness of the inverse problem for the Banzhaf indices and the Shapley values, arguably the most popular power indices.

Optimization method to find the voter power index in weighted voting systems

2009 ◽  
Vol 20 (4) ◽  
pp. 416-426
Author(s):  
V. S. Levchenkov ◽  
L. G. Levchenkova
Keyword(s):  
Power Index ◽  
Optimization Method ◽  
Voting Systems ◽  
Weighted Voting

scholarly journals False-Name Manipulations in Weighted Voting Games

2011 ◽  
Vol 40 ◽  
pp. 57-93 ◽  
Author(s):  
H. Aziz ◽  
Y. Bachrach ◽  
E. Elkind ◽  
M. Paterson
Keyword(s):  
Decision Making ◽  
Computational Complexity ◽  
Lower Bounds ◽  
Experimental Evaluation ◽  
Randomized Algorithms ◽  
Power Index ◽  
Upper And Lower Bounds ◽  
Banzhaf Index ◽  
Weighted Voting ◽  
Voting Games

Weighted voting is a classic model of cooperation among agents in decision-making domains. In such games, each player has a weight, and a coalition of players wins the game if its total weight meets or exceeds a given quota. A player's power in such games is usually not directly proportional to his weight, and is measured by a power index, the most prominent among which are the Shapley-Shubik index and the Banzhaf index.In this paper, we investigate by how much a player can change his power, as measured by the Shapley-Shubik index or the Banzhaf index, by means of a false-name manipulation, i.e., splitting his weight among two or more identities. For both indices, we provide upper and lower bounds on the effect of weight-splitting. We then show that checking whether a beneficial split exists is NP-hard, and discuss efficient algorithms for restricted cases of this problem, as well as randomized algorithms for the general case. We also provide an experimental evaluation of these algorithms. Finally, we examine related forms of manipulative behavior, such as annexation, where a player subsumes other players, or merging, where several players unite into one. We characterize the computational complexity of such manipulations and provide limits on their effects. For the Banzhaf index, we describe a new paradox, which we term the Annexation Non-monotonicity Paradox.

Using Shapley’s asymmetric power index to measure banks’ contributions to systemic risk

2016 ◽  
Vol 2 (2) ◽  
pp. 35-55
Author(s):  
Rodney Garratt ◽  
Lewis Webber ◽  
Matthew Willison
Keyword(s):  
Systemic Risk ◽  
Power Index ◽  
Asymmetric Power

scholarly journals Weight Feedback-Based Harmonic MDG-Ensemble Model for Prediction of Traffic Accident Severity

2021 ◽  
Vol 11 (11) ◽  
pp. 5072
Author(s):  
Byung-Kook Koo ◽  
Ji-Won Baek ◽  
Kyung-Yong Chung
Keyword(s):  
Traffic Accidents ◽  
Average Rate ◽  
Modern Society ◽  
Rate Of Change ◽  
Weighted Voting ◽  
Independent Variables ◽  
Dependent Variables ◽  
Accident Severity ◽  
Harmonic Average ◽  
Bagging Method

Traffic accidents are emerging as a serious social problem in modern society but if the severity of an accident is quickly grasped, countermeasures can be organized efficiently. To solve this problem, the method proposed in this paper derives the MDG (Mean Decrease Gini) coefficient between variables to assess the severity of traffic accidents. Single models are designed to use coefficient, independent variables to determine and predict accident severity. The generated single models are fused using a weighted-voting-based bagging method ensemble to consider various characteristics and avoid overfitting. The variables used for predicting accidents are classified as dependent or independent and the variables that affect the severity of traffic accidents are predicted using the characteristics of causal relationships. Independent variables are classified as categorical and numerical variables. For this reason, a problem arises when the variation among dependent variables is imbalanced. Therefore, a harmonic average is applied to the weights to maintain the variables’ balance and determine the average rate of change. Through this, it is possible to establish objective criteria for determining the severity of traffic accidents, thereby improving reliability.

scholarly journals Weighted voting procedure having a unique blocker

2021 ◽  
Author(s):  
Sanjay Bhattacherjee ◽  
Palash Sarkar
Keyword(s):  
Weighted Voting ◽  
Trade Off ◽  
Voting Weights ◽  
Goods And Services ◽  
Voting Games ◽  
Formal Study ◽  
Theoretical Results

AbstractThe Goods and Services Tax (GST) Council of India has a non-conventional weighted voting procedure having a primary player who is a blocker and a set of secondary players. The voting weights are not fixed and are determined based on the subset of players which participate in the voting. We introduce the notion of voting schema to formally model such a voting procedure. Individual voting games arise from a voting schema depending on the subset of secondary players who participate in the voting. We make a detailed formal study of the trade-off between the minimal sizes of winning and blocking coalitions in the voting games that can arise from a voting schema. Finally, the GST voting procedure is assessed using the theoretical results leading to suggestions for improvement.

Human-computer Coalition Formation in Weighted Voting Games

2020 ◽  
Vol 11 (6) ◽  
pp. 1-20
Author(s):  
Moshe Mash ◽  
Roy Fairstein ◽  
Yoram Bachrach ◽  
Kobi Gal ◽  
Yair Zick
Keyword(s):  
Coalition Formation ◽  
Weighted Voting ◽  
Weighted Voting Games ◽  
Voting Games
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