Achievable hierarchies in voting games with abstention

It is well known that he influence relation orders the voters the same way as the classical Banzhaf and Shapley-Shubik indices do when they are extended to the voting games with abstention (VGA) in the class of complete games. Moreover, all hierarchies for the influence relation are achievable in the class of complete VGA. The aim of this paper is twofold. Firstly, we show that all hierarchies are achievable in a subclass of weighted VGA, the class of weighted games for which a single weight is assigned to voters. Secondly, we conduct a partial study of achievable hierarchies within the subclass of H-complete games, that is, complete games under stronger versions of influence relation. (C) 2013 Elsevier B.V. All rights reserved.Peer ReviewedPostprint (author’s final draft

Probabilistic power indices for games with abstention

S'introdueixen vuit índexs de poder que admeten una interpretació probabilística per les normes de votació amb abstenció o amb tres nivells d'aprovació en l'entrada. S'analitzen les semblances i diferències entre els índexs estàndards coneguts pels jocs simples i per les extensions per aquest context més general. Es conclou la feina proporcionant procediments basats en la generació de funcions per jocs(3,2) extensibles a jocs (j,k).Preprin

ASSESSMENT OF VOTING SITUATIONS: THE PROBABILISTIC FOUNDATIONS

In this paper we revise the probabilistic foundations of the theory of the measurement of 'voting power' either as success or decisiveness. For an assessment of these features two inputs are claimed to be necessary: the voting procedure and the voters' behavior. We propose a simple model in which the voters' behavior is summarized by a probability distribution over all vote configurations. This basic model, at once simpler and more general that other probabilistic models, provides a clear conceptual common basis to reinterpret coherently from a unified point of view di.erent power indices and some related game theoretic notions, as well as a wider perspective for a dispassionate assessment of the power indices themselves, their merits and their limitations.Voting rules, voting power, decisiveness, success, power indices

Different Approaches to Influence Based on Social Networks and Simple Games

We present an overview of research on a certain model of influence in a social network. Each agent has to make an acceptance/rejection decision, and he has an inclination to choose either the yes-action or the no-action. The agents are embedded in a social network which models influence between them. Due to the influence, a decision of an agent may differ from his preliminary inclination. Such a transformation between the agents' inclinations and their decisions are represented by an influence function. Follower functions encode the players who constantly follow the opinion of a given unanimous coalition. We examine properties of the influence and follower functions and study the relation between them. The model of influence is also compared to the framework of command games in which a simple game is built for each agent. We study the relation between command games and influence functions. We also define influence indices and determine the relations between these indices and some well-known power indices. Furthermore, we enlarge the set of possible yes/no actions to multi-choice games and investigate the analogous tools related to influence in the multi-choice model.influence ; social network ; influence function ; command game ; follower ; voting

Measuring voting power in convex policy spaces

Classical power index analysis considers the individual's ability to influence the aggregated group decision by changing its own vote, where all decisions and votes are assumed to be binary. In many practical applications we have more options than either "yes" or "no". Here we generalize three important power indices to continuous convex policy spaces. This allows the analysis of a collection of economic problems like e.g. tax rates or spending that otherwise would not be covered in binary models.Comment: 31 pages, 9 table

Generalized roll-call model for the Shapley-Shubik index

In 1996 Dan Felsenthal and Mosh\'e Machover considered the following model. An assembly consisting of $n$ voters exercises roll-call. All $n!$ possible orders in which the voters may be called are assumed to be equiprobable. The votes of each voter are independent with expectation $0<p<1$ for an individual vote {\lq\lq}yea{\rq\rq}. For a given decision rule $v$ the \emph{pivotal} voter in a roll-call is the one whose vote finally decides the aggregated outcome. It turned out that the probability to be pivotal is equivalent to the Shapley-Shubik index. Here we give an easy combinatorial proof of this coincidence, further weaken the assumptions of the underlying model, and study generalizations to the case of more than two alternatives.Comment: 19 pages; we added a reference to an earlier proof of our main resul

Essays on Voter Behavior and Government Performance: Econometric Comparative Analysis in America, Europe and Africa

To reduce poverty and undernutrition, as well as promote economic growth, is necessary the development and implementation of efficient policies. In political theory, elections are considered a fundamental democratic mechanism to guarantee high government performance, since they should reflect the interests of the whole society and serve to control the government. However, in reality, electoral competition often leads to the implementation of distorted policies and low governmental performance. It is widely accepted that democracy, when compared to other political systems, is more efficient promoting economic growth and well-being. The question then arises as to how can be explained the difference in economic development between countries that are democracies with multi-party systems. In this dissertation we study the factors that influence voting behavior in Honduras, as well as in other developing and developed countries. In addition, we analyze the impact of the electoral decision to either vote or abstain on government performance. For the analysis of voting behavior, we consider the three voting motives: policy, retrospective and non-policy. Also, since democratically elected politicians seek to maximize their vote share, the understanding of inefficient and biased policy implementation has to be based on voting behavior analysis and, nowadays, the probabilistic voter model is the workhorse model applied in voter studies. More specifically, we apply two different approaches: the Latent Class Model to allow for heterogeneity, and the Nested Multinomial Logit Model. With the results of these estimations, we calculated marginal and relative marginal effects to measure the relative importance of the three voting motives. Finally, with the relative marginal effects we derive indices to measure government performance and to empirically analyze how voting behavior incentives de government to develop efficient policies adapted to the needs of the country

10101 Abstracts Collection -- Computational Foundations of Social Choice

From March 7 to March 12, 2010, the Dagstuhl Seminar 10101 ``Computational Foundations of Social Choice \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Power in voting rules with abstention: an axiomatization of a two components power index

The final publication is available at Springer via http://dx.doi.org/10.1007/s10479-016-2124-5In order to study voting situations when voters can also abstain and the output is binary, i.e., either approval or rejection, a new extended model of voting rule was defined. Accordingly, indices of power, in particular Banzhaf’s index, were considered. In this paper we argue that in this context a power index should be a pair of real numbers, since this better highlights the power of a voter in two different cases, i.e., her being crucial when switching from being in favor to abstain, and from abstain to be contrary. We also provide an axiomatization for both indices, and from this a characterization as well of the standard Banzhaf index (the sum of the former two) is obtained. Some examples are provided to show how the indices behave.Peer ReviewedPostprint (author's final draft

On the not-preference-based Hoede-Bakker index

The paper concerns a certain modification of the generalized Hoede-Bakker index - a notion defined for a social network of players. In the original Hoede-Bakker set up, preferences of players are involved. It is assumed that a player has an inclination either to accept or to reject a proposal, but due to the influence of others, his final decision may be different from his original inclination. In this paper, we propose the not-preference-based (NPB) generalized Hoede-Bakker index, where feasible strategies instead of players' inclinations are considered. We show that if all feasible strategy profiles are equally probable, then the NPB generalized Hoede-Bakker index is a 'net' Success, i.e., 'Success - Failure', where Success and Failure of a player is defined as the probability that the player is successful and fails, respectively. Moreover, under the assumption of equal probabilities of all feasible strategy profiles, we show that the probability that a player is lucky (Luck) equals the probability that he fails (Failure). Since Success - Luck = Decisiveness, it follows that, under the same assumption, the NPB generalized Hoede-Bakker index is equal to the probability that a player is decisive.Hoede-Bakker index ; feasible strategy ; success ; failure ; decisiveness