Committees are an important scenario for reaching consensus. Beyond standard consensus-seeking issues, committee decisions are complicated by a deadline, e.g., the next start date for a budget, or the start of a semester. In committee hiring decisions, it may be that if no candidate is supported by a strong majority, the default is to hire no one---an option that may cost committee members dearly. As a result, committee members might prefer to agree on a reasonable, if not necessarily the best, candidate, to avoid unfilled positions. In this paper we propose a model for the above scenario------based on a time-bounded iterative voting process. We explore theoretical features of CUDs, particularly focusing on convergence guarantees and quality of the final decision. An extensive experimental study demonstrates more subtle features of CUDs, e.g., the difference between two simple types of committee member behavior, lazy vs. proactive voters. Finally, a user study examines the differences between the behavior of rational voting bots and real voters, concluding that it may often be best to have bots play on the voters' behalf.
A CUD game is a type of iterative voting game, e.g., @cite_8 @cite_24 @cite_14 @cite_6 @cite_16 . However, CUDs have several unique features. First, although CUDs do utilise a known voting rule, they work directly with the set of possible winners (i.e., alternatives that might be chosen by the majority), and behave much like non-myopic games based on local-dominance (see, e.g., @cite_19 @cite_18 @cite_5 ). On the other hand, the distinction between lazy and proactive voter behaviour links CUDs with biased voting (see, e.g., @cite_10 ).
@cite_18 @cite_14 @cite_8 @cite_6 @cite_24 @cite_19 @cite_5 @cite_16 @cite_10
2050727325 1605139543 1852468282 2015247315
Simple games cover voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes–no voting system is a set of rules that specifies exactly which collections of “yea” votes yield passage of the issue at hand, each of these collections of “yea” voters forms a winning coalition. We are interested in performing a complexity analysis on problems defined on such families of games. This analysis as usual depends on the game representation used as input. We consider four natural explicit representations: winning, losing, minimal winning, and maximal losing. We first analyze the complexity of testing whether a game is simple and testing whether a game is weighted. We show that, for the four types of representations, both problems can be solved in polynomial time. Finally, we provide results on the complexity of testing whether a simple game or a weighted game is of a special type. We analyze strongness, properness, decisiveness and homogeneity, which are desirable properties to be fulfilled for a simple game. We finalize with some considerations on the possibility of representing a game in a more succinct representation showing a natural representation in which the recognition problem is hard. Simple coalitional games are a fundamental class of cooperative games and voting games which are used to model coalition formation, resource allocation and decision making in computer science, artificial intelligence and multiagent systems. Although simple coalitional games are well studied in the domain of game theory and social choice, their algorithmic and computational complexity aspects have received less attention till recently. The computational aspects of simple coalitional games are of increased importance as these games are used by computer scientists to model distributed settings. This thesis fits in the wider setting of the interplay between economics and computer science which has led to the development of algorithmic game theory and computational social choice. A unified view of the computational aspects of simple coalitional games is presented here for the first time. Certain complexity results also apply to other coalitional games such as skill games and matching games. The following issues are given special consideration: influence of players, limit and complexity of manipulations in the coalitional games and complexity of resource allocation on networks. The complexity of comparison of influence between players in simple games is characterized. The simple games considered are represented by winning coalitions, minimal winning coalitions, weighted voting games or multiple weighted voting games. A comprehensive classification of weighted voting games which can be solved in polynomial time is presented. An efficient algorithm which uses generating functions and interpolation to compute an integer weight vector for target power indices is proposed. Voting theory, especially the Penrose Square Root Law, is used to investigate the fairness of a real life voting model. Computational complexity of manipulation in social choice protocols can determine whether manipulation is computationally feasible or not. The computational complexity and bounds of manipulation are considered from various angles including control, false-name manipulation and bribery. Moreover, the computational complexity of computing various cooperative game solutions of simple games in dierent representations is studied. Certain structural results regarding least core payos extend to the general monotone cooperative game. The thesis also studies a coalitional game called the spanning connectivity game. It is proved that whereas computing the Banzhaf values and Shapley-Shubik indices of such games is #P-complete, there is a polynomial time combinatorial algorithm to compute the nucleolus. The results have interesting significance for optimal strategies for the wiretapping game which is a noncooperative game defined on a network. Weighted voting games are a popular model of collaboration in multiagent systems. In such games, each agent has a weight (intuitively corresponding to resources he can contribute), and a coalition of agents wins if its total weight meets or exceeds a given threshold. Even though coalitional stability in such games is important, existing research has nonetheless only considered the stability of the grand coalition. In this paper, we introduce a model for weighted voting games with coalition structures. This is a natural extension in the context of multiagent systems, as several groups of agents may be simultaneously at work, each serving a different task. We then proceed to study stability in this context. First, we define the CS-core, a notion of the core for such settings, discuss its non-emptiness, and relate it to the traditional notion of the core in weighted voting games. We then investigate its computational properties. We show that, in contrast with the traditional setting, it is computationally hard to decide whether a game has a non-empty CS-core, or whether a given outcome is in the CS-core. However, we then provide an efficient algorithm that verifies whether an outcome is in the CS-core if all weights are small (polynomially bounded). Finally, we also suggest heuristic algorithms for checking the non-emptiness of the CS-core. A simple game is a pair consisting of a finite set N of players and a set of winning coalitions. (Vector-) weighted majority games ((V) WMG) are a special case of simple games, in which an integer (vector) weight can be assigned to each player and there is a quota which a coalition has to achieve in order to win. Binary decision diagrams (BDDs) are used as compact representations for Boolean functions and sets of subsets. This paper shows, how a quasi-reduced and ordered BDD (QOBDD) of the winning coalitions of a (V) WMG can be build, how one can compute the minimal winning coalitions and how one can easily compute the Banzhaf, Shapley-Shubik, Holler-Packel and Deegan-Packel indices of the players. E.g. in case of weighted majority games it is shown that the Banzhaf and Holler-Packel indices of all players can be computed in expected time and in general, the Banzhaf indices can be computed in time linear in the size of the QOBDD representation of the winning coalitions. Other running times are proven as well. The algorithms were tested on some real world games, e.g. the International Monetary Fund and the EU Treaty of Nice.