False-Name Manipulation in Weighted Voting Games Is Hard for Probabilistic Polynomial Time (original) (raw)

False-Name Manipulations in Weighted Voting Games

Journal of Artificial Intelligence Research, 2011

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.

Divide and conquer: False-name manipulations in weighted voting games

2008

Weighted voting is a well-known model of cooperation among agents in decisionmaking domains. In such games, each player has a weight, and a coalition of players wins if its total weight meets or exceeds a given quota. Usually, the agents' power in such games is measured by a power index, such as, e.g., Shapley-Shubik index.

False‐Name Manipulation in Weighted Voting Games: Empirical and Theoretical Analysis

Computational Intelligence, 2016

Weighted voting games are important in multiagent systems because of their usage in automated decision making. However, they are not immune from the vulnerability of false-name manipulation by strategic agents that may be present in the games. False-name manipulation involves an agent splitting its weight among several false identities in anticipation of power increase. Previous works have considered false-name manipulation using the well-known Shapley-Shubik and Banzhaf power indices. Bounds on the extent of power that a manipulator may gain exist when it splits into k D 2 false identities for both the Shapley-Shubik and Banzhaf indices. The bounds when an agent splits into k > 2 false identities, until now, have remained open for the two indices. This article answers this open problem by providing four nontrivial bounds when an agent splits into k > 2 false identities for the two indices. Furthermore, we propose a new bound on the extent of power that a manipulator may gain when it splits into several false identities in a class of games referred to as excess unanimity weighted voting games. Finally, we complement our theoretical results with empirical evaluation. Results from our experiments confirm the existence of beneficial splits into several false identities for the two indices, and also establish that splitting into more than two false identities is qualitatively different than the previously known splitting into exactly two false identities.

NP-completeness of some problems concerning voting games

International Journal of Game Theory, 1990

The problem of confirming lower bounds on the number of coalitions for which an individual is pivoting is NP-complete. Consequently, the problem of confirming non-zero values of power indices is NP-complete. The problem of computing the Absolute Banzhaf index is #P-complete. Related problems for power indices are discussed.

Complexity of some aspects of control and manipulation in weighted voting games}

2009

An important aspect of mechanism design in social choice protocols and multiagent systems is to discourage insincere behaviour. Manipulative behaviour has received increased attention since the famous Gibbard-Satterthwaite theorem. We examine the computational complexity of manipulation in weighted voting games which are ubiquitous mathematical models used in economics, political science, neuroscience, threshold logic, reliability theory and distributed systems. It is a natural question to check how changes in weighted voting game may affect the overall game. Tolerance and amplitude of a weighted voting game signify the possible variations in a weighted voting game which still keep the game unchanged. We characterize the complexity of computing the tolerance and amplitude of weighted voting games. Tighter bounds and results for the tolerance and amplitude of key weighted voting games are also provided. Moreover, we examine the complexity of manipulation and show limits to how much the Banzhaf index of a player increases or decreases if it splits up into sub-players. It is shown that the limits are similar to the previously examined limits for the Shapley-Shubik index. A pseudo-polynomial algorithm to find the optimal split is also provided.

An approximation method for power indices for voting games

2011

The Shapley value and Banzhaf index are two well known indices for measuring the power a player has in a voting game. However, the problem of computing these indices is computationally hard. To overcome this problem, we analyze approximation methods for computing these indices. Although these methods have polynomial time complexity, finding an approximate Shapley value using them is easier than finding an approximate Banzhaf index. We also find the absolute error for the methods and show that this error for the Shapley value is lower than that for the Banzhaf index.

Manipulating the quota in weighted voting games

Artificial Intelligence, 2012

Weighted voting games provide a popular model of decision making in multiagent systems. Such games are described by a set of players, a list of players' weights, and a quota; a coalition of the players is said to be winning if the total weight of its members meets or exceeds the quota. The power of a player in such games is traditionally identified with her Shapley-Shubik index or her Banzhaf index, two classical power measures that reflect the player's marginal contributions under different coalition formation scenarios. In this paper, we investigate by how much the central authority can change a player's power, as measured by these indices, by modifying the quota. We provide tight upper and lower bounds on the changes in the individual player's power that can result from a change in quota. We also study how the choice of quota can affect the relative power of the players. From the algorithmic perspective, we provide an efficient algorithm for determining whether there is a value of the quota that makes a given player a dummy, i.e., reduces his power (as measured by both indices) to 0. On the other hand, we show that checking which of the two values of the quota makes this player more powerful is computationally hard, namely, complete for the complexity class PP, which is believed to be significantly more powerful than NP.

Optimal False-Name-Proof Voting Rules with Costly Voting

Proceedings of the 23rd National Conference on Artificial Intelligence Volume 1, 2008

One way for agents to reach a joint decision is to vote over the alternatives. In open, anonymous settings such as the Internet, an agent can vote more than once without being detected. A voting rule is false-name-proof if no agent ever benefits from casting additional votes. Previous work has shown that all false-name-proof voting rules are unresponsive to agents' preferences. However, that work implicitly assumes that casting additional votes is costless. In this paper, we consider what happens if there is a cost to casting additional votes. We characterize the optimal (most responsive) false-name-proofwith-costs voting rule for 2 alternatives. In sharp contrast to the costless setting, we prove that as the voting population grows larger, the probability that this rule selects the majority winner converges to 1. We also characterize the optimal group false-name-proof rule for 2 alternatives, which is robust to coalitions of agents sharing the costs of additional votes. Unfortunately, the probability that this rule chooses the majority winner as the voting population grows larger is relatively low. We derive an analogous rule in a setting with 3 alternatives, and provide bounding results and computational approaches for settings with 4 or more alternatives.

Annexations and Merging in Weighted Voting Games

This paper discusses weighted voting games and two methods of manipulating those games, called annexation and merging. These manipulations allow either an agent, called an annexer to take over the voting weights of some other agents in the game, or the coming together of some agents to form a bloc of manipulators to have more power over the outcomes of the games. We evaluate the extent of susceptibility to these manipulations in weighted voting games of the following prominent power indices: Shapley-Shubik, Banzhaf, and Deegan-Packel indices. We found that for unanimity weighted voting games of n agents and for the three indices: the manipulability, (i.e., the extent of susceptibility to manipulation) via annexation of any one index does not dominate that of other indices, and the upper bound on the extent to which an annexer may gain while annexing other agents is at most n times the power of the agent in the original game. Experiments on non unanimity weighted voting games suggest that the three indices are highly susceptible to manipulation via annexation while they are less susceptible to manipulation via merging. In both annexation and merging, the Shapley-Shubik index is the most susceptible to manipulation among the indices.

ANNEXATIONS AND MERGING IN WEIGHTED VOTING GAMES - The Extent of Susceptibility of Power Indices

Proceedings of the 3rd International Conference on Agents and Artificial Intelligence, 2011

False-Name Manipulation in Weighted Voting Games Is Hard for Probabilistic Polynomial Time (original) (raw)

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