Manipulating the Quota in Weighted Voting Games


Zuckerman, Michael, Faliszewski, Piotr , Bachrach, Yoram and Elkind, Edith (2008) Manipulating the Quota in Weighted Voting Games. In, Twenty-Third AAAI Conference on Artificial Intelligence, Chicago, 13 - 17 Jul 2008.

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Description/Abstract

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 {\em 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.

Item Type: Conference or Workshop Item (Paper)
Additional Information: Event Dates: July 13--17, 2008
Divisions: Faculty of Physical Sciences and Engineering > Electronics and Computer Science
ePrint ID: 266715
Date Deposited: 25 Sep 2008 11:24
Last Modified: 27 Mar 2014 20:12
Further Information:Google Scholar
URI: http://eprints.soton.ac.uk/id/eprint/266715

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