TY - JOUR
T1 - Analyzing Power in Weighted Voting Games with Super-Increasing Weights
AU - Filmus, Yuval
AU - Oren, Joel
AU - Zick, Yair
AU - Bachrach, Yoram
N1 - Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2019/1/15
Y1 - 2019/1/15
N2 - Weighted voting games (WVGs) are a class of cooperative games that capture settings of group decision making in various domains, such as parliaments or committees. Earlier work has revealed that the effective decision making power, or influence of agents in WVGs is not necessarily proportional to their weight. This gave rise to measures of influence for WVGs. However, recent work in the algorithmic game theory community have shown that computing agent voting power is computationally intractable. In an effort to characterize WVG instances for which polynomial-time computation of voting power is possible, several classes of WVGs have been proposed and analyzed in the literature. One of the most prominent of these are super increasing weight sequences. Recent papers show that when agent weights are super-increasing, it is possible to compute the agents’ voting power (as measured by the Shapley value) in polynomial-time. We provide the first set of explicit closed-form formulas for the Shapley value for super-increasing sequences. We bound the effects of changes to the quota, and relate the behavior of voting power to a novel function. This set of results constitutes a complete characterization of the Shapley value in weighted voting games, and answers a number of open questions presented in previous work.
AB - Weighted voting games (WVGs) are a class of cooperative games that capture settings of group decision making in various domains, such as parliaments or committees. Earlier work has revealed that the effective decision making power, or influence of agents in WVGs is not necessarily proportional to their weight. This gave rise to measures of influence for WVGs. However, recent work in the algorithmic game theory community have shown that computing agent voting power is computationally intractable. In an effort to characterize WVG instances for which polynomial-time computation of voting power is possible, several classes of WVGs have been proposed and analyzed in the literature. One of the most prominent of these are super increasing weight sequences. Recent papers show that when agent weights are super-increasing, it is possible to compute the agents’ voting power (as measured by the Shapley value) in polynomial-time. We provide the first set of explicit closed-form formulas for the Shapley value for super-increasing sequences. We bound the effects of changes to the quota, and relate the behavior of voting power to a novel function. This set of results constitutes a complete characterization of the Shapley value in weighted voting games, and answers a number of open questions presented in previous work.
KW - Weighted voting games
KW - Shapley values
UR - http://www.scopus.com/inward/record.url?scp=85046396672&partnerID=8YFLogxK
U2 - 10.1007/s00224-018-9865-2
DO - 10.1007/s00224-018-9865-2
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
SN - 1432-4350
VL - 63
SP - 150
EP - 174
JO - Theory of Computing Systems
JF - Theory of Computing Systems
IS - 1
ER -