Shapley values in random weighted voting games

Yuval Filmus, Joel Oren and Kannan Soundararajan

We study the distribution of Shapley values in weighted voting games. The Shapley values measure the voting power collective decision making systems. While easy to estimate empirically given the parameters of a weighted voting game, the Shapley values are hard to reason about analytically.

We propose a probabilistic approach, in which the agent weights are drawn i.i.d. from some known exponentially decaying distribution. We provide a general closed-form characterization of the highest and lowest expected Shapley values in such a game, as a function of the parameters of the underlying distribution. To do so, we give a novel reinterpretation of the stochastic process that generates the Shapley variables as a renewal process. We demonstrate the use of our results on the uniform and exponential distributions.


 author = {Yuval Filmus and Joel Oren and Kannan Soundararajan},
 title = {Shapley values in weighted voting games with random weights},
 note = {Manuscript},
 year = {2017}
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