, Volume 179, Supplement 1, pp 35–56 | Cite as

Measuring voting power for dependent voters through causal models

  • Luc Bovens
  • Claus Beisbart


We construct a new measure of voting power that yields reasonable measurements even if the individual votes are not cast independently. Our measure hinges on probabilities of counterfactuals, such as the probability that the outcome of a collective decision would have been yes, had a voter voted yes rather than no as she did in the real world. The probabilities of such counterfactuals are calculated on the basis of causal information, following the approach by Balke and Pearl. Opinion leaders whose votes have causal influence on other voters’ votes can have significantly more voting power under our measure. But the new measure of voting power is also sensitive to the voting rule. We show that our measure can be regarded as an average treatment effect, we provide examples in which it yields intuitively plausible results and we prove that it reduces to Banzhaf voting power in the limiting case of independent and equiprobable votes.


Voting power Banzhaf measure Counterfactuals Causal models Average treatment effect 


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of Philosophy, Logic and Scientific MethodLondon School of Economics and Political ScienceLondonUK
  2. 2.Institute for Philosophy and Political ScienceTU DortmundDortmundGermany

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