Synthese 179 (1):35 - 56 (2011)

Authors
Claus Beisbart
University of Bern
Luc Bovens
University of North Carolina, Chapel Hill
Abstract
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
Keywords Voting power  Banzhaf measure  Counterfactuals  Causal models  Average treatment effect
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DOI 10.1007/s11229-010-9854-8
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Causality: Models, Reasoning and Inference.Judea Pearl - 2000 - Cambridge University Press.
Causation, Prediction, and Search.Peter Spirtes, Clark Glymour & Richard Scheines - 1996 - British Journal for the Philosophy of Science 47 (1):113-123.

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