Multilinear extensions and the banzhaf value
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It is shown that the Banzhaf value can be obtained by differentiating the multilinear extension of a game at the midpoint of the unit cube. This gives us a composition theorem for the value of compound games. As an example, the values of the electoral college and presidential election “games” are approximated by the method of extensions.
[1] Guillermo Owen,et al. Evaluation of a Presidential Election Game , 1975, American Political Science Review.
[2] G. Owen. Multilinear Extensions of Games , 1972 .
[3] Banzhaf,et al. One Man, 3.312 Votes: A Mathematical Analysis of the Electoral College , 1968 .