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In a YES-NO voting system, the Shapley-Shubik index and the Banzhaf index can sometimes give different values. If it turns out, though, that any voter

In a YES-NO voting system, the Shapley-Shubik index and the Banzhaf index can sometimes give different values. If it turns out, though, that any voter that has Shapley-Shubik index 0% also has Banzhaf index 0%, and the other way around (any voter with Banzhaf index 0% also has Shapley-Shubik index 0%; so the indices can be different, but only if neither of them is 0%). Explain why this is true. Your explanation should start from the definitions of these indices (that, is, don't just say that it's because these are the dummy voters).

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