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Ron_s+Theorem

# Ron_s+Theorem - Rons connection between veto power and...

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Ron’s connection between veto power and Banzhaf power The weight of a player is not a good predictor of a player’s Banzhaf power. As Ron pointed out in class, the key is not the weight, but the number of times a player is a critical player in a winning coalition. Ron reminded us that since a player P with veto power is critical in every winning coalition, then player P will be critical the maximum number of times possible, giving player P the largest amount of Banzhaf power. In summary, if a player has veto power, then this player will have the largest amount of Banzhaf power. We have: Ron’s Theorem : If a player P in a weighted voting system has veto power, then player P has the largest amount of Banzhaf power in this weighted voting system. Proof: Player P has veto power. Hence player P is in every winning coalition. Moreover, player P is critical in every winning coalition. So the numerator of the Banzhaf power distribution for player P will be the

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