Ron_s+Theorem

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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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 largest possible, making player P’s Banzhaf power the largest possible in
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/20/2012 for the course MATH 103 taught by Professor Berkowitz during the Spring '07 term at Rutgers.

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online