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Chapter 2 Weighted Voting Systems

# Chapter 2 Weighted Voting Systems - Excursions in Modern...

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1 Excursions in Modern Mathematics Sixth Edition Peter Tannenbaum

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2 Chapter 2 Weighted Voting Systems The Power Game
3 Weighted Voting Systems Outline/learning Objectives Represent a weighted voting system using a mathematical model. Use the Banzhaf and Shapley-Shubik indices to calculate the distribution of power in a weighted voting system.

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4 Weighted Voting Systems 2.1 Weighted Voting Systems
5 Weighted Voting Systems The Players The Players The voters in a weighted voting system. The Weights The Weights That each player controls a certain number of votes. The Quota The Quota The minimum number of votes needed to pass a motion (yes-no votes)

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6 Weighted Voting Systems Dictator Dictator The player’s weight is bigger than or equal to the quota. Consider [11:12, 5, 4] owns enough votes to carry a motion single handedly. P 1
7 Weighted Voting Systems Dummy Dummy A player with no power. Consider [30: 10, 10, 10, 9] turns out to be a dummy! There is never going to be a time when is going to make a difference in the outcome of the voting. P 4 P 4

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8 Weighted Voting Systems Veto Power Veto Power If a motion cannot pass unless player votes in favor of the motion. Consider [12: 9, 5, 4, 2] has the power to obstruct by preventing any motion from passing. P 1
9 Weighted Voting Systems 2.2 The Banzhaf Power Index

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10 Weighted Voting Systems Coalitions Coalitions Any set of players that might join forces and vote the same way. The coalition consisting of all the players is called a grand coalition .
11 Weighted Voting Systems Winning Coalitions Winning Coalitions Some coalitions have enough votes to win and some don’t. We call the former winning coalitions and the latter losing coalitions .

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Chapter 2 Weighted Voting Systems - Excursions in Modern...

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