Math Problem Statement

Consider the weighted voting system [51: 30, 30, 30, 10]. Write a few sentences explaining to a friend who hasn't taken this class why it might not make sense to say that Player 4 has 10% of the power in this system even though they have 10% of the votes. You can assume that your friend understands how a weighted voting system works.

Solution

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Math Problem Analysis

Mathematical Concepts

Weighted Voting Systems
Voting Power
Banzhaf Power Index
Coalition Formation

Formulas

Banzhaf Power Index formula: Number of times a player is critical ÷ Total critical instances

Theorems

Banzhaf Power Theorem

Suitable Grade Level

Undergraduate Level