1. What is the Shubik Power Index?

The Shubik Power Index is a mathematical measurement of the voting power of participants in a weighted voting system. It calculates the probability that a voter will be the pivotal voter who turns a losing coalition into a winning one.

2. How Does the Calculator Work?

The calculator uses the Shubik Power Index formula:

Where:

• Pivotal Positions - Number of times a voter is the critical voter
• Total Sequences - Total number of possible voting sequences (2^(n-1))

Explanation: The index considers all possible orders in which voters could join a coalition and identifies how often each voter is the one that makes the coalition reach the quota.

3. Importance of Power Index Calculation

Details: Power indices help analyze voting systems, determine fair representation, and understand the actual influence of voters beyond their nominal voting weights.

4. Using the Calculator

Tips: Enter the number of voters, their voting weights (comma separated), and the quota required to pass a motion. All values must be positive integers.

5. Frequently Asked Questions (FAQ)

Q1: What is a pivotal voter?
A: A voter whose addition to a coalition turns it from losing to winning, making them the critical voter in that sequence.

Q2: How does this differ from Banzhaf Power Index?
A: Shubik considers the order of joining coalitions, while Banzhaf considers all possible coalitions without regard to order.

Q3: What are typical SPI values?
A: Values range from 0 (no power) to 1 (complete power), with the sum of all voters' SPI equaling 1.

Q4: When is the Shubik index used?
A: Commonly used in political science, corporate governance, and any weighted voting system analysis.

Q5: Are there limitations to this index?
A: Computational complexity increases exponentially with more voters, making it impractical for very large voting bodies.