1. What is the Shapley-Shubik Index?

Definition: The Shapley-Shubik Index measures a voter's power in a weighted voting system by calculating their likelihood of being pivotal in a coalition.

Purpose: It helps analyze voting systems and determine the relative influence of different voters or parties.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( SSI \) — Shapley-Shubik Index (dimensionless)
• Number of Winning Coalitions — Coalitions where voter is pivotal (dimensionless)
• Total Coalitions — Total possible coalitions (dimensionless)

Explanation: The index represents the probability that a voter will be the swing vote in a randomly ordered coalition.

3. Importance of Shapley-Shubik Index

Details: This index is crucial for understanding power distribution in voting systems, political science research, and corporate governance analysis.

4. Using the Calculator

Tips: Enter the number of winning coalitions where the voter is pivotal and the total number of possible coalitions. Both must be positive integers.

5. Frequently Asked Questions (FAQ)

Q1: What does a higher SSI value mean?
A: A higher value (closer to 1) indicates greater voting power in the system.

Q2: What's considered a "winning coalition"?
A: A coalition where the voter's inclusion changes the outcome from losing to winning.

Q3: How is this different from Banzhaf power index?
A: SSI considers order of joining coalitions while Banzhaf doesn't - they measure different aspects of power.

Q4: What's a typical SSI range?
A: Usually between 0 (no power) and 1 (dictator), often fractions in between for most voters.

Q5: Can SSI be calculated for multiple voters?
A: Yes, but this calculator shows for one voter - you'd need to repeat for each voter in the system.