1. What is a Weighted Voting System Calculator?

Definition: This calculator determines the voting power of participants in a weighted voting system using power indices.

Purpose: It helps analyze political systems, corporate voting, or any scenario where voters have different weights.

2. How Does the Calculator Work?

The calculator evaluates power using the formula:

Where:

• Power — Voting power as a percentage
• Number of Winning Coalitions — Coalitions where voter is pivotal
• Total Coalitions — All possible voting combinations

Explanation: The calculator examines all possible voter combinations to determine how often each voter's support is crucial to reaching the quota.

3. Importance of Voting Power Analysis

Details: Understanding voting power reveals whether weight distributions actually translate to influence, helping design fairer systems.

4. Using the Calculator

Tips: Enter the number of voters, the quota (threshold to pass a motion), and each voter's weight (comma separated).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between weight and power?
A: Weight is a voter's assigned value, while power is their actual influence considering all possible voting scenarios.

Q2: How is the quota determined?
A: Typically a majority (e.g., 51 for weights summing to 100) or supermajority (e.g., 67 for 2/3 majority).

Q3: What are common power indices?
A: The Banzhaf index (used here) and Shapley-Shubik index are most common for measuring voting power.

Q4: Can small voters have disproportionate power?
A: Yes, in some systems small voters can be pivotal more often than their weight suggests.

Q5: How does the number of voters affect calculation time?
A: Computation grows exponentially with more voters (2^n possible coalitions).