Enter the number of winning coalitions a player is a part of and the total number of winning coalitions in the game into the calculator to determine the Banzhaf Index. This calculator can also evaluate any of the variables given the others are known.

## Banzhaf Index Formula

The following formula is used to calculate the Banzhaf Index.

BI = (W / T) * 100

Variables:

• BI is the Banzhaf Index (%)
• W is the number of winning coalitions a player is a part of
• T is the total number of winning coalitions in the game

To calculate the Banzhaf Index, divide the number of winning coalitions a player is a part of by the total number of winning coalitions in the game. Multiply the result by 100 to convert it to a percentage. This will give you the Banzhaf Index, which measures a player’s voting power in a weighted voting game.

## What is a Banzhaf Index?

The Banzhaf Index, also known as the Banzhaf Power Index, is a measure used in game theory and voting theory to quantify the power of a player in a weighted voting game. It is based on the concept of a “swing vote” and calculates the probability that a player’s vote will change the outcome of a decision. The index is named after legal scholar John F. Banzhaf III, who introduced it in the context of the United States Electoral College system.

## How to Calculate Banzhaf Index?

The following steps outline how to calculate the Banzhaf Index.

1. First, determine the number of winning coalitions a player is a part of (W).
2. Next, determine the total number of winning coalitions in the game (T).
3. Next, use the formula BI = (W / T) * 100 to calculate the Banzhaf Index.
4. Finally, calculate the Banzhaf Index.
5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge.

W: 5 (number of winning coalitions a player is a part of)

T: 20 (total number of winning coalitions in the game)