The Banzhaf Index Calculator is a valuable tool for calculating a player’s power in a voting system or coalition game, represented as a percentage.
By knowing how often a player is critical in winning coalitions, this calculator provides insights into their influence over decisions. This is especially useful in political science, economics, and game theory.
How to use the Calculator:
- Enter any two of the following values:
- Number of Winning Coalitions a Player is Part of
- Total Number of Winning Coalitions in the Game
- Banzhaf Index (%)
- The calculator will compute the missing value based on the provided inputs.
- Click Calculate to get the result or Reset to clear the fields.
Solved Calculations
Example 1
Step |
Calculation |
Winning Coalitions a Player is Part of |
15 |
Total Winning Coalitions |
50 |
Banzhaf Index (%) |
(to be calculated) |
Calculation |
(15 / 50) × 100 = 30% |
In this example, if a player is part of 15 out of 50 winning coalitions, their Banzhaf Index is calculated to be 30%.
Example 2
Step |
Calculation |
Winning Coalitions a Player is Part of |
10 |
Banzhaf Index (%) |
20% |
Total Winning Coalitions |
(to be calculated) |
Calculation |
10 / (20 / 100) = 50 coalitions |
Here, with 10 winning coalitions for the player and a Banzhaf Index of 20%, the total number of winning coalitions in the game is calculated to be 50. This calculation provides insights into the player’s proportional power in decision-making processes.