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Banzhaf Index Calculator

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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.

Banzhaf Index Calculator

Enter the number of winning coalitions involving the player:

Enter the total number of winning coalitions in the game:

Enter the Banzhaf Index as a percentage (optional):

How to use the Calculator:

  1. 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 (%)
  2. The calculator will compute the missing value based on the provided inputs.
  3. 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.

 

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