https://file.aiquickdraw.com/mathbot/file/1726344962699l20o4r11.jpg

It looks like you've uploaded an image related to finding the **Shapley-Shubik power distribution** for different weighted voting systems. Let me help you work through the problem shown in the image.

In the problem, the goal is to calculate the Shapley-Shubik power index for each player in different voting systems represented by weights:

1. **System (a)**: [14: 14, 8, 3, 2]
2. **System (b)**: [17: 14, 8, 3, 2]
3. **System (c)**: [25: 14, 8, 3, 2]

For system (b), you already have the following results:
\[
\sigma_1 = \frac{2}{3}, \, \sigma_2 = \frac{1}{6}, \, \sigma_3 = \frac{1}{6}, \, \sigma_4 = 0
\]

Would you like me to calculate the power indices for system (c) or explain the details of how the Shapley-Shubik power index works? I can also help you fill in any missing steps for system (a) or (c).

Let me know if you need a detailed explanation or would like to proceed with calculations for part (c).

Also, here are five questions related to Shapley-Shubik power indices:
1. What is the intuition behind the Shapley-Shubik power index in voting systems?
2. How do the weights in a voting system affect the power distribution among players?
3. What is the difference between the Shapley-Shubik index and other power indices like Banzhaf?
4. Why might a player with zero votes in a system still influence the Shapley-Shubik power index?
5. How does the quota in a weighted voting system impact the outcome of power indices?

**Tip**: In many voting systems, the largest weight doesn’t always equate to the greatest power.

Find the Shapley-Shubik power distribution of each of the following weighted voting systems: (a) [14: 14, 8, 3, 2], (b) [17: 14, 8, 3, 2], (c) [25: 14, 8, 3, 2]

This problem involves calculating the Shapley-Shubik power index for different weighted voting systems, including [14: 14, 8, 3, 2], [17: 14, 8, 3, 2], and [25: 14, 8, 3, 2]. The solution includes detailed steps for determining the power distribution across voters.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation