Answer to Question #139390 in Operations Research for Ethan

Question

A. What is weighted voting system?

B. What are the different types of weighted voting?

C. Describe Banzhaf Power Index.

Answer 1

1) Weighted voting is an electoral system that can exist in a legislative body, in which each elected representative has a different voting power as determined by the total number of citizens who voted for them in the general election. Instead, votes of different voters are given different weight during the election.

2) The different types of weighted voting are;

1. Shareholder meetings, where votes are weighted by the number of share that each shareholder owns.
2. United States Electoral College
3. The European Council where the number of votes of each member is proportional to the size of that state's population.

3)The Banzhaf power index refers to a measure of the power of the players in a weighted voting system. Using this index, a player’s power is determined by the ratio of the number of times that player is critical to the total number of times any and all players are critical.

P_i=B_I/T

where Bi is number of times player Pi is critical and T is total number of times all players are critical.