Chapter 13 – Weighted Voting. Lecture Part 2. Chapter 13 – Lecture Part 2. The Banzhaf Power Index Counting the number of subsets of a set Listing winning coalitions and blocking coalitions Listing a coalition’s critical voters. Counting Subsets – Finding Banzhaf Power Index.
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Lecture Part 2
A = 26, B = 26
C = 26, D = 22
q = 51
Here we list only the winning coalitions.
Note that A is critical in 4 of the winning coalitions, B is also critical in 4 winning and likewise, C is critical in exactly 4 winning coalitions.
Notice that D is not critical in any winning coalitions.
There are 26 = 64 coalitions, however not all of them are winning coalitions.
= 1 coalition of 6
= 6 coalitions of 5
= 15 coalitions of 4
= 20 coalitions of 3
= 15 coalitions of 2
= 6 coalitions of 1
Let’s refer to the Smith’s as s1 and s2 and the others by the first letter of their last name.
Note: tables list winning coalitions, weight, extra votes, and critical voters, in that order, from left to right.
For each voter, we count the number of times that voter is critical to some coalition ….