A committee has four voters with the system [30: 20, 17, 10, 5]. Which voters are critical in the coalition {A, C, D}?
A) A only
B) A and C
C) C and D
D) D only

Question

Quizplus · Accepted Answer

To identify the critical voters in the coalition {A, C, D}, we need to find the minimum number of voters whose absence would cause the coalition to no longer have enough votes to pass a motion. 
We can calculate the critical number of voters by summing the weights of the voters in the coalition, and then subtracting 29 (one less than the quota required for passage).

Critical number of voters for {A, C, D}:
= weight of A + weight of C + weight of D - 29
= 30 + 17 + 5 - 29
= 23

This means that any subset of the coalition {A, C, D} with only two voters would not have enough votes to pass a motion. Therefore, the critical voters are A and C, as they both have weights greater than 23.

A Committee Has Four Voters with the System [30: 20