Question

The given table shows the schedule for an election with five candidates (A, B, C, D, and E). The number of voters in this election was very large, so the of the preference schedule give the percent of voters instead of the number of voters. Find the winner of the election using the method of pairwise comparisons. 24 23 17 15 12 1st 2 of 3

Answer 1

Number of pair-wise comparisons = n(n - 1)/2 = 5(5 - 1)/2 = 10
The comparison pairs are {AB, AC, AD, AE, BC, BD, BE, CD, CE, DE}
A vs B:	A = 24 + 23 + 15 + 12 = 74			Winner = A
	B = 17 + 9 = 26
A vs C:	A = 15			Winner = C
	C = 24 + 23 + 17 + 12 + 9 = 85
A vs D:	A = 24 + 15 + 12 = 51			Winner = A
	D = 23 + 17 + 9 = 49
A vs E:	A = 15			Winner = E
	E = 24 + 23 + 17 + 12 + 9 = 85
B vs C:	B = 0			Winner = C
	C = 24 + 23 + 17 + 15 + 12 + 9 = 100
B vs D:	B = 24 + 12 = 36			Winner = D
	D = 23 + 17 + 15 + 9 = 64
B vs E:	B = 17			Winner = E
	E = 24 + 23 + 15 + 12 + 9 = 83
C vs D:	C = 24 + 15 + 12 = 51			Winner = C
	D = 23 + 17 + 9 = 49
C vs E:	C = 23 + 17 + 12 = 52			Winner = C
	E = 24 + 15 + 9 = 48
D vs E:	D = 23 + 17 + 9 = 49			Winner = D
	E = 24 + 15 + 12 = 51

Points Table: A = 2, B = 0, C = 4, D = 2, E = 2
Winner of the election = C