Lesson 1.5: Pairwise Comparisons
* Similar to Condorcet head-to-head count, compare all candidates and give 1 point to the winner. If
it is a tie, each gets ½ points. Get the total points for each candidate then declare the winner.
( N  1) N
numbers of comparisons
2
(10  1)10
 45 pairs
For example: for an election of 10 candidates, there are
2
If we have N candidates, then there are
Problem 1: Find the winner under Pairwise Comparisons method
14
A
B
C
D
10
C
B
D
A
8
D
C
B
A
4
B
D
C
A
1
C
D
B
A
Problem 2: Find the winner under Pairwise Comparisons method
2
A
D
C
B
E
6
B
A
C
D
E
4
B
A
D
E
C
1
C
B
A
D
E
1
C
D
A
B
E
4
D
A
E
C
B
4
E
C
D
B
A
The Independent-of-Irrelevant-Alternatives Criterion
If X is a winner of an election and in a recount, one of the non-winning candidates is dropped, then X
should still be the winner.
Problem 3:
4
A
B
C
2
B
C
A
6
C
A
B
3
B
A
C
A) Use the Plurality method to find the winner
B) Use the Plurality with Elimination method to find the winner
C) Use the Borda Count method to find the winner
D) Use Pairwise Comparisons method to find the winner