2 Similar Ways to Compare Winners

Pairwise Comparisons Method and Condorcet Criterion Method

Pairwise Comparisons Method

How does it work?

The pairwise comparisons method places each competitor head to head in a round robin type matchup. The winner of each matchup gains one point towards their final score. After all the matchups are done, the competitor with the most points wins.


Example:

Say the competitors are for favorite color: Blue, Red, and Green

Below are the votes for each order of choice.

12 votes- B>R>G

9 Votes- R>B>G

7 votes- G>R>B


We then compare each head to head to determine a winner.

Blue vs. Red

12 votes for blue, 9 votes for red, and 7 votes for red

Red had 16 votes which is more than blue's 12 votes; Red gets a point

Red vs. Green

12 votes for red, 9 votes for red, 7 votes for green

Red wins with 21 votes and gets another point

Green vs. Blue

12 votes for blue, 9 votes for blue, 7 votes for green

Blue wins with 21 votes and gets a point

Red would win overall because it had two point while blue had one and green had zero.

Condorcet Criterion Method

How does it work?

Similar to the pairwise comparisons method, the Condorcet method also places each competitor head to head. The difference is that in the pairwise method, the winner had the most points. In the Condorcet method, the winner must win ALL of its matchups. If no competitor wins all of their matchups, there is no Condorcet winner.


Example:

Say we are deciding between favorite brand. There is Nike, Adidas, and Under Armour.

8 votes- N>A>UA

7 votes- UA>N>A

5 votes- A>N>UA


Now compare head to head.

Nike vs. Under Armour

Nike wins with 13 votes compared to 7 votes

Nike vs. Adidas

Nike wins 15 votes compared to 5 votes

Adidas vs. Under Armour

Adidas wins with 13 votes compared to 7 votes


The Condorcet winner would be Nike because it won both (All) of its matchups. The Condorcet loser is Under Armour because it lost both (All) of its matchups.

By: Zach and Derrick