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.
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.
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.