In the earlier post, we saw how the plurality method of voting works. In the plurality method, the choice with the most first preference votes is declared the winner. In the example, the library won the election event (with 66 out of 150 first-choice votes), although it did not get a majority.
| # Voters | 41 | 25 | 13 | 26 | 30 | 15 |
| 1st Choice | L | L | F | F | C | C |
| 2nd Choice | F | C | L | C | F | L |
| 3rd Choice | C | F | C | L | L | F |
Condorcet criterion
If there is a winner in this case that wins every one-to-one comparison, we call it a Condorcet winner. Let’s find out who the Condorcet winner is in the earlier example.
Step 1: Ignore the one not in the comparison
Step 2: Add all votes of each
Step 3: The one that has the most votes is the winner of the matchup
L vs F
| # Voters | 41 | 25 | 13 | 26 | 30 | 15 |
| 1st Choice | L | L | F | F | ||
| 2nd Choice | F | L | F | L | ||
| 3rd Choice | F | L | L | F |
L is preferred over F by 41 + 25 + 15 = 81 votes
F is preferred over L by 13 + 26 + 30 = 69 votes
L wins the matchup
C vs F
| # Voters | 41 | 25 | 13 | 26 | 30 | 15 |
| 1st Choice | F | F | C | C | ||
| 2nd Choice | F | C | C | F | ||
| 3rd Choice | C | F | C | F |
C = 25 + 30 + 15 = 70
F = 41 + 13 + 26 = 80
F wins
L vs C
| # Voters | 41 | 25 | 13 | 26 | 30 | 15 |
| 1st Choice | L | L | C | C | ||
| 2nd Choice | C | L | C | L | ||
| 3rd Choice | C | C | L | L |
L = 41 + 25 + 13 = 79
C = 26 + 30 + 15 = 71
L wins
Since L wins both its one-to-one comparisons, it becomes the Condorcet winner.
