Back to Condorcet Method Labs: Voting and Social Choice. Part 1. Math Alive

## Detailed Explanation for Condorcet Method Example

group of 18 group of 12 group of 10 group of 9 group of 4 group of 2
Killians512424
Molson155555
Guinness441242
Meister Brau323311

Let's first start with Killians. Here are the results of comparing Killians against every other beer:

Killians

Ratio of Killians supportersWinner
Molson 37 / 18Killians
Guinness 16 / 39Guinness
Meister Brau22 / 33Meister Brau

37 / 18 means that 37 people prefer Killians over Molson. Killians only wins one of the four pairings, and is therefore not the winner. Now let's look at Molson:

Molson

Ratio of Molson supportersWinner
Killians 18 / 37Killians
Guinness 18 / 37Guinness
Meister Brau18 / 37Meister Brau

Molson doesn't win any pairings; clearly it is not the winner. Comparing Samuel Adams with every other beer yields the following results:

Meister Brau27 / 28Meister Brau

Samuel Adams lost when compared with Meister Brau, and therefore does not win. Next we look at Guinness:

Guinness

Ratio of Guinness supportersWinner
Killians 39 / 16Guinness
Molson37 / 18Guinness
Meister Brau19 / 36Meister Brau

Guinness only wins half of the time; it is not the winner. Finally, we compare Meister Brau against every other beer. Here are the results:

Meister Brau

Ratio of Meister Brau supportersWinner
Killians 33 / 22Meister Brau
Molson37 / 18Meister Brau
Samuel Adams 28 / 27Meister Brau
Guinness36 / 19Meister Brau

Meister Brau wins every match-up. Therefore, it is the overall winner.