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The Pairwise Comparison Method and the Condorcet Criterion

BREAK DOWN: The Pairwise Comparison Method.

The Pairwise Comparison Method is a method of comparing many things. In our case we are going to use soda. Let's use Dr. Pepper, Coca-Cola, and Sprite.


SODA:

VOTES: 9 DP > CC > Sprite

7 CC > Sprite > DP

12 Sprite > DP > CC

Now begins the 'math' process. You're going to break it down into groups of two. Kind of like a versus battle. Let's start with Dr. Pepper (DP) vs. Coca-Cola (CC). In the first test (test with 9 votes) Dr. Pepper beats Coca-Cola with votes. You can tell this by looking and seeing that it goes DP > CC. Therefore, DP had more votes total. Even though you don't know the exact votes you know that DP had to gave more votes so you give Dr. Pepper 9 points. Let's go to the next column with 7 voters. In this one you can see that Coca- Cola destroyed Dr. Pepper so you know that Coca- Cola had to have beaten it so you're going to give CC 7 points. Now, let's go to the last column. This one is for 12 points, so it's a big one! In this test neither CC or Dr. Pepper won. However, Dr. Pepper had more votes than CC in total so you're going to give Dr. Pepper 12 points. Now, you add up the points each one got.


Dr. Pepper Coca-Cola

9 ........................7

+ 12.................+ 0

_____ ................_____

21...................... 7


Now you can tell that overall Dr. Pepper had more votes so in the...


Dr. Pepper VS. Coca-Cola VS. Sprite comparison now Dr. Pepper has 1 point.

.........1........................ 0............... 0


You're going to continue this process until you've done DP VS Sprite and CC VS. Sprite, and eventually it should end up with a tie between CC and Sprite. Each should have one point, and Dr. Pepper will have 2. So therefore, Dr. Pepper wins.


Dr. Pepper VS. Coca-Cola VS. Sprite

.........2......................1 ......................1

The Condorcet Criterion and the Pairwise Comparison Method.

The Condorcet Method

The Condorcet Method is very similar to the Pairwise Comparison Method. You're going to look at the same type of thing.

7 A > B > C > D

9 A > D > B > C

8 A > D > C > B

6 A > C > B > D


The difference is the fact that using the Condorcet Criterion A or B or C or D have to win all of their 'battles'. So, for example, A VS. B. If A doesn't win it cannot be your condorcet. In this case A will win all of it's battles and therefore, get the most points and become your condorcet. But D cannot be you're condorcet because in battle 2 If it goes against A it will lose. Even though in battle 3 it will beat C, it cannot win. Make sense? I hope so! If not talk to your math teacher or email: fisha@remsenstmarys.net today!