Question

If there are 6 candidates in an election and voters are asked to rank all of the candidates, how many different pairwise comparisons are there?

Answer 1

Answer:

15 pairwise comparisons; 30 pairwise rankings.

Step-by-step explanation:

Each of the 6 candidates can be ranked #1 in relation to the other 5, for a total of 30 pairwise rankings.

Of course, two of those are comparisons of the same pair of candidates. The same is true of all pairs of candiates, so the number of pairwise comparisons is half the possible number of rankings: 30/2 = 15.

_____

For example, for the pair of candidates A and B, you can have the two rankings ...

• A > B
• B > A

These cases are possible outcomes of the the one pairwise comparison ...

• A vs B