## The Borda Count method

The Borda count method was designed to avoid some of the problems with the simple plurality method.

The idea is pretty simple: give the candidates points according to their places on each ballot. Give 1 point for last place, 2 for next-to-last and so on up to N points for a first place vote (if there are N candidates).

For our Math Anxiety Club election, recall the summary of the ballots:

 Number of voters 14 10 8 4 1 1st choice (4 points) A (56) C (40) D (32) B (16) C (4) 2nd choice (3 points) B (42) B (30) C (24) D (12) D (3) 3rd choice (2 points) C (28) D (20) B (16) C (8) B (2) 4th choice (1 point) D (14) A (10) A (8) A (4) A (1)

So we will conclude that

A gets 56 + 10 + 8 + 4 + 1 = 79 points
B gets 42 + 30 + 16 + 16 + 2 = 106 points
C gets 28 + 40 + 24 + 8 + 4 = 104 points
D gets 14 + 20 + 32 + 12 + 3 = 81 points

So the winner with this method is B (Boris) -- a different result that will make Alisha unhappy!

### A problem -- the majority criterion

Here's a different election, involving A, B, C and D:

 Number of voters 6 2 3 1st choice A B C 2nd choice B C D 3rd choice C D B 4th choice D A A

Check that even though A has a majority of the first-place votes, B wins under the Borda count method.