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 1410841
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 voters623
1st choiceABC
2nd choiceBCD
3rd choiceCDB
4th choiceDAA

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