Mathematics in Action

Borda Count Example with MAS Election

Basic Borda Count Method
In an election with k candidates, the first place candidate of each ballot receives k points. The second place candidate receives (k-1) points, and so on, until the last candidate, who receives 1 point. The candidate with the largest number of points is the winner.


Preference Schedule for the MAS Election
Number of voters	14	10	8	4	1
1st choice	A	C	D	B	C
2nd choice	B	B	C	D	D
3rd choice	C	D	B	C	B
4th choice	D	A	A	A	A

In this example, there are 4 candidates. So every 1st choice vote receives 4 points, every 2nd choice vote receives 3 points, every 3rd choice vote receives 2 points, and every 4th choice vote receives 1 point.

Points for A:
A has 14 first place votes, no second or third place votes, and 23 fourth place votes. So A has:
(14*4) + (23*1) = 56 + 23 = 79 points.

Points for B:
B has 4 first place votes, 24 second place votes, 9 third place votes, and no fourth place votes. So B has:
(4*4) + (24*3) + (9*2) = 16 + 72 + 18 = 106 points.

Points for C:
C has 11 first place votes, 8 second place votes, 18 third place votes and no fourth place votes. So C has:
(11*4) + (8*3) + (18*2) = 44 + 24 + 36 = 104 points.

Points for D: D has 8 first place votes, 5 second place votes, 10 third place votes, and 14 fourth place votes. So D has:
(8*4) + (5*3) + (10*2) + (14*1) = 32 + 15 + 20 + 14 = 81 points.

So the winner is B with 106 points.

An equivalent way to calculate this is:


Preference Schedule for the MAS Election
Number of voters	14	10	8	4	1
1st choice	A	C	D	B	C	x 4
2nd choice	B	B	C	D	D	x 3
3rd choice	C	D	B	C	B	x 2
4th choice	D	A	A	A	A	x 1

Points for A:
(14*4) + (10*1) + (8*1) + (4*1) + (1*1) = 56 + 10 + 8 + 4 + 1 = 79

Points for B:
(14*3) + (10*3) + (8*2) + (4*4) + (1*2) = 42 + 30 + 16 + 16 + 2 = 106

Points for C:
(14*2) + (10*4) + (8*3) + (4*2) + (1*4) = 28 + 40 + 24 + 8 + 4 = 104

Points for D:
(14*1) + (10*2) + (8*4) + (4*3) + (1*3) = 14 + 20 + 32 + 12 + 3 = 81

The winner is B with 106 points.