ruby - How to deal with the sum of rounded percentage not being 100?

Question

Suppose we have a list of items with an integer:

USA:       3 people
Australia: 2 people
Germany:   2 people

If we calculate the percentage of each value against the sum over the whole list, we get:

USA:       3/(3+2+2)*100 = 42.857...%
Australia: 2/(3+2+2)*100 = 28.571...%
Germany:   2/(3+2+2)*100 = 28.571...%

and if we round it, we get:

USA:       43%
Australia: 29%
Germany:   29%

The sum 43+29+29 = 101 is not 100, and it looks a little bit strange to the user of the software. How would you solve this problem?

Answer 1

You can refer to the Largest Remainder Method used in election: Wikipedia: Largest Remainder Method

In your case, you have

USA:       42.857...
Australia: 28.571...
Germany:   28.571...

If you take the integer part, you get

USA:       42
Australia: 28
Germany:   28

which adds up to 98, and you want to take two more. Now, you look at the decimal parts, which are

USA:       0.857...
Australia: 0.571...
Germany:   0.571...

and take the largest ones until the total reaches 100. If you take USA, the total becomes 99, and you want to take one more. Here the problem arises. Since you are left with a tie of 0.571... between Australia and Germany, if you take both, the total will be 101. So you have two ways to choose from:

(a) If you strongly want the total to be 100, just take Australia, and take no more:

USA:       43
Australia: 29
Germany:   28

(b) If you rather want to respect the fact that Australia and Germany are in a tie, you stop at that point:

USA:       43
Australia: 28
Germany:   28