An interesting application of mathematics is that pertaining to the idea of preferential voting. By this we mean that if you don't get your first choices elected then you should still have some input into those who candidates who are. For example, suppose there are 20 candidates running for 5 positions. In this case it is assumed that you will rank all 20 candidates from 1 through 20 so that your 6th and later preferences get some weighting as well as the first five.

The ideas are illustrated by considering the elementary case in which three of six candidates are to be elected. In each example it assumed that the voters must rank the candidates in order of preference, with 1 being the first choice and 6 the last choice.