A common method of determining the outcome of an election, or the ranking of several candidates or issues, is through the use of point counts. The simplest such method, known as the Borda count, has each voter rank the candidates (assume that there are n of them). Each first place vote is worth n points each second place vote is worth n - 1 points, and so forth, with each last place vote worth just one point. The candidate with the highest point total is ranked first, the next highest is ranked second, and so forth.
One of the problems with the Borda count method is that it can lead to insincere voting. For example, suppose that a voter likes candidate A best, but also thinks highly of candidate B and would normally (i.e., voting sincerely) rank B second. However, if he suspects that B is a strong candidate, then placing him second may boost B's chances of winning. This thought process might prompt the voter to place B lower down than he deserves. (Of course, this entails some danger, since this improves the chances of other candidates, including some who might not be especially liked by the voter.)
In our mini-spreadsheet below we have set up a preference schedule with 26 voters and four candidates. Using the Borda method the total for A would be:
Calculate the totals for the remaining candidates. Who is the winner? Click the Rank tab to check your answers.
Consider the case of the voters in the first column, whose order of preference is ACBD. While A is their first choice, he is far behind. Can they improve the chances of their second choice, C? Try a different preference order for the first column voters.
Let's try another problem. Click the trash can to clear the previous preference schedule and enter the following:
| Votes | 6 | 5 | 5 | 4 |
| 1st | A | A | B | C |
| 2nd | B | C | C | B |
| 3rd | C | B | A | A |
What is the final ranking of A, B & C? Check your answers by clicking the Rank tab.
The 4 voters in the fourth column (the ones whose preference list is CBA) can affect the outcome in a way more favorable to them by voting insincerely. Make a change in their preference so that candidate B (their second choice) wins instead of candidate A.