Lesson 6:  Other Voting Methods


As mentioned before, there are lots of voting methods which have been proposed over the years. In this lesson we will take a look at a few of them.

You should have noticed that elections with only two candidates are easy. One candidate has to get at least half of the votes; that is not only a plurality but also a majority (barring ties).  This gives us a pretty clear cut winner. The difficulty comes when we have three or more candidates. 

This observation leads to the idea of comparing the candidates only two at a time, or "head to head." So for example, if we have three candidates Alice, Bob and Carol we have three comparisons to make: Alice versus Bob, Alice versus Carol, and Bob versus Carol. We could hold three separate elections, but it is simpler to use the information in the preference tables we have used before. As the number of candidates grows, so do the number of head to head competitions. For n candidates there are  n(n + 1) / 2 comparisons. So if we had 10 candidates we would need 55 comparisons.

 Suppose we use our preference tables to calculate the winner in all of the possible head to head comparisons. What do we do with this information?