Voting Methods

Voting is simple, right? Everyone just votes for their favorite and the votes are counted. The person (or alternative) with the most votes wins!
But is that always the best way?

Suppose a family decides to vote on a place to visit on vacation.
Dad loves the mountains but hates the beach (too sandy!). He would enjoy Disneyland (but not as much as the mountains).
Mom loves the beach but hates the mountains (too many steep trails to climb!). She would enjoy Disneyland (but not as much as the beach).
Alice loves the beach but hates the mountains (just like Mom!). She also would enjoy Disneyland (but not as much as the beach).
Tommy loves Disneyland more than anything else! He can't stand the mountains (boring!) or the beach (too hot!)
If everyone votes for their favorite, the BEACH will get 2 votes (Mom and Alice), the MOUNTAINS will get 1 vote (Dad), and DISNEYLAND will get 1 vote (Tommy). So, the BEACH wins!

Is the BEACH really the best choice for the family vacation? Think about it. Half of the family members (Dad and Tommy) hate the beach. Should the family really go to a spot that half of the family hates? Is there a better choice? Look back at the preferences of each family member and see if you can suggest a 'better' vacation spot. Is 'the most first place votes wins' method really the best method here?

The previous example suggests that perhaps there should be different voting methods in different situations. For instance, in the above example, maybe the family should consider a voting method that takes into consideration what each family member likes and DISLIKES. Counting first place votes takes care of the likes but completely ignores the dislikes.

In this course, we will consider 5 different voting methods (although there are many more). We will look at how each method works and examine the strengths and weaknesses of each. In particular, we will look at each preferential voting method in light of the 4 Fairness Criteria. (Remember, from Kenneth Arrow's work, we know that no preferential voting method can satisify all the Fairness Criteria.)

4 Preferential Voting Methods

1 Nonpreferential Voting Method

Back to topics listing for section V. THE MATHEMATICS OF VOTING