Differnent Procedures -- Different Results

Suppose 15 people are deciding on what beverage to buy for a party, and they have the preferences seen in the table above.

They decide to vote on it using the plurality method -- that is, each person votes for his or her top choice of beverage and the beverage with the most votes is chosen. Thus Dr. Pepper is chosen. But wait! There are 9 people who rank Dr. Pepper last! Dr. Pepper would seem to be a bad choice.

So the folks decide that having a runoff would be more fair. Since Dr. Pepper and Pepsi have the most first place votes, Coke is eliminated. Then the people vote between Dr. Pepper and Pepsi. Since 9 people prefer Pepsi to Dr. Pepper, Pepsi is the winner. But wait! There are 10 people who prefer Coke to Pepsi! Pepsi looks like a bad choice, too.

What can be done...?