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Card 8 / 15:
Anastasia, Emma, and Greta are deciding what to do on a weekend getaway. They each suggest a first, second, and third choice and then vote on the options. Their first choice, second choice, and third choice preferences are as shown in . Explain why they will have a hard time reaching a decision. Does the group prefer mountain biking to canoeing? What about canoeing compared to the beach? What about the beach compared to the original choice of mountain biking? Anastasia Emma Greta First Choice Beach Mountain biking Canoeing Second Choice Mountain biking Canoeing Beach Third Choice Canoeing Beach Mountain biking
The problem is an example of a voting cycle. The group will vote for mountain biking over canoeing by 2–1. It will vote for canoeing over the beach by 2–1. If mountain biking is preferred to canoeing and canoeing is preferred to the beach, it might seem that it must be true that mountain biking is the favorite. But in a vote of the beach versus mountain biking, the beach wins by a 2–1 vote. When a voting cycle occurs, choosing a single favorite that is always preferred by a majority becomes impossible.
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