Voting Strategies: The Whammy Awards

There are three candidates: Classical, Country, and Pop. Each voter is asked to provide a preference ranking. Five different voting schemes are considered.

Plurality: Each voter votes for one person, and the candidate with the most votes wins.

Borda Count: Each voter ranks all candidates on a scale from 1 to 3, with 1 being the highest ranking. The candidate with the lowest total score wins.

Runoff: Voters in the first round select their top candidate. Then the two highest vote-getters are pitted against each other in a runoff election.

Least Favorite: Voters are asked to indicate their least-favorite candidate. The candidate who is the least favorite of most voters is eliminated from the next ballot. If two candidates tie for least favorite, they are both eliminated. The process is repeated until a winner is determined. A tie is possible.

Vote for 2: Each voter must vote for two different candidates, and the candidate with the most votes wins.

Arrow's Election Disaster

Arrow's Election Disaster Theorem asserts that every voting method will contain fundamental flaws.

Clear all votes and set the ballot manipulative to five voters. Fill in the preference rankings so that the winners based on Plurality, Borda Count, and Runoff (the three most popular voting schemes) are all different. Can you obtain the same kind of result with seven voters? With nine voters?

Lots of Winners

With nine voters is it possible for the Plurality method to result in a tie? How about with seven voters?

With nine voters, is it possible to get the Borda Count scheme to produce a three-way tie? Is this possible with seven voters?

Can you get the Least Favorite scheme to result in a tie when there are seven voters?