At the state convention on May 11, 2002, the Utah Republican Party used instant runoff v...

At the state convention on May 11, 2002, the Utah Republican Party used instant runoff voting to nominate candidates to the U.S. House of Representatives. The delegates ranked the candidates using a preferential ballot. In the first round, the candidate with the lowest number of first-place votes was eliminated and his or her votes were redistributed. This continued round by round until one candidate achieved at least 60% of the vote or until there were two candidates left, in which case they would face each other in a primary election in June.

Consider the following summary of each round of the process for Utah Congressional District 2.

a. How many delegates voted in this election?

b. Who were the first two candidates to be eliminated? Create a list of the first- and second-place candidates for each of the ballots that were redistributed in those first two rounds.

c. Despite the fact that 12 candidates ran for office, not every voter ranked every candidate. Determine from the table the fewest number of rankings provided by a voter and the total number of voters who failed to rank every candidate.

d. Suppose the plurality method had been used. Who would have won in round 1? Now suppose that Harmsen was disqualified and that all the ballots listing Harmsen as the first choice also listed Bridgewater as the second choice. What would the plurality method’s outcome be in this case, and what fairness criterion would be violated?