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 1.

a. How many delegates voted in this election?

b. Who were the first three candidates to be eliminated? For each of the ballots that were redistributed in those first three rounds, determine and list the first- and second-place candidates.

c. Despite the fact that 10 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 instead. Who would have won in round 1? Now suppose that Wyatt was disqualified and that all ballots listing Wyatt as the first choice also listed McCall as the second choice. What would the plurality method’s outcome be in this case, and what fairness criterion would be violated?