Olympic skaters complete two programs in their competition, one short and one long. In each program, the skaters are scored and then ranked by a panel of nine judges. The skaters’ positions in the rankings are used to determine their final scores. A skater’s ranking depends on the number of judges placing her first (or second or third); the skater judged to be best by the most judges is ranked number one, and so on. In the calculation of a skater’s final score, the short program gets half the weight of the long program. That is, Final score 5 0.5 (Rank in short program) 1 Rank in long program. The skater with the lowest final score wins the gold medal. In the event of a tie, the skater judged best in the long program by the most judges takes the gold. In the 2002 women’s individual figure-skating competition in Salt Lake City, Michelle Kwan was in first place after the short program. She was followed by Irina Slutskaya, Sasha Cohen, and Sarah Hughes, who were in second, third, and fourth places, respectively. In the long program, the judges’ cards for these four skaters were as follows:
(a) At the Olympics, Slutskaya skated last of the top skaters. Use the information from the judges’ cards to determine the judges’ long-program ranks for Kwan, Cohen, and Hughes before Slutskaya skated. Then, using the standings already given for the short program in conjunction with your calculated ranks for the long program, determine the final scores and standings among these three skaters before Slutskaya skated. (Note that Kwan’s rank in the short program was 1, and so her partial score after the short program is 0.5.)
(b) Given your answer to part (a), what would have been the final outcome of the competition if the judges had ranked Slutskaya’s long program above all three of the others?
(c) Use the judges’ cards to determine the actual final scores for all four skaters after Slutskaya skated. Who won each medal?
(d) What important principle, of those identified by Arrow, does the Olympic figure-skating scoring system violate? Explain.