# Olympic skaters complete two programs in their competition, one short and one long. In each program,

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:

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(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.)

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.