Winter Olympics Figure Skating 1994

In figure skating contests, a judge's technical and artistic points only matter in that they determine the judge's ranking of the skaters. In the 1994 Winter Olympics, Oksana Baiul from Ukraine won the gold medal since she had the most first place votes. American Nancy Kerrigan came in second, and Chen Lu from China got the bronze. Notice that Kerrigan received no third place judges' votes. Baiul received two third place votes. Should those third place votes have counted against Baiul?

Does a voting system which ignores the voters second and third place choices seem like the best way to go? Should that information really be thrown away?