In the 1995 women’s figure skating championship, something weird happened. Just before the last skater performed, Nicole Bobek was ranked second and looked to take home a silver medal. Surya Bonally was ranked third and looked to take home a bronze medal. Their skating was done; the die was cast. Only Michelle Kwan needed to skate. Kwan’s performance was strong, but she merely placed fourth. Here’s the weird part: Kwan’s performance caused Bobek and Bonally to switch places.

Bobek fell to third place and Bonally moved up to second place. What did Kwan’s merit have to do with Bobek’s and Bonally’s relative merit?

During the 1997 men’s competition, the same thing happened. The final contestant switched the second and third place holders. People were outraged by both of these results. We Intuitively think that there has to be something wrong with the voting system because a skater shouldn’t change the relative merits of two other skaters.

But it’s mathematically impossible to create a ranking system that won’t do this.

So if irrelevant options bedevil mathematical voting systems. we can be as rational as we want and still have this problem. Mathematics is pure logic and it can’t avoid this weird quirk. Why should we think we can?