It seems the mid-1990s was a wild time for sports scoring. Whoo, boy, that whole Barbados-Grenada thing, for a start. But I wanted to take a moment to look at another, semi-legendary sports story: the 1995 World Figure Skating Championships in “Solihull (branded as Birmingham)”. I’ll let you judge whether that’s an improvement.

I heard about this curiosity on Carry The Two, an excellent podcast featuring my old frenemy Sam Hansen and Sadie Witkowski. It talked about voting systems, my favourite food! But it only mentioned the 95 Worlds in passing, and I hungered for more.

One of the desirable criteria for a voting system is called Independence of Irrelevant Alternatives (IIA). That means, if I prefer Solihull to Birmingham, that should still be the case even if someone says “Droitwich is also an option.” The existence of Droitwich should not have any effect on the Solihull/Birmingham dilemma – at least in a perfect system.

(There is no perfect system. Thanks, Professor Arrow.)

The 1995 World Championship is frequently held up as an example of IIA failing, but I struggled to find a decent write-up. sigh. I’d better do it myself. I think it’s less complicated that some people make it out.

The set-up involves four skaters: Lu Chen of China, Surya Bonaly of France, Nicole Bobek of the USA, and Michelle Kwan, also of the USA.

Reaching the end of the competition, with only Kwan still to skate, Chen leads the standings, with Bobek second and Bonaly third. Kwan’s performance is good but not quite enough to win a medal (she finished fourth); however, it has the side-effect of causing Bonaly to overtake Bobek into second place.

Wait… what? How could Kwan’s performance suddenly make two athletes, who have already skated, switch places? Allow me to explain, at least to the best of my understanding. As far as I know, a triple Axel is a front-loaded G’n’R tribute band.

The event consisted of three programs:

  • the qualifying free-skate, which appears to be irrelevant to us
  • the short progam; and
  • the free skate.

The winner of the short program (Bobek) earned half a point. Second place earned one point, third (Chen) 1.5 points, fourth (Bonaly) 2 points, and so on.

The free skate is twice as important: the winner would earn a point, second place two points, third three points, and so on.

The overall rankings are decided by who gets the fewer points overall. This does not appear controversial.

Let’s recap the standings just before Kwan skates:

  • Chen has 1.5 points from the short program, and leads the free skate. As it stands, she has 2.5 points.
  • Bobek has 0.5 points from the short program, and lies third in the free skate – so she’s on 3.5 points.
  • Bonaly has 2 points from the short program, and is second in the free skate, making 4 points.

Kwan’s free skate scores well enough for her to reach third in the standings. That moves Bobek down to fourth, costing her a point; she now has 4.5 points and a bronze medal rather than a silver.

(Aside: there’s a certain amount of noise about how the method for combining the judges’ scores is to blame for this – I don’t believe that’s the case. It’s the ranking-based points, a variant on the Borda count that’s to blame; any method that allows Kwan to finish third would have the same effect in this case.)

Skating has gone through several scoring evolutions over the last three decades, and this method is (I understand) no longer used. That’s probably for the best.