20 December 2008

Strictly Voting Systems

One striking thing about the successive controversies over Strictly Come Dancing is the apparent lack of attention to detail paid to the technicalities.

When it first occurred to me that John Sergeant was likely to win the competition, I spent a while trying to work out whether the judges would be able to get rid of him somehow. I was handicapped by not knowing what the scoring system was, or how many couples were supposed to get to the final.

A day or two later he announced he was quitting, and, after kicking myself for not seeing that coming, I immediately wondered how they were going to handle being one couple short in the last few rounds.

Neither of the two questions I spent time pondering seemed to occur to the show's organizers. They've now got round to explaining in detail how the scoring works. Even there there are oversights; I think it is an error to give both couples in a tie the higher number of points, although it doesn't matter this late in the competition. Last week's judge points should have been 2.5, 2.5, 1, rather than 3,3,1. That could have made a difference earlier in the competition.

However, I would take a more drastic approach. Collapsing the judges' votes into an ordering of the contestants is throwing away information to begin with. It might be better to keep the actual points awarded by the judges, and then add the popular votes, scaled down to the same maximum. For instance, if there were a million votes, each judge point would be worth 1000000/160 phone votes. (about 6000). Apart from making the actual number of votes more important, that would encourage the judges not to bunch their votes into the 8-10 range all the time.

These type of shows have been going for years and years; I still think the problems appearing now are all because previously they never took the voting seriously, and would just cheat if they didn't like the way it was going. Having people like Undercover Economist Tim Harford discussing it now is a real step forward. Maybe next year's competitions will be designed by people who've heard of Arrow's Theorem.

Update

20:05 - phone voting is currently going on to select the last two.

Scores carried from last week are

Rachel 5 (3 judges + 2 phone)
Tom 4 (1 judges + 3 phone)
Lisa 4 (3 judges + 1 phone)

Tom ranks above Lisa because in a tie phone votes are worth more than judge votes.

The points from the judges this evening were

Lisa 3 (80)
Rachel 2 (79)
Tom 1 (73 or thereabouts, I can't remember)

So the running total is:

Rachel 7 (3+2 judges, 2 phone)
Lisa 7 (3+3 judges, 1 phone)
Tom 5 (1+1 judges, 3 phone)

So Tom needs to win the popular vote to make it to the last 2, while the girls each just need to come second to make it.

Again, the compression of the judges' votes has been very evident - no vote lower than an 8, no vote from 3 of the 4 judges lower than a 9. Len and Arlene, I think, each gave 9 to Tom's first dance and 10 to the other 5 dances. What's the point of being there if they can't say which dance is better?

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