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Today, a German TV casting show ("Unser Star Fur Baku") introduced a new "real-time" voting system that works as follows:

10 contestants take part in a song competition. Viewers can call in and vote for their favorite candidate. By the end of the show, the 5 participants with the highest scores advance to the next round (broadcast next week), the rest drop out.

The great "novelty" of the show is that the real-time voting results (percentages) are visible on-screen during the entire show, i.e. viewers can immediately react (call in) when their favorite is in danger of dropping out of the top 5.

By the end of the show, the result table looked like this:

15.5%
14.9%
14.7%
14.7%
14.7%
--------------------- candidates below this line drop out of the contest
14.5%
5.9%
2.4%
1.4%
1.0%

Shortly before the end of the voting phase, positions 1-6 were fluctuating wildly (except maybe position 1 who was some kind of girl-whisperer).

I wonder if this voting procedure is essentially bogus, creating a more or less random ordering of the contestants as an artifact of the feedback loop...

My questions:

  1. Was it to be expected that the table would look like this (first 6 candidates having practically identical scores)?
  2. Why the first six (maybe due to something like "struggle for position 5")?
  3. Is there any special significance to the number 14% (=100 % / 7)?
  4. Could it be that the 6 top positions are picked more or less randomly, from chaotic fluctuations in the beginning phase that tend to self-enforce?

Sorry if this is not a valid question, or wrongly tagged (maybe it's more about psychology than math)... I just saw this and really wondered how sound that procedure was, and if the result table will look practically identical next week (same voting system).

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1 Answer 1

It is possible to give a rationalisation for this in the context of behavioural economics. That does not necessarily make such an explanation true, and you would want to test it in future.

Essentially it is an example of tactical voting and cost minimisation since voters have to pay each time they vote. For many of the voters there is little point in wasting money by voting for anybody who will win anyway, or by voting for somebody who will lose anyway. The only value seems to come from voting for candidates who are just above the line or just below, even if they are not your most preferred candidate, since you think that this way you can influence the result. The unusual feature here is that by being able to see votes already cast, you think you have increased confidence over who the marginal candidates are: in real elections you have to rely on opinion polls.

The effect during the voting process is that those candidates who appear to be winning comfortably will see the rate at which they receive votes decline: they will still get some as not all voters think along these lines. So too will those candidates who appear to be losing. But the marginal candidates will see their votes increase, moving them towards those previous well ahead. So the vote shares of leading and marginal candidates will tend to converge and the vote shares of clearly losing candidates will decline over time.

The number of leading and marginal candidates will be at least one more than the number of winners. It could be higher, but a larger number would be unstable as if anybody started to fall slightly behind, some voters would stop considering them as viable even if they preferred them, and they would fall behind faster.

So in answer to your numbered questions:

  1. It would have been possible to predict this behaviour, but it is much easier to rationalise it after the event.
  2. Having one more than than the number of winners in contention is the stable outcome; having even more is possible but unstable.
  3. There is nothing special about 7 except that it is more than 6: some votes will go to the clearly losing candidates, either from voters with different behaviour, or early in the voting when the leading and marginal candidates are less obvious. So the 6 candidates in contention have less than 100% of the votes to share between them.
  4. It is possible that the top 6 are random, but it may be affected by early voters who care, either because of the qualities of the candidates or for other reasons. If you expect this kind of behaviour from other voters then it is worth following the Tammany Hall slogan "Vote early, vote often".
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