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Posted by on Oct 21, 2007 in Richard and Judy - and probability | 6 comments

Channel 4 phone-in puzzle

The puzzle in a nutshell, is this. On the one hand, most of us feel intuitively that the competition was unfair. Trouble is, now I have started to think more carefully about it, I cannot identify precisely why it was unfair. I am wondering if it was unfair.


  1. Stephen, I’ve only had a quick browse over your last two main posts so forgiven me if I’m shooting off target here.”A winner is to be picked at random from one million callers. The whittling down is in two stages. Stage one is: half the time the phones are being answered, those entries go straight in the bin. The remaining entries are then entered into a lottery from which the winner is picked.”In this circumstance there doesn’t appear to be a problem, even if the contestants don’t know how they are being whittled down, they do know they will be whittled down in some fashion. I doubt any would object from names drawn out of a hat for instance. This is not, I think, what R&J were doing.Now for R&J. It’s my understanding that in their competition the scrutiny lies in when people were accepted into the actual draw. Viewers were urged to phone in when the winner had already been picked. They couldn’t win in any circumstance. They didn’t even have a chance.It worked like this:First three quarters of the show audience was told they could ring in and in the final break the winner would be picked/called back and put on air ready.However the actual selection of winner was taken from the first half hour of calls only, so in the 15 minutes following those who rang in weren’t even entered into the competition. Contractually they brought a lot in a competition that didn’t exist, they received NOTHING for their consideration. That’s clearly unfair. If we look back at your example of the lot being thrown away (say by half chance) they have still provided consideration, as much as would be provided to the actual winner. Unfortunately they just didn’t win. Just the stress the point; “But if that is so, then, if the telephonists taking the entries that go straight in the bin know they are doing so, does that matter? I don’t see how it does, despite the fact that, were they to tell those phoning in they cannot win, those punters wouldn’t spend their money.” This could be accepted if the rules of the competition stated that “ the lots will only be taken from a 5 minute space of calls, this space is chosen at random and changed daily, those outside this time will not be accepted into the draw.” I think if R&J could have been shown to have been doing this they would have been let off, it’s random and it just whittles down the selection process like any other. The fact it was a certain space of time every day that wasn’t entered into the draw (thus no consideration) and yet it was calls made at this time were still accepted and charged despite the production staff knowing this and the customers not knowing.Well, I hope that helped…

  2. Stephen, does the problem lie in the meaning of “fair”? It seems to me the word is being used in two different senses, and whereas you have provided a meaning of fairness as essentially the absence of interference in the result (in which case the competition is not “unfair” according to the rules), it seems to me there is another sense of fairness that has been violated and it is the perception of this that has generated the public angst – a kind of moral sense of “fairness of opportunity to withdraw”, which is violated by essentially a period of foreknown, and so deliberately enforced, futility. I think of two analogies:It would be like a company tendering for a position, and interviewing prospective employees for 2 months – because that is the “rules” of the corporation – even though they have already selected someone for the job. This would clearly be an injustice to subsequent applicants, and the unfairness seems to me to be in the treatment of those arriving after the decision, withholding from them the fact that a decision has been already made. This is essentially treating those people’s time and effort and money as of no import or concern. There is probably a more subtle moral term for this, but I think it would generally be labelled as “unfairness”. Once there is no further chance to obtain a prize or position, then if this is known to the organisers, they have to close the competition or position.Another analogy might be with the situation of clinical trials of medications. It happens quite regularly that if it is discovered, even before the end of the formal trial period, that the new drug is significantly better (or worse) than placebo or alternative therapies, the trials are ceased in order to give all participants the opportunity to gain the benefit of the new therapy, or to remove them from a now recognised risk of harm. It is deemed unethical to continue to subject people to a greater relative risk of harm, even though when they signed up and agreed to participate in the trial they were supposedly fully aware and consented to any risks. In summary, I think the morality or immortality lies in the fact of a foreknowledge of the outcome which is withheld from those it might affect. To withhold in such a case seems to imply a judgment of the (lack of) worth of the participants, or worse, a desire to obtain financial gain from keeping them in ignorance. This was surely not the terms under which they decided to play. How is it different from loading the deck in a casino or fixing a roulette?A completely unrelated matter I wanted to raise and get your comment on is the furore over the reported comments of Nobel Prize winning Prof. James Watson, and the subsequent decision to cancel his invitation to speak at a London science museum. I have just finished reading your book “The War for Children’s Minds” and in view of your vigorous defense of “Liberalism of Thought” (and particularly you used the example of science as an example of a necessarily liberal discipline) would I be correct in assuming you would condemn as “Authoritarian” the decision to not allow Prof. Watson to speak. I’m not sure that you listed “political correctness” among the tools of authoritarians, but certainly it is. I’d love to read your thoughts on this.

  3. Stephen, I agree. The charge of unfairness seems to be based on when – the time – it was determined that an entrant was a non-winner.But why does this time matter? Yes, lots of people got nothing for their entry, but that is the nature of gambling.We like to think the ‘chance’ to win is worth something, but this ‘chance’ is pretty notional. Its existence and value depends on what perspective and information you have.Let’s say half a million calls come in. Then we toss a coin, but don’t look at it. Then another half million calls come in, we close the lines and look at the coin. If it is heads, we pick the winner from the first half million, if it is tails we pick the winner from the second.Is this unfair? If it is heads, the later callers have “no chance to win”. But while we don’t know, everybody has an equal chance.(Personally I think this sort of gambling operation is pretty fraudulent even when the operators don’t cheat, but that is another issue.)

  4. Sorry, I wrote all that before I noticed the previous two blog posts on the same topic. Carry on.

  5. StephenI think others have covered this in some detail so I won’t go into it in any great depth. I think your problems with this arise from the fact that you are not a mathematician: To you the difference between a zero chance of winning and an infinitesimally small chance of winning are so close as to make no difference, hence your confusion. What I really wanted to say was that, although I enjoy your blog and your books, I find this topic to be a little below your usual standard – it does seem as if you were scrabbling around a little desperately for something to write about. I hope to see normal service resumed as soon as possible. CheersMike

  6. Well, I’d just like to say that I happen to find this topic interesting, and I am immensely grateful that you bother to give of your time, Stephen, to engage with us. (I personally would have no other access to ‘live’ philosophy.)Much appreciated

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