...the R&J show was basically scamming a significant proportion of the population into believing that they had a chance of winning... when they had NO chance at all at the time they decided to commit their money. It is in the withholding of this information that I think the unfairness lies.
I'm not sure that's it, as, in my example where stage 1 of whittling down is that half the time entries are received they go straight in the bin, a significant proportion of the population have no chance of winning at the time they decide to commit their money (because their entry is immediately binned). Yet there is no unfairness in withholding this info from them.
I didn't make my point about determinism clear, as some of you think it irrelevant. Well, may be it is irrelevant, but let me try again (as the point I was trying to illustrate is the crux of my question)!
I was trying to illustrate the point that what we consider "random" and "non-random" depends on how we set the parameters. Given the parameters include the laws of nature and all antecedent physical conditions, that this dice should now roll 6 is not random. There's "no chance" of it doing anything else. On the other hand, given no more info than that the unloaded dice is given a vigorous unseen shake before being rolled in the normal way, it's getting a 6 is random (there's "just as good a chance it'll roll a 5 or 4 etc.").
We say the Richard and Judy case was unfair, and we say this because certain contestants - those who phoned after a certain point - were not excluded at random, but were ruled out from the start (so they had "no chance" of winning), whereas in my example where half the entries go in the bin, and the rest go into a random lottery, we say that those that went into the bin were fairly excluded at random: they did still have the "same chance of winning" as everyone else.
There's a question about what we consider "random" and "non-random", and thus fair (a "chance" of winning [even if very, very low, Mike!]) and unfair ("no chance" of winning at all), to which I don't know the answer.
Why, in the RandJ competion, is it right to say certain entrants have "no chance of winning" whereas in my hypothetical competition those who phone in during times when entries go in the bin have "the same chance of winning as everyone else"?
[[N.B. Note this problem is not, Mike, that I cannot tell difference between very low, and no, probability. I do know about that (in methodology I teach the Bayesian response to the paradox of the ravens, which hinges on precisely that point).]]