Now what if I was to tell you that you couldn’t win the lottery, it’s impossible. Pretty annoying right? I mean that being the case why would you ever buy a lottery ticket. Why, indeed would I ever bother to start a lottery club. So let me now explain to you the lottery paradox….
The ‘Lottery Paradox’ is a philosophical conundrum which has become a central topic within epistemology (Google it!) It was devised by Henry E. Kyburg Jr. (1928–2007) who was Professor of Moral Philosophy at the University of Rochester, USA. The paradox arises when we consider the outcome of a 1000 ticket lottery (although in truth the amount of the tickets is immaterial) that has exactly one winning ticket. Now it is reasonable to assume that if the lottery is run correctly (which for the sake of argument it is) some ticket will win. It is similarly reasonable to assume therefore that the probability of this event occurring has to be greater than 0.99 (0 being in probability terms an absolute impossibility and 1 being an absolute certainty). Are you with me so far?
OK, so on this basis then it is logical to accept the proposition that ticket 1 will not win. The reason for this is that for ticket 1 to win the lottery the probability of it doing so has to be greater than 0.99 which would mean that ticket 1 would be a statistical certainty to win the lottery. Of course ticket 1 cannot be a statistical certainty to win the lottery as it must by definition have the same chance of winning as any other ticket. Agree?
Since the lottery is being run in a fair and honest manner it is logical to accept that using the same principle ticket 2 cannot win either. If we then apply the same rules of logic to each and every ticket in the lottery we can rule out absolutely any ticket’s chances of being the winning ticket. This now becomes a contradiction as we already initially established that some ticket must win the lottery with a probability of greater than 0.99 or an absolute certainty.