What if I told you that buying a winning lottery ticket had nothing to do with mathematics and everything to do with philosophy! Confused? Welcome to the lottery paradox!
I am guessing that like me you have probably at some time sat down and pondered on the great questions of life, ‘why are we here?’ What’s life all about?’ ‘What are my chances of buying a winning lottery ticket?’ Every human being has questions, it is part of who we are to continually seek out the truth and discover new things about ourselves and the world in which we live. Unfortunately, I am unable to answer the meaning of life in this blog post, but I am able to explore your chances of buying a winning lottery ticket, from a purely philosophical point of view anyway. For the thinkers amongst you here is the philosophy of lottery.
The lottery paradox explained
What if I was to tell you that you could never purchase a winning lottery ticket, it’s impossible. Pretty annoying right? I mean if that is the case why would you ever buy a lottery ticket? OK, so now that you are mad at me, let me explain to you about the lottery paradox….
The ‘Lottery Paradox’ is a philosophical conundrum that has become a central topic within epistemology It was devised by Henry E. Kyburg Jr. (1928–2007) who was a 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 tickets is immaterial) that has exactly one winning lottery ticket. Now it is reasonable to assume that if the lottery is run correctly (which for the sake of argument it is) there has to be a winning lottery ticket. It is similarly reasonable to assume therefore that the probability of there being a winning lottery ticket has to be greater than 0.99 (0 in probability terms being an absolute impossibility and 1 being an absolute certainty). Are you with me so far?
Why you can never buy a winning lottery ticket
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 be a winning lottery ticket 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 lottery ticket. This now becomes a contradiction as we already initially established that a ticket must win the lottery with a probability of greater than 0.99 or absolute certainty.
This is the reason therefore that you cannot win the lottery. On the plus side, however, if you commit this basic philosophical principle to memory you will make £20 quid off your mates down the pub after a couple of lagers.
Those of you with an interest in philosophy or mathematics may wish to check out The Logical Foundations of Statistical Inference by Henry E. Kyburg Jr available at the Book Depository.