Thursday, August 09, 2007

Discussion Question - A Lucky Lunch Guess?

OK, time for a change of pace - an open discussion for the comments. This problem came to me in that fuzzy just-waking-up-after-a-nap period. If anyone knows a formal name for it or sees a parallel to a similar question, please let me know. OK,

We'll say you have two friends that you always eat lunch with, Sheila and Dave, and the three of you are joined by one (and only one) of two other friends everyday, George or Ringo. Everyday, you, Sheila, and Dave sit down. Sheila and Dave always try to guess which of the the other two will be joining you guys for lunch. Dave always makes a guess based on compelling evidence (for example, Dave didn't see George in class today and predicts Ringo will turn up for lunch), while Sheila always takes a random guess, based on whoever she feels like naming that day (she has no more knowledge that you). For the past 14 days, Sheila has correctly predicted the fellow luncher, without fail, even though Dave, in every instance, had some good reason to suppose his prediction would come true. Dave has been wrong every single time (we'll assume that Sheila and Dave both whispered their predictions in your ear, not knowing who the other picked).

So, the next time you have lunch, a fanatical Demon comes up to you, Sheila, and Dave. He wants you to guess (choosing either Sheila or Dave) who will be correct in predicting the lunchmate joining your group. If you choose a person who guesses incorrectly, you have to drink deadly poison.

The question: Who would you choose? Why? Does any real evidence point towards Sheila being the good pick? Is there a good reason NOT to pick Dave in this instance, other than a horrendous track record? Is there a clear logical answer to this? Does Sheila's "luck" outweigh Dave's perfectly reasonable predictions? Leave your thoughts in the comments below! And let me know if there's some obvious loophole in this that I'm missing in how the question was set up.