Next week's post will discuss a mind-boggling economic choice paradox - one of my favorites. Before I discuss it in full, I am posting it here, as a puzzle, for any readers who enjoy trying to figure these things out on their own.
You are an archaeologist are exploring an ancient Viking tomb, and, by accident stumble upon a chamber inhabited by a magical and ancient Norse spirit. In gratitude for releasing him, the spirit offers you your choice of one of two wooden boxes. One contains a certain unspecified number of golden coins. The other contains double that number of coins. The boxes look identical; the first one you touch is the one you pick. Which one do you choose?
Obviously it doesn't matter which one you pick. Or does it?
Suppose you are about to pick box A.
The expected value of box A is, let's say, $X.
The value of box B is thus either $2X or $½X. Both options are equally likely, so they have a 50% chance. By all definitions, the expected value of box B is ($2X+$½ X)/2, or $1.25X. So the expected value of box B is ... 25% greater than the value of box A?
But, by the same exact logic, if we assign the value X to box B, then the expected value of box A is 25% greater. But, surely it can't matter which box we thought about choosing first???
Obviously, the boxes have to have equal expected value (or do they?). Obviously there's a flaw in the math (or is there?). That's the puzzle.
If you think you can resolve the paradox, and can explain it in clear English, send your solution to me at benhaydenlab@gmail.com. I'll acknowledge the best submission next week. Heck, I may even quote your answer if it's that good. Please use the comments section here for general thoughts, queries, or clarifications, but don't try to answer the question there - I'll delete it. Some people like the feeling of mystery.
P.S. If you enjoy this blog, you can now follow me on Twitter (ben_hayden) or Google Plus. I'll link to my new posts there, starting today.
