Sidney Morgenbesser, a philosopher, while ordering dessert at the restaurant one time, was told by the waitress that he could have either apple pie or blueberry pie. He ordered the apple pie. The waitress then came back and told him that cherry pie was available as well. Sidney then said, “In that case, I’ll have the blueberry pie.”
Was Sidney just being silly, or can there be any possible logic for his choice?
We’ve heard about non-transistive dice, where
Die A has sides....2, 2, 4, 4, 9, 9
Die B has sides....1, 1, 6, 6, 8, 8
Die C has sides....3, 3, 5, 5, 7, 7
which have the property that when any two are rolled together,
Die A beats die B
Die B beats die C
Die C beats die A
But how can something like this work for pies A, B, C, in this example, where the mere existence of another pie being available (the cherry pie), would cause Sidney to switch to a different pie? Is this something out of quantum physics, where, by opening a new slot, light could cease striking some particular photodetector?
There is, in fact, one possible rationale for Sidney’s strange decision. No quantum wierdness is necessary. Let’s say that each pie is ranked 1st, 2nd, or 3rd in 7 different criteria (such as flavor, aroma, texture, nutrition, etc.). The pies can be ranked as follows:
Criteria......1, 2, 3, 4, 5, 6, 7
Pie A.........1, 1, 2, 2, 2, 2, 2
Pie B.........3, 3, 3, 3, 1, 1, 1
Pie C.........2, 2, 1, 1, 3, 3, 3
The “best pie” is the one that has the highest ranking in the most categories, among those that happen to be available. So, we have, between the different pies that are available:
Pie A beats Pie B because it tops in 4 categories
Pie A beats Pie C because it tops in 5 categories
Pie C beats Pie B because it tops in 4 categories
Pie B beats both Pie A and Pie C (when they are all available) because it tops in 3 categories, which is the most among the three pies!