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September 12, 2007
The Trouble with Preferences
I may have told this story here before, but I'll tell it here again. (Hey, it's my blog; I get to repeat myself at will.)Eons ago during my grad school program in business I took a course in logic. There was one super-bright, hyperrational (and ill-socialized) guy in the class who delighted in being ... well, a prick. He liked catching the professor on logical consistencies, and generally being a pain in the ass.
Well, one day we finished up the session talking about the transitivity of preferences. The sort thing where if a < b and b < c then c > a. In other words, I like bananas more than apples, and apples more than grapes, so I'm must like bananas more than grapes.
Fair enough, right? Well, as many readers will know, preference transitivity is a useful assumption, but not a hard and fast rule. It breaks down and preferences become intransitive in a number of cases, one of which this fellow student was dutifully writing on the board before class one night as I came in a few minutes early. He had filled two boards with scrawl, ending with:
Person A prefers Peace to WarWithout getting into the whys and wherefores of how preferences are sometimes (but not regularly) intransitive, I'll just end with my favorite part of the story. Just as class was supposed to start and he had finished his scrawl I noticed that there were only three of us in the room out of a class of 25. Someone poked their head in about then, saying, "You guys know we changed rooms tonight, don't you?" The look on scrawler's face at that point was one of my favorite moments in grad school.
Person A prefers War to Soviet Rule
But he can't also prefer Peace to Soviet rule, as transitivity would imply!
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on a glance it strikes me that there might be a direction to transitive relationships that if necessary make reversing the direction of the relationship nonsensical...
Person A hates War more than Peace
Person A hates Soviet Rule more than War
now i hope everyone hasn't already left this class!