This example from the book Subjective Probability: The Real
Thing by Richard Jeffrey was pointed out to me by a friend of
mine yesterday. Let's draw a little diagram of possible outcomes
and their utility: The '*' indicates an outcome with probability
zero and the other outcomes are considered to be equally likely.
A is the variable describing your state of liveness and B is the
variable representing your honour. E(utility|A=death) = 1.5
E(utility|B=dishonour) = 1 E(utility|B=honour) = 2.5
E(utility|A=life) = 3 With this set of utilities one does indeed
rate death before dishonour but not honour before life. This
gets mixed reactions. Some people think that it's a nice
counterintuitive result. Some people think it's so trivial they
don't see why anyone would even mention it. If you're in the
latter group, sorry for wasting your time. :-) (I leave the
Haskell program using a probability monad as an exercise...)