Death>Dishonour =/=> ~Dishonour>~Death

That you rate death before dishonour should not imply that you rate honour above life. Or more precisely: if A and B are (not necessarily disjoint) outcomes, define A>B to mean that the expected utility of outcome A is higher than the expected utility of outcome B. Use the symbol '~' to mean the negation of an outcome. Then Death>Dishonour does not imply that ~Dishonour>~Death, or more generally, A>B =/=> ~B>~A.

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:

B\A	death	life
dishonour	1	*
honour	2	3

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.

We have:

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...)