  We provide a general argument against value incomparability, based on a new
style of impossibility result. In particular, we show that, against plausible
background assumptions, value incomparability creates an incompatibility
between two very plausible principles for ranking lotteries: a weak ``negative
dominance'' principle (to the effect that Lottery 1 can be better than Lottery
2 only if some possible outcome of Lottery 1 is better than some possible
outcome of Lottery 2) and a weak form of ex ante Pareto (to the effect that, if
Lottery 1 gives an unambiguously better prospect to some individuals than
Lottery 2, and equally good prospects to everyone else, then Lottery 1 is
better than Lottery 2). After spelling out our results, and the arguments based
on them, we consider which principle the proponent of incomparability ought to
reject.
