[drdeca]

Sure, they don't run up against /Arrow's/ impossibility theorem, but Gibbard's 1978 theorem shows that "Any straightforward game form (deterministic or not) is a probability mixture of game forms each of which is either unilateral or duple."

(For an explanation of what that means, see : https://politics.stackexchange.com/a/14245 )

Edit: though, if I had to recommend one, I'd probably either recommend "ranked pairs" or something exotic with a substantial deal of randomness.

Or, really, maybe I'd advocate that the primaries use ranked pairs, and that the general use FPTP (or something very similar) because it is easier to understand the mechanism, so easier for people to trust it / keep results seen as legitimate, and because parties narrow down the options to 2 for the most part anyway, and all the usual systems are the same once it gets down to two candidates (in random ballot voting, it is still different though)