Indeed, if you allow randomness, you can get all the other desired attributes listed in Arrow’s impossibility theorem. Random ballot voting, for instance, has n

Indeed, if you allow randomness, you can get all the other desired attributes listed in Arrow’s impossibility theorem. Random ballot voting, for instance, has nearly every desirable property. There’s no reason to vote strategically (dishonestly). The race between candidates A and B can’t be affected by the presence or absence of any third candidate (there are no spoiler candidates). At least one voter is guaranteed to be happy with the election results (ok, that one is sort of a joke). But of course, random ballot has just one pesky undesirable property: the fact that it’s random.