Fair enough. Although in considering the implications of more than two options for the other conditions, I noticed something else worrisome.

The solution you present weakens a social welfare function, after all if I have two voters, and they vote (10,0,5) and (0,10,5) the result is an ambiguous ordering, not a strict ordering as required by Arrow's theorem (which is really a property of very particular endomorphisms on permutation groups).

It seems like a classic algorithmic sacrifice of completeness for power. Was that your intent?