In that case, there are nondictatorial voting systems that both respect unanimity and eliminate flip-flops.
The only voting system that respects unanimity and stops flip-flops is a dictatorial one. 
mnli hypothesis: The only voting system that respects unanimity and stops flip-flops is a dictatorial one.  premise: In that case, there are nondictatorial voting systems that both respect unanimity and eliminate flip-flops.