  We propose six axioms concerning when one candidate should defeat another in
a democratic election involving two or more candidates. Five of the axioms are
widely satisfied by known voting procedures. The sixth axiom is a weakening of
Kenneth Arrow's famous condition of the Independence of Irrelevant Alternatives
(IIA). We call this weakening Coherent IIA. We prove that the five axioms plus
Coherent IIA single out a method of determining defeats studied in our recent
work: Split Cycle. In particular, Split Cycle provides the most resolute
definition of defeat among any satisfying the six axioms for democratic defeat.
In addition, we analyze how Split Cycle escapes Arrow's Impossibility Theorem
and related impossibility results.
