Monotonicity Failure in Ranked Choice Voting -- Necessary and Sufficient Conditions for 3-Candidate Elections

Abstract: Ranked choice voting is vulnerable to monotonicity failure - a voting failure where a candidate is cost an election due to losing voter preference or granted an election due to gaining voter preference. Despite increasing use of ranked choice voting at the time of writing of this paper, the frequency of monotonicity failure is still a very open question. This paper builds on previous work to develop conditions which can be used to test if it's possible that monotonicity failure has happened in a 3-candidate ranked choice voting election.