Arrows impossibility theorem
Mathematically impossible for a democratic voting method to be completely fair 3+ candidates
Ivr
Instant runoff voting
Monotonicity criterion
If a candidate wins, and in reelection, the only vote changes favor the winner, then the winner should still win
Condorcet criterion
If a candidate wins all their head to heads, then they should win
Independence of irrelevant alternatives criterion IIA
If a non winning candidate drops from the election, the original winner should still win
Majority criterion
If a candidate has majority of votes, they should win