May's Theorem

If the number of voters is odd, and we are interested only in voting systems that never result in a tie, then the majority rule is the only voting system for two candidates so that :

  • All voters are treated equally;
  • The two candidates are treated equally; and
  • The monotonocity criterion is obeyed

 

• Simple Plurality

+ Violates the Condorcet Criterion

+ Falls victim to insincere voting

Borda Count

+ Violates the Condorcet Criterion

+ Violates the Majority Criterion

Plurality-With-Elimination

+ Violates the Condorcet Criterion

+ Violates the Monotonicity Criterion

Pairwise voting

+ Violates the IIA Criterion

Arrow's Impossibility Theorem

It is mathematically impossible for a democratic voting method to satisfy all four of the fairness criteria.