A note on Approval Voting and electing the Condorcet loser

• We propose a framework to compare Approval Voting (AV) and Plurality Rule (PR).
• We compute the probability of electing the Condorcet Loser (Borda’s Paradox).
• We show that this probability is significantly reduced when PR is replaced by AV.
• Some results regarding Negative Plurality Rule are also offered.

Analytical representations are developed for the probability that Approval Voting (AV) elects the Condorcet Loser in three-alternative elections with large electorates. A comparison of AV is then made to Plurality Rule (PR) to show that AV is much less susceptible to the risk of electing the Condorcet loser than PR. All calculations in this analysis are based on IAC-like assumptions.