Condorcet//FPTP

Condorcet//FPTP is a voting method which elects the Condorcet winner if one exists, but otherwise elects the candidate with the most 1st choices (the FPTP winner). It is arguably the simplest possible Condorcet method, even when compared to methods like Minimax and Condorcet-cardinal hybrids.

When a voter equally ranks multiple candidates 1st, this can either be interpreted as each of those candidates receiving one 1st choice vote, or as each of them receiving an equal fraction of one 1st choice vote. The former interpretation is equivalent to Approval voting, the latter to cumulative voting.

Most Condorcet advocates would likely at the very least prefer the similar, but more complicated Condorcet//Approval and Smith//Score methods, as their cycle resolution methods are less prone to the spoiler effect.

Smith//FPTP is where the candidate with the most 1st choices in the Smith set wins.

Example of both:

49 A>B>C

3 B

48 C>B>A

A is the FPTP winner (has 49 1st choices, the most of any candidate), but B is both the Condorcet winner and the only candidate in the Smith set, thus both Condorcet//FPTP and Smith//FPTP would pick B. Example of divergence between the two:

18 A1>A2>A3

17 A2>A3>A1

16 A3>A1>A2

49 B1

The Smith set here is (A1, A2, A3). There is no Condorcet winner, and the FPTP winner is B1 (49 1st choices), so Condorcet//FPTP would pick B1. Within the Smith set, the FPTP winner is A1 (has 18 1st choices to A2's 17 and A3's 16), so Smith//FPTP would pick A1. Notice that if any two candidates in the Smith set drop out of the race, the remaining candidate would be the majority's 1st choice by 51 voters to 49, and thus win in either Condorcet//FPTP or Smith//FPTP. Thus, this is an example of a mutual majority criterion failure for Condorcet//FPTP (a majority preferred the (A1, A2, A3) set of candidates above all other candidates (B1) but none of the majority-preferred candidates won).