Condorcet//FPTP: Difference between revisions
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'''Smith//FPTP''' is where the candidate with the most 1st choices in the [[Smith set]] wins.
Example of both:<blockquote>49 A>B>C
3 B
48 C>B>A</blockquote>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:<blockquote>18 A1>A2>A3
17 A2>A3>A1
16 A3>A1>A2
49 B1</blockquote>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 criterion|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|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).
[[Category:Preferential voting methods]]
[[Category:Condorcet methods]]
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