@NevinBR Thank you for the Game Theory Voting link. I see that there is an assumption that when a Condorcet selection exists that it's the best choice. I think there are situations where that is NOT a correct assumption. I tried to modify the scenario that the authors, Rivest and Shen, used, but it wasn't working out very well, so I simplified one of the scenarios that I had previously come across, which was from using randomly generated numbers.
Scenario: There are 4 candidates and 13, 138 voters. With FPTP, candidate B gets 3,900 votes, C 3,547, D 3,456 and A 2,325. B wins Condorcet buy 2 votes, 6570/6568, over each of the other candidates. At first blush, B seems to be clearly the best choice.
I exaggerated the randomly generated numbers into a scenario where ALL of the voters that picked B as their first choice picked D as their second choice. So, in a head to head with B and D, B got 2 more votes than D, but D was the second choice of all 3,900 supporters of B. Conversely, only 639 of the 3,456 D supporters chose B as their second choice.
It seems to me that candidate D is preferred by the most people to the greatest degree.
I didn't try to understand all of the Game Theory details, but it seems to me that there is a way to modify it so that it considers this in the weighting and sets the probabilities accordingly.
I'm wondering what people think of this. (Both of the assertion of D being the best choice, and the potential of Game Theory to account for this.)
Here are the full numbers for the scenario:
0:Option A
819:Option A>Option B>Option C>Option D
52:Option A>Option B>Option D>Option C
141:Option A>Option C>Option B>Option D
898:Option A>Option C>Option D>Option B
116:Option A>Option D>Option B>Option C
299:Option A>Option D>Option C>Option B
0:Option B
0:Option B>Option A>Option C>Option D
0:Option B>Option A>Option D>Option C
0:Option B>Option C>Option A>Option D
0:Option B>Option C>Option D>Option A
1800:Option B>Option D>Option A>Option C
2100:Option B>Option D>Option C>Option A
0:Option C
988:Option C>Option A>Option B>Option D
658:Option C>Option A>Option D>Option B
3:Option C>Option B>Option A>Option D
667:Option C>Option B>Option D>Option A
473:Option C>Option D>Option A>Option B
668:Option C>Option D>Option B>Option A
0:Option D
1044:Option D>Option A>Option B>Option C
445:Option D>Option A>Option C>Option B
382:Option D>Option B>Option A>Option C
257:Option D>Option B>Option C>Option A
635:Option D>Option C>Option A>Option B
693:Option D>Option C>Option B>Option A