@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