## A salvage idea that failed – Condorcet with "candidate-equalities permitted in votes" still exhibits "favorite betrayal" and hence presumably leads to 2-party domination.

Here is an 11-voter 3-candidate election example proving that Condorcet schemes with ranking-equalities allowed suffer from favorite-betrayal, and that is true whether you use "winning-votes" or "margins" – doesn't matter – same example kills both:

C wins
#voters their vote
2 A>B>C
3 C>A>B
4 C=B>A
2 A>B>C

Defeats are A>B by 7:4, B>C by 4:3, and C>A by 7:4. There is an A>B>C>A cycle in which B>C is the weakest defeat (measured by either winning votes or by margins), so that C is elected.

Notice that the two A>B>C voters shown in blue on the bottom line can turn the "lesser evil" B into the Condorcet Winner by "betraying" their favorite "third party" candidate A and voting B>A>C or B>A=C or B>C>A.

However, changing their vote instead to A=B>C or A>B=C or A=C>B or A>C>B or A>B>C or B=C>A or A=B=C (or C>B>A or C>A>B or C>A=B) does not suffice: then C still uniquely wins in all cases. Hence favorite-betrayal of A was strategically necessary.

All this is true regardless of whether you use "margins" or "winning votes." However I have cheated a bit by assuming the Condorcet method is such that it elects the candidate with the weakest defeat in a 3-cycle.

You may also see the other example with ranking-equalities forbidden and Venzke's original careful proof (which doesn't cheat).