A salvage idea that failed – Kevin Venzke points out that "winning votes" Condorcet with "candidate-equalities permitted in votes" still looks like it leads to 2-party domination. (Simpler unified proof)

Consider this 100-voter election involving one third-party candidate A and two major-party candidates B and C.

C wins.
#voters their vote
8% B>C>A
29% C=B>A
31% C>A>B
32% A>B>C

[Defeats are A>B by 63:37, B>C by 40:31, and C>A by 68:32. There is an A>B>C>A cycle in which B>C is the weakest defeat, so that C is elected.]

Consider what happens if 18 of the 32 A>B>C voters in the last line change their vote. They turn B into the Condorcet Winner by voting B>A>C or B>A=C or B>C>A, but not by voting 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.

The moral of this example is that exaggeration pays: these 18 voters are able to make their preferred major-party candidate B win over his archrival C only by dishonestly pretending B was their unique strict favorite, "betraying" their true favorite third-party candidate A. (Merely moving B up to co-equal with their favorite A would not do the job.) This kind of strategic exaggeration is precisely the sort of behavior that leads to two-party domination.

This example refutes the plausibility of the idea that using "`winning-votes' not `margins' with candidate-equalities permitted in votes" should save Condorcet methods from 2-party domination.

This page is a simplification of an example that Kevin Venzke gave in an electorama web post in May 2005.


You can confirm all the above claims (with "Tideman Ranked Pairs Condorcet system based on `winning-votes' not `margins' with candidate-equalities permitted in votes") by feeding the following input to Eric Gorr's Condorcet voting calculator (select "Ranked Pairs (Deterministic #1-Winning Votes)" and "tell me some things"):

18:B>A>C or B>A=C or B>C>A
(B wins solo in all 3 of these cases)


18:A>B>C or A=B>C or A>B=C or A=C>B or A>C>B or B=C>A or A=B=C
(C wins solo in all 14 of these cases)

For example, it reports (for the original input votes in the table at top):


The defeats matrix was:
Now Keeping: C defeats A
Now Keeping: A defeats B
C wins solo.

This same example also shows that Schulze(wv), Tideman(wv), Eppley-MAM(wv), River, and Condorcet-MinMax(wv) all fail weak FBC even with only three candidates. No ties are involved in this example anywhere.

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