## 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.

### Details

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"):

```14:A>B>C
8:B>C>A
31:C>A>B
29:C=B>A
18:B>A>C or B>A=C or B>C>A
(B wins solo in all 3 of these cases)
```

and

```14:A>B>C
8:B>C>A
31:C>A>B
29:C=B>A
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):

 Option A B C A 0 63 32 B 37 0 40 C 68 31 0

The defeats matrix was:
 Option A B C A 0 63 0 B 0 0 40 C 68 0 0
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.