[EM] Condorcet cyclic drop rule

[LAYTON Craig]

I wrote:

>It is worth noting, too, that defeat support is more likely to
>punish a voter for truncating a vote.

Mike replied:

>It doesn't punish the voter for truncating. It merely doesn't reward
>him by letting him thereby steal the election from a sincere CW.

Okay, I think this is the correct example to show that defeat support
punishes truncated votes, and, in fact, any voter who votes two candidates
equally.

Sincere preference votes:

22 A>B=C (or just A)
13 B>C>A
 7 B>A>C
 9 C>A>B
 8 C>B>A

There are 22 supporters of A, 20 of B and 17 of C.  The B and C voters are
split on their second preferences.

Pairwise Table:
A>B 31-28
C>A 30-29
B>C 20-17

Using defeat support, C will win (in most Condorcet system, I think.  The
candidate with the smallest pairwise loss in a three candidate cycle should
win in PC, Smith//PC, Ranked Pairs [Tideman] & SSD).

The A voters are punished by voting a sincere tie between B and C (or bullet
voting A).  If they randomly broke their ties (ie voted insincerely), they
would get a better result. B would beat C by 31 to 28 (assuming the ties are
broken fifty/fifty) and A would win.  This would be the result in the first
place if we add 0.5 to each candidate in a tie or use margins (they are
equivalent).

It doesn't seem to make sense that the 22 voters voting B and C equally
return a different result than if 11 of them voted B over C and 11 voted C
over B.  This is what I meant when I said that defeat support behaves
erratically.  Note that it will always be the best strategy in defeat
support not to tie any candidates or truncate, encouraging you to vote
insincerely every time you do not have a preference between two candidates.