# Condorcet cyclic drop rule

DEMOREP1 at aol.com DEMOREP1 at aol.com
Sat Mar 31 17:09:52 PST 2001

```Mr. Layton wrote in part--

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.
----
D- As usual --- with 3 choices and divided majorities, some seemingly strange
stuff can happen.

votes (to get *complete* results -- 59 total votes in all columns and rows),
there is

1    2   3

A   22   16   21   59
B   20   19   20   59
C   17   24   18   59

59   59   59

Standard mantra-- Who, if anybody, has majority YES support (since mere
rankings do NOT show *absolute* support but only *relative* support) ???

If mere YES majority support is ignored, then which majority of the 59 voters
(using the first plus 2nd place votes) is the happiest the earliest ---

A 38
B 39
C 41
118

Regarding the ---

Pairwise Table:

A>B 31-28

C>A 30-29

B>C 20-17

Do votes cancel out whether ranked or unranked/tied ???

Is the table thus

A>B 31-28

C>A 30-29

B>C 31-28

or

A>B 3-0

C>A 1-0

B>C 3-0   ???

Do the A>B and B>C results cancel each other (leaving the C>A 1-0 result) ???

Even a friendly 2 choice result may be deemed determined by the margin-

51 (or 1,000,001) K
50 (or 1,000,000) M

Practical result-

K 1
M 0

Recount time (as in the infamous 2000 U.S.A. President election in Florida)
???

```