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--
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.
----
D- As usual --- with 3 choices and divided majorities, some seemingly strange
stuff can happen.
Putting the votes in a place votes table and treating the B=C votes as half
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)
???
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