[EM] Improved Copeland (was "A New Spinoff of Our Recent Discussions")
km_elmet at t-online.de
Fri Jun 7 13:16:56 PDT 2019
On 06/06/2019 23.11, Forest Simmons wrote:
> Here's another slightly simpler approach aimed at the lay voter:
> Tell the audience that the Condorcet ideal is a candidate that is not
> pairwise beaten by any other candidate.
> When that is not possible, it is natural to consider a candidate that is
> beaten pairwise by the fewest other candidates. This idea is the basis
> of the Copeland Method.
> There are two problems with the Copeland method: (1) It has a strong
> tendency to produce ties, and (2) More subtle problems created by
> cloning certain candidates to increase the number of defeats suffered by
> certain other candidates without increasing the number of defeats of the
> cloned candidates.
> Because of these two problems, Copeland is not considered a serious
> contender for use in public elections.
> But what if there were a simple modification of Copeland that would
> totally resolve these two problems in one fell swoop?
> There is; instead of counting the number of candidates that defeat
> candidate X, (and electing the candidate with the smallest count), we
> add up all of the first place votes of all of the candidates that defeat
> X, and elect the candidate with the smallest sum.
This sounds like what I called first preference Copeland and you called
Clone-proofed Copeland back in 2006:
In the examples below, I'll call the candidates' sums "penalties".
It's not cloneproof. Example outline by Warren Smith
ABCA cycle, so A's penalty is 3, B's penalty is 6, and C's penalty is 4.
Now clone A in a Condorcet cycle (into D,E,F below):
B is beaten by D, E, and F, so his penalty is 6.
C is beaten by B, so his penalty is 4.
D is beaten by C and F, so his penalty is 5.
E is beaten by C and D, so his penalty is 5.
F is beaten by C and E, so his penalty is 5.
Cloning A made A lose and C win.
Also, compared to ordinary Copeland, it loses monotonicity:
Everybody has a penalty of 3, so we have a tie.
Now raise A to the top on one of the B>C>A ballots:
A is beaten by C: penalty 3
B is beaten by A: penalty 4
C is beaten by B: penalty 2
so C wins.
The problem here is that putting A top may harm A by concealing a
candidate (here, B) who would otherwise penalize someone else (here, C)
enough to keep A from losing.
The fpA - fpC method avoids nonmonotonicity by crediting A with A-top
ballots. If raising A to the top conceals some penalizer's first
preferences, that doesn't matter because whatever A loses to the third
candidate, he regains by the fpA term.
So the fpA-fpC method seems better than first preference Copeland for
three candidates. If only we could cloneproof it! (And hopefully retain
its anti-strategy properties, like CD compliance and unmanipulable majority)
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