Hello, everyone, new to the list here,

what I really like about First preference Copeland is that it implies a
nice method for calculating a sort of "Condorcet score": just count 1st
preferences of all candidates (including candidate X) that do not beat X
pairwise. Although it is highly resistant to burial, FPC is not cloneproof
and fails ISDA.

However, there is an easy way to fix these two problems: just do sequential
loser elimination using FPC score!
(And when there is a tie at the bottom, break it by applying the same
method to the candidates involved in the tie and finding the loser.)

This method could be named FPCE (First Preference Copeland Elimination) or
ISCR (Instant Simmons-Copeland Runoff). It is cloneproof (because even if
there are clones which hurt one another, eventually there is only one of
them left) and ISDA-compliant (because all candidates outside the Smith set
get eliminated before any Smith set member is eliminated). I think its
burial resistance might be weakened, though, as it fails DMTBR.

Could anyone help with proving/disproving monotonicity, or even LIIA? I
applied the method to the 5-candidate Smith set from the Wikipedia article
about Schulze and there turned out to be an LIIA-compliant order: ADCEB.
I'm curious if it was by accident or not.

Filip Ejlak

It is my impression that all elimination methods are not monotonic, though I certainly can't prove that.

In this case, if I've understood it correctly, try

7 A>B>C
2 B>A>C
7 B>C>A
8 C>A>B

Pairwise we have a cycle: A>B>C>A, so FPC scores are A:9; B:8; C:7. Thus, the method eliminates C and A beats B and A wins.

Now suppose the two B>A>C voters increase their appreciation of A and vote A>B>C instead.

9 A>B>C
7 B>C>A
8 C>A>B

We've got the same pairwise cycle, but now A gets eliminated first and B wins.

Did I calculate correctly?  Is this the type of monotonicity you were asking about?

Jim Faran

From: Election-Methods election-methods-bounces@lists.electorama.com on behalf of Filip Ejlak tersander@gmail.com
Sent: Monday, April 17, 2023 12:19 PM
To: election-methods@lists.electorama.com election-methods@lists.electorama.com
Subject: [EM] a simple, great ISDA-compliant method I've never seen mentioned

Hello, everyone, new to the list here,

what I really like about First preference Copeland is that it implies a nice method for calculating a sort of "Condorcet score": just count 1st preferences of all candidates (including candidate X) that do not beat X pairwise. Although it is highly resistant to burial, FPC is not cloneproof and fails ISDA.

However, there is an easy way to fix these two problems: just do sequential loser elimination using FPC score!
(And when there is a tie at the bottom, break it by applying the same method to the candidates involved in the tie and finding the loser.)

This method could be named FPCE (First Preference Copeland Elimination) or ISCR (Instant Simmons-Copeland Runoff). It is cloneproof (because even if there are clones which hurt one another, eventually there is only one of them left) and ISDA-compliant (because all candidates outside the Smith set get eliminated before any Smith set member is eliminated). I think its burial resistance might be weakened, though, as it fails DMTBR.

Could anyone help with proving/disproving monotonicity, or even LIIA? I applied the method to the 5-candidate Smith set from the Wikipedia article about Schulze and there turned out to be an LIIA-compliant order: ADCEB. I'm curious if it was by accident or not.

Filip Ejlak