Kevin,
I'm afraid that IA/MPO does fail Plurality:
33 A
17:A=C
17:B=C
33 B
The IA/MPO ratio for both A and B is 50/50 = 1, while the ratio for C is
34/33, which is greater than 1.
But this is about the worst violation posssible, and it doesn't seem too
bad to me.
If equal top ranking were not allowed, then Plurality would not be
violated. Or (in other words) the method satisfies a weaker version of
Plurality that says if C is ranked on fewer ballots than X is ranked top
but not equal to) C, then C cannot win.
I don't know if that is helpful.
When i get more time, I'll show you why I think that IA/MPO is a good
method when the true preferences are given by something like
30 A
3 AC
15 CA
4 C
15 CB
3 BC
30 B
All of our favorite methods, including IA/MPO, say that C should win.
But disinformation when A and B are the two big party candidates, may
easily result in voted ballots of
30 A
3 AC
15 C=A
4 C
15 C=B
3 BC
30 B
Candidate C still wins under IA/MPO, even though this is a violation of
Plurality.
Message: 1
Date: Sun, 6 Oct 2013 15:21:35 -0700
From: Forest Simmons fsimm...@pcc.edu
To: EM election-methods@lists.electorama.com
Subject: [EM] Try this method on your favorite election scenario
Message-ID:
cap29onfvlcopwcx7c0i-hqz_2qujtc332cjtyux2yhurhnr...@mail.gmail.com
Content-Type: text/plain; charset=iso-8859-1
Ballots are ranked or rated. If ranked, then equal ranking and truncation
are allowed.
Let IA stand for Implicit Approval, which for any candidate X is the number
of ballots on which X is ranked or rated above bottom, i.e. neither
truncated nor rated at zero.
Let MPO stand for maximum pairwise opposition, which (for candidate X) is
the maximum (as Y varies over the other candidates) of the number of
ballots on which a strict preference of Y over X is indicated.
The winner of this method (IA/MPO) is the candidate with the highest ratio
of IA to MPO.
Example
45 AB
35 BC
20 C
For A IA is 45 and MPO is 55, so IA/MPO is 45/55 or 9/11.
For B IA is 80 and MPO is 45, so IA/MPO is 80/45 or 16/9.
For C IA is 55 and MPO is 80, so IA/MPO is 55/80 or 11/16.
The IA/MPO winner is B.
If, instead, the A faction votes 45 A, then the ratios become ...
For A (the same) 9/11.
For B IA is 35 and MPO is still 45, so the ratio is 7/9.
For C IA is still 55 and MPO is 45, so the ratio is 11/9.
This time C wins.
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Message: 2
Date: Mon, 7 Oct 2013 17:51:37 +0100 (BST)
From: Kevin Venzke step...@yahoo.fr
To: em election-meth...@electorama.com
Subject: Re: [EM] Try this method on your favorite election scenario
Message-ID:
1381164697.61992.yahoomail...@web171501.mail.ir2.yahoo.com
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Hi Forest,
De?: Forest Simmons fsimm...@pcc.edu
??: EM election-methods@lists.electorama.com
Envoy? le : Dimanche 6 octobre 2013 17h21
Objet?: [EM] Try this method on your favorite election scenario
Ballots are ranked or rated.? If ranked, then equal ranking and
truncation are allowed.
?
Let IA stand for Implicit Approval, which for any candidate X?is the
number of ballots on which?X is?ranked or rated above bottom, i.e. neither
truncated nor rated at zero.
?
Let MPO stand for maximum pairwise opposition, which (for candidate X)?is
the maximum (as?Y varies over the other candidates) of the number of
ballots on which a strict preference of Y over?X is indicated.
?
The winner of this method (IA/MPO) is the candidate with the highest
ratio of IA to MPO.
?
Example
?
45 AB
35 BC
20 C
?
For A? IA is 45 and MPO is 55, so IA/MPO is 45/55 or 9/11.
For B IA is 80 and MPO is 45, so IA/MPO is 80/45 or 16/9.
For C IA is 55 and MPO is 80, so IA/MPO is 55/80 or 11/16.
?
The IA/MPO winner is B.
?
If, instead, the A faction votes 45 A, then the ratios become ...
?
For A? (the same) 9/11.
For B? IA is 35 and MPO is still 45, so the ratio is 7/9.
For C IA is still 55 and MPO is 45, so the ratio is 11/9.
?
This time C wins.
IA/MPO seems like a pretty good method. It seems to be guaranteed that at
least one candidate will have a score = 100%. That's elegant. With that
assumption it seems easy to demonstrate that the method satisfies Plurality
and SDSC/Minimal Defense.
My guess is that it must satisfy FBC since the component scores each do,
and the only processing is taking the ratio.
I suspect that we have lost SFC compared to MMPO (Strategy-Free:
roughly, if A has a majority over B and there is no majority over A, B
can't win), but it might be hard to contrive a failure scenario.
If it's right that IA/MPO satisfies FBC, MD, and Plurality, it's not in a
crowded space... Though MAMPO satisfies those as well as SFC, it's
