<div dir="ltr"><div><div><div><div><div>Kevin,<br><br></div>I'm afraid that IA/MPO does fail Plurality:<br><br></div>33 A<br></div>17:A=C<br></div>17:B=C<br></div>33 B<br><div><div><div><div><div><div><div><div class="gmail_extra">
<br></div><div class="gmail_extra">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.<br><br></div><div class="gmail_extra">But this is about the worst violation posssible, and it doesn't seem too bad to me.<br>
<br></div><div class="gmail_extra">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.<br>
<br></div><div class="gmail_extra">I don't know if that is helpful.<br><br></div><div class="gmail_extra">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<br>
<br></div><div class="gmail_extra">30 A<br></div><div class="gmail_extra">3 A>C<br></div><div class="gmail_extra">15 C>A<br></div><div class="gmail_extra">4 C<br></div><div class="gmail_extra">15 C>B<br></div><div class="gmail_extra">
3 B>C<br></div><div class="gmail_extra">30 B<br><br></div><div class="gmail_extra">All of our favorite methods, including IA/MPO, say that C should win.<br><br></div><div class="gmail_extra">But disinformation when A and B are the two big party candidates, may easily result in voted ballots of<br>
<br><div class="gmail_extra">30 A<br></div><div class="gmail_extra">3 A>C<br></div><div class="gmail_extra">15 C=A<br></div><div class="gmail_extra">4 C<br></div><div class="gmail_extra">15 C=B<br></div><div class="gmail_extra">
3 B>C<br></div>30 B<br><br></div><div class="gmail_extra">Candidate C still wins under IA/MPO, even though this is a violation of Plurality.<br></div><div class="gmail_extra"><br><br></div><div class="gmail_extra"><div class="gmail_quote">
<br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
Message: 1<br>
Date: Sun, 6 Oct 2013 15:21:35 -0700<br>
From: Forest Simmons <<a href="mailto:fsimmons@pcc.edu">fsimmons@pcc.edu</a>><br>
To: EM <<a href="mailto:election-methods@lists.electorama.com">election-methods@lists.electorama.com</a>><br>
Subject: [EM] Try this method on your favorite election scenario<br>
Message-ID:<br>
<<a href="mailto:CAP29onfVLcoPWCX7C0i-hQz_2qUJtC332cJtYuX2YHURHNrJUA@mail.gmail.com">CAP29onfVLcoPWCX7C0i-hQz_2qUJtC332cJtYuX2YHURHNrJUA@mail.gmail.com</a>><br>
Content-Type: text/plain; charset="iso-8859-1"<br>
<br>
Ballots are ranked or rated. If ranked, then equal ranking and truncation<br>
are allowed.<br>
<br>
Let IA stand for Implicit Approval, which for any candidate X is the number<br>
of ballots on which X is ranked or rated above bottom, i.e. neither<br>
truncated nor rated at zero.<br>
<br>
Let MPO stand for maximum pairwise opposition, which (for candidate X) is<br>
the maximum (as Y varies over the other candidates) of the number of<br>
ballots on which a strict preference of Y over X is indicated.<br>
<br>
The winner of this method (IA/MPO) is the candidate with the highest ratio<br>
of IA to MPO.<br>
<br>
Example<br>
<br>
45 A>B<br>
35 B>C<br>
20 C<br>
<br>
For A IA is 45 and MPO is 55, so IA/MPO is 45/55 or 9/11.<br>
For B IA is 80 and MPO is 45, so IA/MPO is 80/45 or 16/9.<br>
For C IA is 55 and MPO is 80, so IA/MPO is 55/80 or 11/16.<br>
<br>
The IA/MPO winner is B.<br>
<br>
If, instead, the A faction votes 45 A, then the ratios become ...<br>
<br>
For A (the same) 9/11.<br>
For B IA is 35 and MPO is still 45, so the ratio is 7/9.<br>
For C IA is still 55 and MPO is 45, so the ratio is 11/9.<br>
<br>
This time C wins.<br>
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Message: 2<br>
Date: Mon, 7 Oct 2013 17:51:37 +0100 (BST)<br>
From: Kevin Venzke <<a href="mailto:stepjak@yahoo.fr">stepjak@yahoo.fr</a>><br>
To: em <<a href="mailto:election-methods@electorama.com">election-methods@electorama.com</a>><br>
Subject: Re: [EM] Try this method on your favorite election scenario<br>
Message-ID:<br>
<<a href="mailto:1381164697.61992.YahooMailNeo@web171501.mail.ir2.yahoo.com">1381164697.61992.YahooMailNeo@web171501.mail.ir2.yahoo.com</a>><br>
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<br>
Hi Forest,<br>
<br>
<br>
>________________________________<br>
> De?: Forest Simmons <<a href="mailto:fsimmons@pcc.edu">fsimmons@pcc.edu</a>><br>
>??: EM <<a href="mailto:election-methods@lists.electorama.com">election-methods@lists.electorama.com</a>><br>
>Envoy? le : Dimanche 6 octobre 2013 17h21<br>
>Objet?: [EM] Try this method on your favorite election scenario<br>
><br>
>Ballots are ranked or rated.? If ranked, then equal ranking and truncation are allowed.<br>
>?<br>
>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.<br>
>?<br>
>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.<br>
>?<br>
>The winner of this method (IA/MPO) is the candidate with the highest ratio of IA to MPO.<br>
>?<br>
>Example<br>
>?<br>
>45 A>B<br>
>35 B>C<br>
>20 C<br>
>?<br>
>For A? IA is 45 and MPO is 55, so IA/MPO is 45/55 or 9/11.<br>
>For B IA is 80 and MPO is 45, so IA/MPO is 80/45 or 16/9.<br>
>For C IA is 55 and MPO is 80, so IA/MPO is 55/80 or 11/16.<br>
>?<br>
>The IA/MPO winner is B.<br>
>?<br>
>If, instead, the A faction votes 45 A, then the ratios become ...<br>
>?<br>
>For A? (the same) 9/11.<br>
>For B? IA is 35 and MPO is still 45, so the ratio is 7/9.<br>
>For C IA is still 55 and MPO is 45, so the ratio is 11/9.<br>
>?<br>
>This time C wins.<br>
<br>
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.<br>
<br>
My guess is that it must satisfy FBC since the component scores each do, and the only "processing" is taking the ratio.<br>
<br>
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.<br>
<br>
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 probably less sensitive to the rankings. (MDDA has SFC but can fail Plurality.)<br>
<br>
I should get my simulations running again. I seem to recall being disappointed with the performance of MDDA and MAMPO.<br>
<br>
<br>
Kevin Venzke<br>
<br>
<br>
<br>
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End of Election-Methods Digest, Vol 112, Issue 2<br>
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