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<div dir="ltr" data-setdir="false">Hi Rob,</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">I'm not quite seeing the connection between the goal of renaming monotonicity, and the introduction (or popularization) of another eight criteria. Woodall still referred to it all as monotonicity, so how does his work help?</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">A couple of the criteria are so hard to satisfy that for most people it's probably not worth learning about them. Namely, Mono-raise-random and Mono-sub-top are apparently only satisfied by FPP and certain top-heavy Borda-like rules that Woodall didn't even see fit to name. His motivation for having these criteria was clearly not advocacy...</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">If you categorize the criteria, doing it by the operation performed gives the expected results I'd say:</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">modifying existing ballots: Mono-raise, Mono-raise-delete, Mono-raise-random, Mono-append. All four of these involve raising a candidate, except for the odd edge case that happens to exist within Woodall's framework, that "appending" the least liked candidate of the ballot could actually fail to raise him over anyone. If your framework doesn't support an "append" operation with that effect, then Mono-raise implies Mono-append, and Mono-raise-random implies all of the other three.</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">substituting ballots: Mono-sub-top and Mono-sub-plump can be categorized the same as Mono-raise because they can be conceived of as special cases (weaker forms) of Mono-raise-random and Mono-raise-delete respectively. (They aren't so much weaker though... Woodall doesn't offer any methods that satisfy the easier criterion of the pair and not the harder one.)</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">adding/dropping ballots: Mono-add-top, Mono-remove-bottom, Mono-add-plump. These are all implied by Participation (though Participation is much stronger than any of these). Note that you can rephrase Mono-remove-bottom to be about adding ballots.</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">Kevin</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false"><br></div><div><br></div>
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Le mardi 17 novembre 2020 à 02:58:35 UTC−6, Rob Lanphier <robla@robla.net> a écrit :
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<div><div dir="ltr">Thanks Toby! Given the private and public responses I've gotten to my<br></div><div dir="ltr">question, and the deeper understanding of "the Monotonicity criterion"<br></div><div dir="ltr">that I'm developing, I think that it makes sense to figure out how<br></div><div dir="ltr">"the Woodall nine" (as I'll start calling them) map to "monotonicity"<br></div><div dir="ltr">when talking to people who understand matrix addition.<br></div><div dir="ltr"><br></div><div dir="ltr">More below...<br></div><div dir="ltr"><br></div><div dir="ltr">On Mon, Nov 16, 2020 at 2:17 AM Toby Pereira <<a href="mailto:tdp201b@yahoo.co.uk" rel="nofollow" target="_blank">tdp201b@yahoo.co.uk</a>> wrote:<br></div><div dir="ltr">> I think the scenarios where new ballots are added have more in common with<br></div><div dir="ltr">> participation than monotonicity, in terms of how it is normally understood in<br></div><div dir="ltr">> voting theory at least.<br></div><div dir="ltr"><br></div><div dir="ltr">Let's use the Woodall Nine to talk about this. What would you say the<br></div><div dir="ltr">mapping is? I started coming up with my own version of the list<br></div><div dir="ltr">(which was serious), but this became a self-parody. The format of<br></div><div dir="ltr">each line is<br></div><div dir="ltr"><br></div><div dir="ltr">* woodall-name - robla-named-criterion ("Proposed Wikipedia/electowiki Article")<br></div><div dir="ltr"><br></div><div dir="ltr">Here's the mappings as I saw them on my first runthough:<br></div><div dir="ltr"><br></div><div dir="ltr">* mono-raise - dont-muck-with-ballots-criterion ("Monotonicity (Classic)")<br></div><div dir="ltr">* mono-raise-delete - participation-criterion ("Monotonicity (Nuke ballots)")<br></div><div dir="ltr">* mono-raise-random - adding-random-ballots-causes-mayhem-criterion<br></div><div dir="ltr">("Monotonicity (Add random)")<br></div><div dir="ltr">* mono-append - fill-in-ballot-bubbles-criterion ("Monotonicity (Add<br></div><div dir="ltr">preference)")<br></div><div dir="ltr">* mono-sub-plump - replace-ballots-criterion ("Monotonicity (Erase preference)")<br></div><div dir="ltr">* mono-sub-top - replace-with-new-winner-criterion ("Monotonicity ()")<br></div><div dir="ltr">* mono-add-plump -<br></div><div dir="ltr">add-incompletely-ranked-ballots-to-cause-loss-criterion ("Monotonicity<br></div><div dir="ltr">(Add incomplete ballots)")<br></div><div dir="ltr">* mono-add-top - add-top-scored-but-mostly-random-criterion<br></div><div dir="ltr">("Monotonicity (Add mostly random)")<br></div><div dir="ltr">* mono-remove-bottom -<br></div><div dir="ltr">remove-bottom-ranked-Condorcet-loser-ballots-criterion ("Monotonicity<br></div><div dir="ltr">(Remove Condorcet loser haters)")<br></div><div dir="ltr"><br></div><div dir="ltr">I think this thing needs to exist in the world, so I'm actually going<br></div><div dir="ltr">to keep working on it here:<br></div><div dir="ltr"><br></div><div dir="ltr"><<a href="https://electowiki.org/wiki/User:RobLa/Woodall-to-RobLa" rel="nofollow" target="_blank">https://electowiki.org/wiki/User:RobLa/Woodall-to-RobLa</a>><br></div><div dir="ltr"><br></div><div dir="ltr">Toby, I would love for you and others on this mailing list to come up<br></div><div dir="ltr">with more serious versions. I spent about an hour trying to be<br></div><div dir="ltr">serious when coming up with my mappings, and I think it was a valuable<br></div><div dir="ltr">exercise. My fear: there are many electoral reform advocates who will<br></div><div dir="ltr">say "I understand the monotonicity criterion". However, most of<br></div><div dir="ltr">those people wouldn't be able to answer this question: "what do YOU<br></div><div dir="ltr">mean when you say 'monotonicity criterion'?" My guess: they would<br></div><div dir="ltr">deflect, and say "I know someone who knows what it means, and I've<br></div><div dir="ltr">never really understood it, but I THINK it means this: xyz", and then<br></div><div dir="ltr">their "xyz" would be an oversimplified example involving Woodall's<br></div><div dir="ltr">"mono-raise" or perhaps "Participation" or something vaguely related<br></div><div dir="ltr">to Pareto efficiency. They probably don't understand very well, and<br></div><div dir="ltr">my hunch is that most people on this mailing list are overconfident<br></div><div dir="ltr">with THEIR understanding of "monotonicity".<br></div><div dir="ltr"><br></div><div dir="ltr">When someone asks "What is the 'monotonicity criterion'?", it seems<br></div><div dir="ltr">the correct answer is to throw the question back at them: "before I<br></div><div dir="ltr">explain: do you know what 'monotonicity' is?". If it seems they<br></div><div dir="ltr">aren't very well-versed in advanced mathematics, and they aren't<br></div><div dir="ltr">familiar with what a monotonically-increasing sequence is, then assume<br></div><div dir="ltr">that it's time to back off the math jargon. I think "monotonicity<br></div><div dir="ltr">criterion" seems to be a terrible name for talking about electoral<br></div><div dir="ltr">reform.<br></div><div dir="ltr"><br></div><div dir="ltr">That's the reason why I want to talk about the Woodall Nine. I'd like<br></div><div dir="ltr">to come up with layperson names for each of them, and possibly map<br></div><div dir="ltr">them to various criteria that have Wikipedia articles about them. If<br></div><div dir="ltr">there's not yet a Wikipedia article, maybe an electowiki article. If<br></div><div dir="ltr">there's not yet an electowiki article, maybe a section of an<br></div><div dir="ltr">electowiki article.<br></div><div dir="ltr"><br></div><div dir="ltr">Responding to one last bit of your email:<br></div><div dir="ltr"><br></div><div dir="ltr">> Mono-add-top is just a specific case of participation.<br></div><div dir="ltr"><br></div><div dir="ltr">Are there any other mono-woodall methods that are subsets of the<br></div><div dir="ltr">Participation criterion?<br></div><div dir="ltr"><<a href="https://electowiki.org/wiki/Participation_criterion" rel="nofollow" target="_blank">https://electowiki.org/wiki/Participation_criterion</a>><br></div><div dir="ltr"><br></div><div dir="ltr">Rob<br></div><div dir="ltr">----<br></div><div dir="ltr">Election-Methods mailing list - see <a href="https://electorama.com/em " rel="nofollow" target="_blank">https://electorama.com/em </a>for list info<br></div></div>
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