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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">For what people usually mean when discussing monotonicity (such as in connection with IRV) this corresponds to Woodall's Mono-raise.</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">I'd say the criterion discussed second most often is Mono-add-top, a weaker form of Participation.</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">I don't see how Woodall can be wrong, it's his choice to define these criteria and characterize them as dealing with monotonicity. But to me, if you say a method "fails monotonicity," or "is monotone," you're either talking about Mono-raise or else you're being unclear. Inserting these into an article called "Monotonicity" could be unhelpful unless it's made clear that these are other criteria connected to the idea, and are used (as far as I know) primarily by Woodall.</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">Note that (at least in other articles) Woodall is/was largely concerned with which sets of properties are compatible with each other, and he didn't usually make statements judging the relative value of criteria. This leaves the job to other people to explain why we should care about a given property.</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><br></div>
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Le dimanche 15 novembre 2020 à 20:32:50 UTC−6, Rob Lanphier <robla@robla.net> a écrit :
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<div><div dir="ltr">Hi folks,<br></div><div dir="ltr"><br></div><div dir="ltr">I don't think I've ever fully prerused the "Voting matters"[1] website<br></div><div dir="ltr">before, and realized how serious of a publication it was (or rather<br></div><div dir="ltr">"is"):<br></div><div dir="ltr">[1]: <<a href="http://www.votingmatters.org.uk/" rel="nofollow" target="_blank">http://www.votingmatters.org.uk/</a>><br></div><div dir="ltr"><br></div><div dir="ltr">Maybe I did, but I forgot about it. It looks like there are several<br></div><div dir="ltr">interesting papers to read there.<br></div><div dir="ltr"><br></div><div dir="ltr">Douglas Woodall published at least a couple of papers there. It also<br></div><div dir="ltr">seems that Woodall's definition of "monotonicity"[2] is the favorite<br></div><div dir="ltr">of many folks who like to discuss election methods. In particular, I<br></div><div dir="ltr">want to highlight Issue 3, paper 5 of "Voting matters":<br></div><div dir="ltr">[2]: <a href="http://www.votingmatters.org.uk/ISSUE3/P5.HTM" rel="nofollow" target="_blank">http://www.votingmatters.org.uk/ISSUE3/P5.HTM</a><br></div><div dir="ltr"><br></div><div dir="ltr">Here's Woodall's definition of monotonicity from that paper, which<br></div><div dir="ltr">breaks up monotonicity into nine different criteria:<br></div><div dir="ltr">> Monotonicity. A candidate x should not be harmed if:<br></div><div dir="ltr">><br></div><div dir="ltr">> * (mono-raise) x is raised on some ballots without changing the orders of the other candidates;<br></div><div dir="ltr">> * (mono-raise-delete) x is raised on some ballots and all candidates now below x on those ballots are deleted from them;<br></div><div dir="ltr">> * (mono-raise-random) x is raised on some ballots and the positions now below x on those ballots are filled (or left vacant) in any way that results in a valid ballot;<br></div><div dir="ltr">> * (mono-append) x is added at the end of some ballots that did not previously contain x;<br></div><div dir="ltr">> * (mono-sub-plump) some ballots that do not have x top are replaced by ballots that have x top with no second choice;<br></div><div dir="ltr">> * (mono-sub-top) some ballots that do not have x top are replaced by ballots that have x top (and are otherwise arbitrary);<br></div><div dir="ltr">> * (mono-add-plump) further ballots are added that have x top with no second choice;<br></div><div dir="ltr">> * (mono-add-top) further ballots are added that have x top (and are otherwise arbitrary);<br></div><div dir="ltr">> * (mono-remove-bottom) some ballots are removed, all of which have x bottom, below all other candidates.<br></div><div dir="ltr"><br></div><div dir="ltr">That's nine different criteria that all could be called<br></div><div dir="ltr">"monotonicity". This raises a few questions for me:<br></div><div dir="ltr"><br></div><div dir="ltr">1. Is Woodall's definition correct?<br></div><div dir="ltr">2. Is Woodall's definition the most useful?<br></div><div dir="ltr">3. Is Woodall's definition overly-complicated, or just<br></div><div dir="ltr">appropriately-complicated?<br></div><div dir="ltr">4. Does breaking up monotonicity into nine different criteria make it<br></div><div dir="ltr">easier to understand, or harder?<br></div><div dir="ltr">5. Was Woodall just copying his definition from someone else when<br></div><div dir="ltr">publishing those nine criteria? If so, who?<br></div><div dir="ltr"><br></div><div dir="ltr">The reason why I ask: I want to improve the electowiki article about<br></div><div dir="ltr">monotonicity[3], and I'm wondering if emphasis on the nine criteria<br></div><div dir="ltr">above would help make the article clearer:<br></div><div dir="ltr">[3]: <a href="https://electowiki.org/wiki/Monotonicity" rel="nofollow" target="_blank">https://electowiki.org/wiki/Monotonicity</a><br></div><div dir="ltr"><br></div><div dir="ltr">Should the electowiki community use Woodall's nine criteria as the<br></div><div dir="ltr">electowiki definition of "monotonicity"?<br></div><div dir="ltr"><br></div><div dir="ltr">Rob<br></div><div dir="ltr">p.s. a YouTube video[4] posted to C4ES's Discord server is what<br></div><div dir="ltr">inspired me to compose this email:<br></div><div dir="ltr">[4]: <a href="https://youtu.be/OI232JSDwDg" rel="nofollow" target="_blank">https://youtu.be/OI232JSDwDg</a><br></div><div dir="ltr"><br></div><div dir="ltr">p.p.s.: What I mean by "C4ES's Discord Server"[5] is the Discord<br></div><div dir="ltr">server that is operated by the Center for Election Science:<br></div><div dir="ltr">[5]: <a href="https://electionscience.org/discord" rel="nofollow" target="_blank">https://electionscience.org/discord</a><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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