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<div dir="ltr" data-setdir="false">I think the scenarios where new ballots are added have more in common with participation than monotonicity, in terms of how it is normally understood in voting theory at least. Mono-add-top is just a specific case of participation.</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">Toby</div><div><br></div>
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On Monday, 16 November 2020, 02:32:50 GMT, Rob Lanphier <robla@robla.net> wrote:
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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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