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<div dir="ltr" data-setdir="false">I think the biggest problem with Schulze, more than that it is complicated to explain, is that you're basically asking people to take it on trust that it is even a method at all. From the Wikipedia article:</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">"<span><span style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;">It can be proven that </span><span class="ydp65aaba9dmwe-math-element" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"><span class="ydp65aaba9dmwe-math-mathml-inline ydp65aaba9dmwe-math-mathml-a11y" style="display: none; width: 1px; font-size: 16.52px; min-height: 1px;">{\displaystyle p[X,Y]>p[Y,X]}</span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/888212514ef5f6aab86a6e178a74bf64285570ac" class="ydp65aaba9dmwe-math-fallback-image-inline" alt="p[X,Y] > p[Y,X]" style="border: 0px; vertical-align: -0.838ex; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; display: inline-block; width: 17.689ex;" data-inlineimagemanipulating="true" data-id="1575546769768"></span><span style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"> and </span><span class="ydp65aaba9dmwe-math-element" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"><span class="ydp65aaba9dmwe-math-mathml-inline ydp65aaba9dmwe-math-mathml-a11y" style="display: none; width: 1px; font-size: 16.52px; min-height: 1px;">{\displaystyle p[Y,Z]>p[Z,Y]}</span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/07668824ec7d421e6c4ba93cdb1113bd31c89161" class="ydp65aaba9dmwe-math-fallback-image-inline" alt="p[Y,Z] > p[Z,Y]" style="border: 0px; vertical-align: -0.838ex; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; display: inline-block; width: 17.089ex;" data-inlineimagemanipulating="true" data-id="1575546769769"></span><span style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"> together imply </span><span class="ydp65aaba9dmwe-math-element" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"><span class="ydp65aaba9dmwe-math-mathml-inline ydp65aaba9dmwe-math-mathml-a11y" style="display: none; width: 1px; font-size: 16.52px; min-height: 1px;">{\displaystyle p[X,Z]>p[Z,X]}</span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a289a31ba341ad5972484971896b7ade6887206" class="ydp65aaba9dmwe-math-fallback-image-inline" alt="p[X,Z] > p[Z,X]" style="border: 0px; vertical-align: -0.838ex; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; display: inline-block; width: 17.503ex;" data-inlineimagemanipulating="true" data-id="1575546769771"></span><span style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;">.</span><sup id="ydp65aaba9dcite_ref-schulze2011_1-1" class="ydp65aaba9dreference" style="line-height: 1; white-space: nowrap; font-size: 11.2px; color: rgb(34, 34, 34); font-family: sans-serif;"><a href="https://en.wikipedia.org/wiki/Schulze_method#cite_note-schulze2011-1" style="color: rgb(11, 0, 128); background: none;" rel="nofollow" target="_blank">[1]</a></sup><sup class="ydp65aaba9dreference" style="line-height: 1; white-space: nowrap; font-size: 11.2px; color: rgb(34, 34, 34); font-family: sans-serif;">:ยง4.1</sup><span style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"> Therefore, it is guaranteed (1) that the above definition of "</span><i style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;">better</i><span style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;">" really defines a </span><a href="https://en.wikipedia.org/wiki/Transitive_relation" title="Transitive relation" style="color: rgb(11, 0, 128); background-image: none; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; font-family: sans-serif; font-size: 14px;" rel="nofollow" target="_blank" class="">transitive relation</a><span style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"> and (2) that there is always at least one candidate </span><span class="ydp65aaba9dmwe-math-element" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"><span class="ydp65aaba9dmwe-math-mathml-inline ydp65aaba9dmwe-math-mathml-a11y" style="display: none; width: 1px; font-size: 16.52px; min-height: 1px;">{\displaystyle D}</span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f34a0c600395e5d4345287e21fb26efd386990e6" class="ydp65aaba9dmwe-math-fallback-image-inline" alt="D" style="border: 0px; vertical-align: -0.338ex; margin: 0px; display: inline-block; width: 1.924ex; min-height: 2.176ex;" data-inlineimagemanipulating="true"></span><span style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"> with </span><span class="ydp65aaba9dmwe-math-element" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"><span class="ydp65aaba9dmwe-math-mathml-inline ydp65aaba9dmwe-math-mathml-a11y" style="display: none; width: 1px; font-size: 16.52px; min-height: 1px;">{\displaystyle p[D,E]\geq p[E,D]}</span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cfb3cce2eb9fad83d31d37a1aa9c13116881b2a3" class="ydp65aaba9dmwe-math-fallback-image-inline" alt="{\displaystyle p[D,E]\geq p[E,D]}" style="border: 0px; vertical-align: -0.838ex; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; display: inline-block; width: 17.582ex;" data-inlineimagemanipulating="true" data-id="1575546769773"></span><span style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"> for every other candidate </span><span class="ydp65aaba9dmwe-math-element" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"><span class="ydp65aaba9dmwe-math-mathml-inline ydp65aaba9dmwe-math-mathml-a11y" style="display: none; width: 1px; font-size: 16.52px; min-height: 1px;">{\displaystyle E}</span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="ydp65aaba9dmwe-math-fallback-image-inline" alt="E" style="border: 0px; vertical-align: -0.338ex; margin: 0px; display: inline-block; width: 1.776ex; min-height: 2.176ex;" data-inlineimagemanipulating="true"></span><span style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;">.</span></span>"</div><div><br></div><div dir="ltr" data-setdir="false">"It can be proven". Well thanks. And also <a href="https://rangevoting.org/SchulzeComplic.html" rel="nofollow" target="_blank">https://rangevoting.org/SchulzeComplic.html</a></div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">"<span><span style="color: rgb(0, 0, 0); font-family: Arial, sans-serif; font-size: medium;">If the strongest path from L to W, is stronger than, or at least as strong as, the strongest path from W to L, and if this is </span><i style="color: rgb(0, 0, 0); font-family: Arial, sans-serif; font-size: medium;">simultaneously</i><span style="color: rgb(0, 0, 0); font-family: Arial, sans-serif; font-size: medium;"> true for </span><i style="color: rgb(0, 0, 0); font-family: Arial, sans-serif; font-size: medium;">every</i><span style="color: rgb(0, 0, 0); font-family: Arial, sans-serif; font-size: medium;"> L, then W is a "Schulze winner." Schulze proved the theorem that such a W always exists (at least using "margins"; I am confused re the "winning-votes" enhancement).</span></span>"<br><div><br></div><div dir="ltr" data-setdir="false">Even less convincing.</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">I know I'm going a bit off-topic, but what is the estimated probability that Schulze and Ranked Pairs would give a different result in a real-life election? I'd be surprised if it was more than about 1 in 10,000, and where there was a different winner between them, neither winner would be so much obviously the "right" winner that it would cause protests in the streets if the other one were to win.</div><div><br></div></div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false"><br></div><div><br></div>
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On Thursday, 5 December 2019, 01:50:13 GMT, robert bristow-johnson <rbj@audioimagination.com> wrote:
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<div><div dir="ltr">Lotsa people to respond to. I feel I must begin with Markus because, as a signal processing algorithmist, I have so much respect for Markus and for the Schulze method.<br clear="none"><br clear="none">I think I understand the Schulze beatpath method and agree with the consensus of the geeks that, technically, it is simply the best currently-known RCV method. Most immune to all of these voting strategies.<br clear="none"><div class="ydp612f87b6yqt7017522591" id="ydp612f87b6yqtfd31609"><br clear="none"></div></div></div>
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