<html><head></head><body><div style="color:#000; background-color:#fff; font-family:Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:13px"><div id="yui_3_16_0_ym19_1_1558691737991_16511" dir="ltr"><span id="yui_3_16_0_ym19_1_1558691737991_16577">I think the problem with Schulze versus Ranked Pairs or River is that Schulze is more complicated to understand/explain, and also it's not even obviously a method. Also, realistically you'll probably never encounter an election where any of these three would give a different result. I've often heard people say that these methods can give different results, but I don't think I've ever seen an example, and this suggests to me that it would have to be pretty contrived and complex.</span></div><div id="yui_3_16_0_ym19_1_1558691737991_16511"><span><br></span></div><div id="yui_3_16_0_ym19_1_1558691737991_16511" dir="ltr"><span id="yui_3_16_0_ym19_1_1558691737991_17347">But about Schulze not obviously being a method - have a look at the Wikipedia article under "Computation" - </span><a href="https://en.wikipedia.org/wiki/Schulze_method#Computation" id="yui_3_16_0_ym19_1_1558691737991_17413" class="">https://en.wikipedia.org/wiki/Schulze_method#Computation</a></div><div id="yui_3_16_0_ym19_1_1558691737991_17421"><br></div><div id="yui_3_16_0_ym19_1_1558691737991_17491">And it's that last bit that sticks out:</div><div id="yui_3_16_0_ym19_1_1558691737991_16511"><span><br></span></div><div id="yui_3_16_0_ym19_1_1558691737991_16511"><span id="yui_3_16_0_ym19_1_1558691737991_17083">"</span><span id="yui_3_16_0_ym19_1_1558691737991_17259" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;">It can be proven that</span><span id="yui_3_16_0_ym19_1_1558691737991_17260" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"> </span><span id="yui_3_16_0_ym19_1_1558691737991_17261" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/888212514ef5f6aab86a6e178a74bf64285570ac" aria-hidden="true" alt="p[X,Y] > p[Y,X]" style="border-width: 0px; border-style: initial; vertical-align: -0.838ex; margin: 0px 0px 0px 0; display: inline-block; width: 17.689ex; min-height: 2.843ex;" id="yui_3_16_0_ym19_1_1558691737991_17262" data-id="c6154e3d-a66a-57f6-6802-76b6b2f3565e" class=""></span><span id="yui_3_16_0_ym19_1_1558691737991_17263" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"> </span><span id="yui_3_16_0_ym19_1_1558691737991_17264" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;">and</span><span id="yui_3_16_0_ym19_1_1558691737991_17265" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"> </span><span id="yui_3_16_0_ym19_1_1558691737991_17266" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/07668824ec7d421e6c4ba93cdb1113bd31c89161" aria-hidden="true" alt="p[Y,Z] > p[Z,Y]" style="border-width: 0px; border-style: initial; vertical-align: -0.838ex; margin: 0px 0px 0px 0; display: inline-block; width: 17.089ex; min-height: 2.843ex;" id="yui_3_16_0_ym19_1_1558691737991_17267" class="" data-id="b11dadef-0d1a-016a-0f0a-9b209c7d2206"></span><span id="yui_3_16_0_ym19_1_1558691737991_17268" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"> </span><span id="yui_3_16_0_ym19_1_1558691737991_17269" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;">together imply</span><span id="yui_3_16_0_ym19_1_1558691737991_17270" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"> </span><span id="yui_3_16_0_ym19_1_1558691737991_17271" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a289a31ba341ad5972484971896b7ade6887206" aria-hidden="true" alt="p[X,Z] > p[Z,X]" style="border-width: 0px; border-style: initial; vertical-align: -0.838ex; margin: 0px 0px 0px 0; display: inline-block; width: 17.503ex; min-height: 2.843ex;" id="yui_3_16_0_ym19_1_1558691737991_17272" data-id="ff47649e-2e35-3cba-31e0-4791cb6d8084" class=""></span><span id="yui_3_16_0_ym19_1_1558691737991_17273" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;">.</span><sup id="yui_3_16_0_ym19_1_1558691737991_17274" style="color: rgb(34, 34, 34); font-family: sans-serif; line-height: 1; unicode-bidi: isolate; white-space: nowrap; font-size: 11.2px;"><a href="https://en.wikipedia.org/wiki/Schulze_method#cite_note-schulze2011-1" style="text-decoration-line: none; color: rgb(11, 0, 128); background-image: none;" id="yui_3_16_0_ym19_1_1558691737991_17275">[1]</a></sup><sup id="yui_3_16_0_ym19_1_1558691737991_17276" style="color: rgb(34, 34, 34); font-family: sans-serif; line-height: 1; unicode-bidi: isolate; white-space: nowrap; font-size: 11.2px;">:ยง4.1</sup><span id="yui_3_16_0_ym19_1_1558691737991_17277" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"> </span><span id="yui_3_16_0_ym19_1_1558691737991_17278" 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 id="yui_3_16_0_ym19_1_1558691737991_17279" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;">better</i><span id="yui_3_16_0_ym19_1_1558691737991_17280" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;">" really defines a</span><span id="yui_3_16_0_ym19_1_1558691737991_17281" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"> </span><a href="https://en.wikipedia.org/wiki/Transitive_relation" title="Transitive relation" id="yui_3_16_0_ym19_1_1558691737991_17282" style="font-family: sans-serif; font-size: 14px; background-color: rgb(255, 255, 255); text-decoration-line: none; color: rgb(11, 0, 128); background-image: none;">transitive relation</a><span id="yui_3_16_0_ym19_1_1558691737991_17283" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"> </span><span id="yui_3_16_0_ym19_1_1558691737991_17284" 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 id="yui_3_16_0_ym19_1_1558691737991_17285" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"> </span><span id="yui_3_16_0_ym19_1_1558691737991_17286" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f34a0c600395e5d4345287e21fb26efd386990e6" aria-hidden="true" alt="D" style="border-width: 0px; border-style: initial; vertical-align: -0.338ex; margin: 0px; display: inline-block; width: 1.924ex; min-height: 2.176ex;" id="yui_3_16_0_ym19_1_1558691737991_17287" data-id="c1d8aade-8607-ed1e-b34c-6b6a1d877c8e"></span><span id="yui_3_16_0_ym19_1_1558691737991_17288" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"> </span><span id="yui_3_16_0_ym19_1_1558691737991_17289" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;">with</span><span id="yui_3_16_0_ym19_1_1558691737991_17290" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"> </span><span id="yui_3_16_0_ym19_1_1558691737991_17291" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cfb3cce2eb9fad83d31d37a1aa9c13116881b2a3" aria-hidden="true" alt="{\displaystyle p[D,E]\geq p[E,D]}" style="border-width: 0px; border-style: initial; vertical-align: -0.838ex; margin: 0px 0px 0px 0; display: inline-block; width: 17.582ex; min-height: 2.843ex;" id="yui_3_16_0_ym19_1_1558691737991_17292" data-id="a5f551c0-e83e-387d-1093-41e2f84de068" class=""></span><span id="yui_3_16_0_ym19_1_1558691737991_17293" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"> </span><span id="yui_3_16_0_ym19_1_1558691737991_17294" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;">for every other candidate</span><span id="yui_3_16_0_ym19_1_1558691737991_17295" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"> </span><span id="yui_3_16_0_ym19_1_1558691737991_17296" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;"><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" aria-hidden="true" alt="E" style="border-width: 0px; border-style: initial; vertical-align: -0.338ex; margin: 0px; display: inline-block; width: 1.776ex; min-height: 2.176ex;" id="yui_3_16_0_ym19_1_1558691737991_17297" class="" data-id="44b4d245-4ad1-0686-e376-52df454c9e2c"></span><span id="yui_3_16_0_ym19_1_1558691737991_17298" style="color: rgb(34, 34, 34); font-family: sans-serif; font-size: 14px;">.</span>"</div><div id="yui_3_16_0_ym19_1_1558691737991_16511"><br></div><div id="yui_3_16_0_ym19_1_1558691737991_16511" dir="ltr">"It can be proven..." I don't necessarily mind if it takes a complex proof to show that a method obeys certain criterion like monotonicity etc. But this is just about it being a method that can elect a winner. How complex is this proof? I'm just taking it on trust that it works as a method. With Ranked Pairs or River, it's pretty trivial.</div><div id="yui_3_16_0_ym19_1_1558691737991_16511" dir="ltr"><br></div><div id="yui_3_16_0_ym19_1_1558691737991_16511" dir="ltr">And on Warren Smith's rangevoting.org, <a href="https://rangevoting.org/SchulzeComplic.html" id="yui_3_16_0_ym19_1_1558691737991_17658">https://rangevoting.org/SchulzeComplic.html</a></div><div id="yui_3_16_0_ym19_1_1558691737991_16511" dir="ltr"><br></div><div id="yui_3_16_0_ym19_1_1558691737991_16511" dir="ltr">"<b style="font-family: Arial, sans-serif; font-size: medium;" id="yui_3_16_0_ym19_1_1558691737991_17711">(4)</b><span style="font-family: Arial, sans-serif; font-size: medium;" id="yui_3_16_0_ym19_1_1558691737991_17712"> 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="font-family: Arial, sans-serif; font-size: medium;" id="yui_3_16_0_ym19_1_1558691737991_17713">simultaneously</i><span style="font-family: Arial, sans-serif; font-size: medium;" id="yui_3_16_0_ym19_1_1558691737991_17714"> true for </span><i style="font-family: Arial, sans-serif; font-size: medium;" id="yui_3_16_0_ym19_1_1558691737991_17715">every</i><span style="font-family: Arial, sans-serif; font-size: medium;" id="yui_3_16_0_ym19_1_1558691737991_17716"> 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>"</div><div id="yui_3_16_0_ym19_1_1558691737991_16511" dir="ltr"><br></div><div id="yui_3_16_0_ym19_1_1558691737991_16511" dir="ltr">So even Warren is confused about the proof for winning votes. And bear in mind, this isn't a proof about some property of the method, but that it is even a method.</div><div id="yui_3_16_0_ym19_1_1558691737991_16511" dir="ltr"><br></div><div id="yui_3_16_0_ym19_1_1558691737991_16511" dir="ltr">Toby</div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1558691737991_16512"><br><br></div><div class="yahoo_quoted" id="yui_3_16_0_ym19_1_1558691737991_16538" style="display: block;"> <div style="font-family: Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 13px;" id="yui_3_16_0_ym19_1_1558691737991_16537"> <div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 16px;" id="yui_3_16_0_ym19_1_1558691737991_16536"> <div dir="ltr" id="yui_3_16_0_ym19_1_1558691737991_16535"> <font size="2" face="Arial" id="yui_3_16_0_ym19_1_1558691737991_16534"> <hr size="1" id="yui_3_16_0_ym19_1_1558691737991_16589"> <b><span style="font-weight:bold;">From:</span></b> robert bristow-johnson <rbj@audioimagination.com><br> <b><span style="font-weight: bold;">To:</span></b> election-methods@lists.electorama.com <br> <b><span style="font-weight: bold;">Sent:</span></b> Wednesday, 22 May 2019, 23:14<br> <b><span style="font-weight: bold;">Subject:</span></b> Re: [EM] Defeat strength, Winning Votes vs. Margins, what to do with equal-ranks on the ballot?<br> </font> </div> <div class="y_msg_container" id="yui_3_16_0_ym19_1_1558691737991_16541"><br><div id="yiv9388643991"><div id="yui_3_16_0_ym19_1_1558691737991_16540"><br>
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---------------------------- Original Message ----------------------------<br>
Subject: Re: [EM] Defeat strength, Winning Votes vs. Margins, what to do with equally-ranks on ballot?<br>
From: "Chris Benham" <cbenhamau@yahoo.com.au><br>
Date: Wed, May 22, 2019 2:35 pm<br>
To: election-methods@lists.electorama.com<br>
--------------------------------------------------------------------------<br>
<br>
<br>
> Another Condorcet-compliant method that might interest you, from a Kevin<br>
> Venzke webpage:<br>
><br>
>> *Jobst Heitzig's River method* is identical to Tideman's method,<br>
>> except that one additionally ignores (without locking) defeats against<br>
>> candidates against whom some defeat has already been locked. This is<br>
>> possibly the easiest of the three to work out by hand.</div><div>maybe someone needs to explain this more to me. i can think of a plausible example where it may differ from RP, but i can't think of what the motivating principle is. if River and RP disagree, why is the River winner a
better choice?</div><div id="yui_3_16_0_ym19_1_1558691737991_16543"><br>> The other two he is referring to are Schulze and Tideman RP. Nearly all<br>
> the time it will elect the same candidate and as far as I know is at<br>
> least as good.</div><div>well, we know when there are only 3 in the Smith Set, that Schulze and Tideman pick the same winner. dunno about this River method, though.</div><div><br>
> I strongly suggest that the measure of defeat strength should be Losing<br>
> Votes and that ballots that equal-rank A and B above bottom should<br>
> contribute a whole vote<br>
> to each in the A-B pairwise comparison. Ballots that rank A and B<br>
> equal-bottom (or truncate both A and B) should contribute nothing to the<br>
> A-B pairwise comparison.</div><div>that's an interesting proposal i hadn't heard before. i'll be interested in hearing the motivation of it. i presume you mean that the defeat strength should be a strictly decreasing function of the losing votes, perhaps -LV (and the greatest
defeat strength is the least negative -LV). in principle, why is this better than Winning Votes or Margins? (seems like Margins is the midpoint compromise between WV and LV since it is WV-LV.)</div><div> </div><div>> I'll be posting more on this soonish, but since you asked the question
I<br>> thought I'd just give you some food for thought to be going along with.</div><div>i am digesting.</div><div>Thank you, Chris.</div><div><br>
--<br>
<br>
r b-j rbj@audioimagination.com<br>
<br>
"Imagination is more important than knowledge."<br>
</div><div> </div><div> </div><div> </div></div>----<br>Election-Methods mailing list - see <a href="https://electorama.com/em" target="_blank">https://electorama.com/em </a>for list info<br><br><br></div> </div> </div> </div></div></body></html>