<div><br></div><div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Mon, Oct 23, 2023 at 06:01 C.Benham <<a href="mailto:cbenham@adam.com.au">cbenham@adam.com.au</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)"><u></u>
<div>
<blockquote type="cite">
<pre style="white-space:pre-wrap;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;font-family:monospace;color:rgb(0,0,0)">Are you referring to how equal-ranking is counted in Borda?</pre>
</blockquote>
Yes, mainly truncated ballots. Do you consider that truncation is
the same thing as ranking equal bottom?</div></blockquote><div dir="auto"><br></div><div dir="auto">Yes.</div><div dir="auto"><br></div><div dir="auto"><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)"><div dir="auto"><br>
<br>
<blockquote type="cite">
<pre style="white-space:pre-wrap;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;font-family:monospace;color:rgb(0,0,0)">I advocate
that, in these methods’ Borda-count, a ranking give each of its
ranked-candidates a number of points equal to the number of candidates in
the ranking who aren’t ranked over hir.</pre>
</blockquote>
<p>Can you clarify the exact meaning of the phrase "in the
ranking"? Is this a hint that your answer to my last<br>
question is "no"?</p></div></blockquote><div dir="auto"><br></div><div dir="auto">“In the ranking” mean written in the ranking :-)</div><div dir="auto"><br></div><div dir="auto">The name of the candidate is written in the ranking, at some rank-position. :-)</div><div dir="auto"><br></div><div dir="auto">It isn’t a hint to anything other than what it says.</div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)"><div dir="auto"><p dir="auto"><br>
<br>
And why is that what you advocate? </p></div></blockquote><div dir="auto"><br></div><div dir="auto">Because burying someone better raises the score of everyone under or with whom you burohir.</div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)"><div dir="auto"><p dir="auto">In some online discussion I
saw it was mentioned (I think by N.Tideman) that<br>
the Baldwin method doesn't meet Condorcet unless the Fractional
(i.e. based on the symmetrically completed ballots)<br>
version of Borda count is used.</p></div></blockquote><div dir="auto"><br></div><div dir="auto">Then it’s a good thing that we aren’t proposing Baldwin.</div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)"><div dir="auto"><p dir="auto"><br>
<br>
So I've tended to assume that that is the "correct" way of doing
Borda counts.</p></div></blockquote><div dir="auto"><br></div><div dir="auto">Depends on the Borda count’s purpose & use in a particular method.</div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)"><div dir="auto"><p dir="auto"><br>
<br>
Say there are three candidates A,B,C. Say 46 ballots bullet-vote
A. In the fractional version these votes are counted the same as<br>
23 A>B, 23 A>C, giving 92 points to A and 23 points each to
B and C.<br>
</p>
<p dir="auto">Is that the same as what you advocate[?]</p></div></blockquote><div dir="auto">is that what I said? :-)</div><div dir="auto"><br></div><div dir="auto">No.</div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)"><div dir="auto"><p dir="auto"> or would you have those
truncating ballots give 2 points to A and zero points to both of B
and C?</p></div></blockquote><div dir="auto"><br></div><div dir="auto">Is that what I said? :-)</div><div dir="auto"><br></div><div dir="auto">No.</div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)"><div dir="auto"><p dir="auto"><br>
Or something else?</p></div></blockquote><div dir="auto"><br></div><div dir="auto">How about what I said?</div><div dir="auto"><br></div><div dir="auto">Of the candidates that your ballot ranks, 3 aren’t ranked over A. </div><div dir="auto"><br></div><div dir="auto">A gets 3 points.</div><div dir="auto"><br></div><div dir="auto">Of the candidates that your ballot ranks, 2 aren’t ranked over B, or over C.</div><div dir="auto"><br></div><div dir="auto">Therefore, by what I said, B & C each get 2 points.</div><div dir="auto"><br></div><div dir="auto">Yes that’s different from any usual Borda count. So it would be better to add the word “other”, & say:</div><div dir="auto"><br></div><div dir="auto">The ranking gives to each candidate a score equal to the number of other candidates (candidates other than itself) in the ranking whom the ranking doesn’t rank over it.</div><div dir="auto"><br></div><div dir="auto">That change obviously doesn’t change the differences in candidates’ scores.</div><div dir="auto"><br></div><div dir="auto">(That’s unnecessary wordy, but I want to make it as explicit as possible.)</div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)"><div dir="auto"><p dir="auto"><br>
<br>
</p><blockquote type="cite">
<pre style="white-space:pre-wrap;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;font-family:monospace;color:rgb(0,0,0)"><i style="font-family:monospace"> So another way of putting it is: "If there is no CW, elect the member of
</i><i style="font-family:monospace"> the Smith set with the second-worst score".
</i><i style="font-family:monospace">
</i>
Would you mind telling why that’s another way of putting it?
</pre>
</blockquote>
<br>
By definition the members of the Smith set all pairwise beat all
the non-member candidates, and also have a pairwise defeat at the
hands<br>
of one of the other members (assuming there are three members). <br>
<br>
So the Smith set member with the highest score must be pairwise
beaten by one with a lower score. That much is clear.<br>
<br>
To be honest I may have confused myself again as to further
details. It seems to be possible for the lowest-scored Smith-set
member to win.</div></blockquote><div dir="auto"><br></div><div dir="auto">Suit yourself & reword it as you wish. </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)"><div dir="auto"><br>
<br>
Say the top cycle is (in terms of score order) Middle > High
> Low > Middle.<br>
<br>
Then High is disqualified by being pairwise beaten by Middle and
Middle is disqualified by being pairwise beaten by Low. <br>
<p></p>
<p>So Low wins.</p></div></blockquote><div dir="auto"><br></div><div dir="auto">Bingo !</div><div dir="auto"><br></div><div dir="auto">Low wins.</div><div dir="auto"><br></div><div dir="auto">Low is probably CW. Low is unlikely to be BF.</div><div dir="auto"><br></div><div dir="auto">The burial didn’t succeed. CW won.</div><div dir="auto"><br></div><div dir="auto"><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)"><div dir="auto"><p dir="auto"><br>
<br>
</p><blockquote type="cite">
<pre style="white-space:pre-wrap;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;font-family:monospace;color:rgb(0,0,0)">Remember that sincere top-cycles are vanishingly rare.</pre>
</blockquote>
<br>
What mind-reading technology have you accessed to determine that?
I don't know how you can know that.</div></blockquote><div dir="auto"><br></div><div dir="auto">I used a crystal-ball, along with every Condorcet poll that I’ve heard of, participated in or conducted.</div><div dir="auto"><br></div><div dir="auto"><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)"><div dir="auto"><br>
<br>
Simple scenarios with lots of truncation and a top cycle look very
plausible to me, so I don't know why I should<br>
accept your assurance that such a thing would be "vanishingly
rare".</div></blockquote><div dir="auto"><br></div><div dir="auto">Howabout experience.</div><div dir="auto"><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)"><div dir="auto"><br>
<br>
Also it seems to me you are giving yourself a marketing problem:
<br>
<br>
"Ok, we admit that Condorcet methods are very vulnerable to Burial
strategy</div></blockquote><div dir="auto"><br></div><div dir="auto">Margins Condorcet is. </div><div dir="auto"><br></div><div dir="auto">wv Condorcet isn’t, if people use defensive truncation.</div><div dir="auto"><br></div><div dir="auto">I believe that has been discussed here. :-)</div><div dir="auto"><br></div><div dir="auto">But probabilistically-auto-deterrent methods protect against burial, preferably by deterrence due to penalty, without anyone using defensive strategy.</div><div dir="auto"><br></div><div dir="auto">As I said I prefer CTE to Duncan, because CTE often deters when Duncan would merely not reward.</div><div dir="auto"><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)"><div dir="auto">so in a effort to combat that we have<br>
to employ this apparently nonsensical, anti-monotonic,
anti-intuitive completion method.</div></blockquote><div dir="auto"><br></div><div dir="auto">The auto-deterrent methods aren’t designed for cosmetics in sincere top-cycles, in which there’s no CW to protect. …& which are unheard-of in Condorcet polls.</div><div dir="auto"><br></div><div dir="auto">Admittedly not all methods are monotonic like IRV. :-)</div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)"><div dir="auto"><br>
<br>
But don't worry, probably we'll never have to use it."</div></blockquote><div dir="auto"><br></div><div dir="auto">Is that what your crystal-ball says?</div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)"><div dir="auto"><br>
<br>
Chris B.</div></blockquote><div dir="auto"><br></div><div dir="auto">The auto-deterrent methods likely aren’t as obvious, briefly-defined, simply-explained, or familiar as MinMax(wv), & so are maybe less likely to be proposed as a 1st single-winner reform.</div><div dir="auto"><br></div><div dir="auto">But it’s desirable that defensive strategy not be needed.</div><div dir="auto"><br></div><div dir="auto">When proposing single-winner reform, I offer a list of proposals. It will include CTE. What the Condorcet Enactment-Committee proposes will be their choice, but I prefer to offer them a variety, including the familiar briefly defined MinMax(wv), CW,Approval, SP, & the auto-deterrent CTE.</div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)"><div dir="auto"><br>
<p></p>
<br>
<blockquote type="cite">
<h1 style="font-family:"Times New Roman";font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;color:rgb(0,0,0)"> <b style="font-family:"Times New Roman";font-size:medium;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;color:rgb(0,0,0)">Michael
Ossipoff</b><span style="font-family:"Times New Roman";font-size:medium;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;float:none;display:inline!important;background-color:rgb(255,255,255);color:rgb(0,0,0)"><span style="font-family:"Times New Roman""> </span></span><a href="mailto:election-methods%40lists.electorama.com?Subject=Re%3A%20%5BEM%5D%20Duncan%20Proposal%20Draft&In-Reply-To=%3CCAOKDY5D-CUNWajrZxSi8VauLY8FAys8vnt6SvX%3D7KiQFeEpeJw%40mail.gmail.com%3E" title="[EM] Duncan Proposal Draft" style="font-family:"Times New Roman";font-size:medium;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal" target="_blank">email9648742
at gmail.com</a></h1>
<i style="font-family:"Times New Roman";font-size:medium;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;color:rgb(0,0,0)">Sat
Oct 21 12:38:58 PDT 2023</i><span style="font-family:"Times New Roman";font-size:medium;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;float:none;display:inline!important;background-color:rgb(255,255,255);color:rgb(0,0,0)"></span>
<p style="font-family:"Times New Roman";font-size:medium;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;color:rgb(0,0,0)"><br>
</p>
<hr style="font-family:"Times New Roman";font-size:medium;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;white-space:normal;color:rgb(0,0,0)">
<pre style="white-space:pre-wrap;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;word-spacing:0px;font-family:monospace;color:rgb(0,0,0)">On Sat, Oct 21, 2023 at 11:05 C.Benham <<a href="http://lists.electorama.com/listinfo.cgi/election-methods-electorama.com" target="_blank" style="font-family:monospace">cbenham at adam.com.au</a>> wrote:
"Am I right in assuming that the Borda counts are based on the symmetrically
completed ballots?"
Are you referring to how equal-ranking is counted in Borda? I advocate
that, in these methods’ Borda-count, a ranking give each of its
ranked-candidates a number of points equal to the number of candidates in
the ranking who aren’t ranked over hir.
><i style="font-family:monospace"> Duncan Definition:
</i>><i style="font-family:monospace">
</i>><i style="font-family:monospace"> In the vast majority of the cases ... those in which the pairwise counts
</i>><i style="font-family:monospace"> of the ballots unambiguously identify the candidate that pairbeats each of
</i>><i style="font-family:monospace"> the others ... elect that candidate.
</i>><i style="font-family:monospace">
</i>><i style="font-family:monospace"> Otherwise, elect the highest score candidate that pairbeats every
</i>><i style="font-family:monospace"> candidate with lower score.
</i>><i style="font-family:monospace">
</i>><i style="font-family:monospace">
</i>><i style="font-family:monospace"> So another way of putting it is: "If there is no CW, elect the member of
</i>><i style="font-family:monospace"> the Smith set with the second-worst score".
</i>><i style="font-family:monospace">
</i>
Would you mind telling why that’s another way of putting it?
><i style="font-family:monospace">
</i>><i style="font-family:monospace"> To put it bluntly, that is bound to have monotonicity problems and doesn't
</i>><i style="font-family:monospace"> fly philosophically.
</i>><i style="font-family:monospace">
</i>
How doesn’t it fly philosophically?
><i style="font-family:monospace">
</i>><i style="font-family:monospace">
</i>><i style="font-family:monospace"> Trying to deter or frustrate order-reversal Burial strategy is fine, but
</i>><i style="font-family:monospace"> the algorithm should "appear fair" and be able to be justified when
</i>><i style="font-family:monospace"> we assume that all the votes are sincere (or even just all equally likely
</i>><i style="font-family:monospace"> to be sincere).
</i>><i style="font-family:monospace">
</i>
Remember that sincere top-cycles are vanishingly rare. That’s why
Sequential-Pairwise’s Pareto failure isn’t important, & it’s why
MinMax(wv)’s Condorcet Loser failure isn’t important.
It matters much more what happens in a strategic cycle. Does the method
reward or penalize burial? …or neither?
Duncan tends to often do neither, because it will likely disqualify both
Bus & BF. (I defined those usages when I defined CTE.
I prefer CTE to Duncan, because it more often penalizes, instead of merely
not rewarding.
But I remind you that these methods are intended to deter
probabilisticallly, but aren’t claimed to penalize burial in every possible
example.
><i style="font-family:monospace">
</i>><i style="font-family:monospace">
</i>
><i style="font-family:monospace">
</i>><i style="font-family:monospace"> That breaks (at least one version of) "Double Defeat". B is pairwise
</i>><i style="font-family:monospace"> beaten by a candidate with a higher "score".
</i>><i style="font-family:monospace">
</i>><i style="font-family:monospace">
</i>><i style="font-family:monospace"> Chris B.
</i>><i style="font-family:monospace">
</i>><i style="font-family:monospace">
</i>><i style="font-family:monospace"> On 14/10/2023 4:43 am, Michael Ossipoff wrote:
</i>><i style="font-family:monospace">
</i>><i style="font-family:monospace"> Yes, I like Duncan because burying the CW in an attempt to help your
</i>><i style="font-family:monospace"> favorite won’t help hir when it causes hir disqualification, as it probably
</i>><i style="font-family:monospace"> will.
</i>><i style="font-family:monospace">
</i>><i style="font-family:monospace"> …& Duncan is remarkably briefly-defined, needing only a very slight
</i>><i style="font-family:monospace"> modification of Black’s method.
</i>></pre>
</blockquote>
<br>
<br>
<br>
<br>
</div>
</blockquote></div></div>