<div dir="auto">PS to previous:<div dir="auto"><br></div><div dir="auto">Since the condorcet winner doesn't have a min lv score, minlv score could be either 0%, 100%, or 50% by default. </div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Thu, Apr 11, 2024, 16:54 Ted Stern <<a href="mailto:dodecatheon@gmail.com">dodecatheon@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="auto">Chris, what I nominated for the poll was essentially the same as what you proposed in October of 2016, but simplified to require no elimination step iteration. Just one margin sort on MinLV(erw). <div dir="auto"><br></div><div dir="auto"><a href="http://lists.electorama.com/pipermail/election-methods-electorama.com/2016-October/000599.html" rel="noreferrer noreferrer noreferrer" target="_blank">http://lists.electorama.com/pipermail/election-methods-electorama.com/2016-October/000599.html</a><br></div><div dir="auto"><br></div><div dir="auto">ERW means that if A and B have equal rank above bottom, we fill in the pairwise array as if it were one whole vote of A>B and one whole vote of B>A.</div><div dir="auto"><br></div><div dir="auto">The reason I proposed it is that seeding the margin sort with MinLV score in descending order is analogous to minimum pairwise opposition in ascending order. MinMaxPO is burial resistant, the property we're looking for, and for margin sort, we want a metric that is analogous to approval, with descending scores. </div><div dir="auto"><br></div><div dir="auto">If we wanted the <i>exact</i> complement, we would do margin sort on <i>min votes</i>, to get the closest approximation to MinMaxPO(wv) possible while still being Smith compliant. However, minmax (or rather maxmin) is not clone proof, as can be seen by applying margin sort min votes to the example you posted last week:</div><div dir="auto"><br></div><div dir="auto"><a href="http://lists.electorama.com/pipermail/election-methods-electorama.com/2024-April/005616.html" rel="noreferrer noreferrer" target="_blank">http://lists.electorama.com/pipermail/election-methods-electorama.com/2024-April/005616.html</a></div><div dir="auto"><br></div><div dir="auto">By using minLV instead of min votes, C's minimum score of 18 (with clone) is ignored and so the seed ranking before margin sort is unchanged by the addition of the clone.</div><div dir="auto"><br></div><div dir="auto">My motivation for the nomination: while margin sorted approval is an excellent method, the approval cutoff (what I prefer to think of as a preference cutoff, since all ranked candidates are approved) is an additional step, requiring either an additional count for implicit approval, or an extra mental judgment by the voter. </div><div dir="auto"><br></div><div dir="auto">Margin Sorted MinLV(erw) is automatic, and from my limited testing, tends to find a candidate with strong top ratings. </div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Thu, Apr 11, 2024, 01:17 Chris Benham <<a href="mailto:cbenhamau@yahoo.com.au" rel="noreferrer noreferrer noreferrer" target="_blank">cbenhamau@yahoo.com.au</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><u></u>
<div>
<p>Ted,<br>
<br>
I'm not completely clear on what the "equal rated whole" part
means, and likely there are some other possible<br>
voters who have no idea what any of it means.<br>
<br>
This is what I think it all means.<br>
<br>
Voters rank the candidates from the top, equal ranking an
truncation allowed. Then we construct a pairwise matrix.<br>
<br>
A ballot voting A over B gives one vote in the A-B comparison to A
and nothing to B. A ballot that truncates (or votes<br>
equal-bottom) both A and B gives nothing to both in the A-B
comparison.<br>
<br>
But in the case a ballot explicitly votes A=B above bottom, do you
propose that the ballot give a whole vote each to<br>
A and B in the A-B comparison? (Until I hear otherwise from you,
I'll assume this is what you mean.)<br>
<br>
An alternative reasonable idea would be for this to be only the
case where the ballot votes A and B below no other<br>
candidates, and if they are voted A=B above bottom but below top
then the ballot gives half a vote to each of A and<br>
B in the A-B comparison.<br>
<br>
In any case I understand that we score each candidate according
to the minimum number of votes they got in a pairwise<br>
loss, and order them from highest to lowest.<br>
<br>
Then candidates are listed in score order and if any adjacent
pairs are pairwise out of order then this is corrected by <br>
flipping the out-of-order pair with the smallest margin. If there
is a tie for this we flip the lowest scored tied pair. Repeat
until <br>
there are no adjacent pairs of candidates that are pairwise out of
order, then elect the highest-ordered candidate.<br>
<br>
I am favourably disposed to this, but I'd like some clarification
(and hopefully some de-confusing justification) on the issue<br>
of how we treat equal ranking (or "rating").<br>
<br>
Chris Benham<br>
<br>
<br>
<blockquote type="cite">
<h1 style="color:rgb(0,0,0);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;text-decoration-style:initial;text-decoration-color:initial"><br>
</h1>
<b style="color:rgb(0,0,0);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;text-decoration-style:initial;text-decoration-color:initial">Ted
Stern</b><span style="color:rgb(0,0,0);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;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;display:inline!important;float:none"><span> </span></span><a href="mailto:election-methods%40lists.electorama.com?Subject=Re%3A%20%5BEM%5D%20Poll%20on%20voting-systems%2C%0A%20to%20inform%20voters%20in%20upcoming%20enactment-elections&In-Reply-To=%3CCAHGFzOTaPTdMnVw7TELxExvM4ZjbAEtaxJWZ-%2Bpcttf4ATXhPw%40mail.gmail.com%3E" title="[EM] Poll on voting-systems, to inform voters in upcoming enactment-elections" 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" rel="noreferrer noreferrer noreferrer noreferrer" target="_blank">dodecatheon
at gmail.com</a><br style="color:rgb(0,0,0);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;text-decoration-style:initial;text-decoration-color:initial">
<i style="color:rgb(0,0,0);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;text-decoration-style:initial;text-decoration-color:initial">Sat
Apr 6 12:33:35 PDT 2024</i><span style="color:rgb(0,0,0);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;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;display:inline!important;float:none"></span>
<p style="color:rgb(0,0,0);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;text-decoration-style:initial;text-decoration-color:initial"><br>
</p>
<hr style="color:rgb(0,0,0);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;text-decoration-style:initial;text-decoration-color:initial">
<pre style="white-space:pre-wrap;color:rgb(0,0,0);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;text-decoration-style:initial;text-decoration-color:initial">I'd like to nominate
Margin Sorted Minimum Losing Votes (equal rated whole)</pre>
</blockquote>
<br>
</p>
</div>
</blockquote></div>
</blockquote></div>