<!DOCTYPE html>
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
</head>
<body>
<p><br>
</p>
<p>The more interesting question is what makes voting systems agree
when so many of them can be made to disagree (and why?)<br>
</p>
<p>The answer I found for a single vacancy was that an ordinal count
is less accurate than a rational count, and the disagreement in
results was merely caused by discrepancies in ordinal counts. This
was shown by changing the unweighted Condorcet count to a weighted
Condorcet count, whereupon it agreed with the only other rational
count (Borda method), in a finely balanced vote.<br>
</p>
<p>Therefore, I concluded that such alleged demonstrations that
there is "no perfect voting system" were an imposition on readers.</p>
<p>For that matter, no scientific (or knowledgable) endeavor ever
claims perfection, but to seek unambiguous results, that could not
mean anything one wants.</p>
<p>Moreover single vacancies may not offer more than half a
democracy. (Known in ancient times as a tyranny.) With more seats
per constituency, in a proportional election, the inaccurate "last
past the post" exclusion count becomes less important. (As well as
being unnecessary.)</p>
<p>Regards,</p>
<p>Richard Lung<br>
</p>
<p><br>
</p>
<div class="moz-cite-prefix">On 25/05/2024 11:35, Abel Stan wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CA+0ALH5wpVd0+q_4bMpUktC8N2GHX3PJQgViB40YcDY3WK=w6A@mail.gmail.com">
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<div dir="ltr">Greetings,
<div><br>
</div>
<div>I have a challenge for all: I need a unified example where
the most possible voting systems lead to different results. I
know it might be easy to construct such a scenario with any
number of runoffs and such, but that would not be in the
spirit of the game. This is the best I came up with so far, 8
different winners, including a Condorcet-winner + 1 who could
win under a dictatorship (or a 4 round system).<br>
<br>
<p class="MsoNormal"
style="margin:0cm 0cm 8pt;line-height:107%;font-size:11pt;font-family:Calibri,sans-serif"><span
style="font-family:Arial,sans-serif;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">1000:Plurality>Bucklin>Coombs></span>IRV>Anti>Borda>Runoff>Condorcet>Dictator<span
style="font-family:Arial,sans-serif"><br>
<span
style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">999:Runoff>Condorcet>Bucklin>Anti>Dictator>Coombs>IRV>Borda>Plurality</span><br>
<span
style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">998:IRV>Condorcet>Borda>Coombs>Anti>Dictator>Plurality>Bucklin>Runoff<br>
<span
style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">997:Coombs>Borda>Bucklin>Anti>Dictator>Runoff>Plurality>Condorcet>IRV<br>
<span
style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">996:Dictator>IRV>Condorcet>Coombs>Anti>Runoff>Plurality>Bucklin>Borda</span><br>
<span
style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">995:Borda>Bucklin>Anti>Dictator>Coombs>IRV>Runoff>Plurality>Condorcet</span><br>
<span
style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">994:Anti>Condorcet>Borda>IRV>Coombs>Dictator>Runoff>Plurality>Bucklin</span><br>
<span
style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">993:Condorcet>IRV>Borda>Dictator>Runoff>Plurality>Anti>Bucklin>Coombs</span><br>
<span
style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">992:Bucklin>Borda>Dictator>Condorcet>Coombs>IRV>Runoff>Plurality>Anti</span></span></span></span></p>
<br>
And one without a Condorcet-winner, 9 different result with 9
candidates:<br>
<br>
<p class="MsoNormal"
style="margin:0cm 0cm 8pt;line-height:107%;font-size:11pt;font-family:Calibri,sans-serif"><span
style="font-family:Arial,sans-serif;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">1000:Plurality>Bucklin>Coombs></span>IRV>Anti>Kemeny>Runoff>Schulze>Borda<span
style="font-family:Arial,sans-serif"><br>
<span
style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">999:Runoff>Schulze>Bucklin>Borda>Anti>Coombs>IRV>Kemeny>Plurality</span><br>
<span
style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">998:IRV>Schulze>Coombs>Kemeny>Borda>Anti>Plurality>Bucklin>Runoff<br>
<span
style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">997:Coombs>Kemeny>Bucklin>Borda>Anti>Runoff>Plurality>Schulze>IRV<br>
<span
style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">996:Borda>IRV>Schulze>Coombs>Anti>Runoff>Plurality>Bucklin>Kemeny</span><br>
<span
style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">995:Kemeny>Bucklin>Borda>Anti>Coombs>IRV>Runoff>Plurality>Schulze</span><br>
<span
style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">994:Anti>Kemeny>Schulze>IRV>Coombs>Borda>Runoff>Plurality>Bucklin</span><br>
<span
style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">993:Schulze>IRV>Borda>Kemeny>Runoff>Plurality>Anti>Bucklin>Coombs</span><br>
<span
style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">992:Bucklin>Kemeny>Borda>Schulze>Coombs>IRV>Runoff>Plurality>Anti</span></span></span></span></p>
<br>
Wonder what's the highest we could get to.</div>
<div>Cheers,</div>
</div>
<br>
<fieldset class="moz-mime-attachment-header"></fieldset>
<pre class="moz-quote-pre" wrap="">----
Election-Methods mailing list - see <a class="moz-txt-link-freetext" href="https://electorama.com/em">https://electorama.com/em</a> for list info
</pre>
</blockquote>
</body>
</html>