<div dir="auto">No difference in practice, because when Smith has only three members, all three have short beatpaths to every candidate.<div dir="auto"><br></div><div dir="auto">Simpler to omit the word "short" and not worry anybody about it.<br><div dir="auto"><br></div><div dir="auto">So whichever is easier to </div></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Mon, Sep 18, 2023, 8:12 PM C.Benham <<a href="mailto:cbenham@adam.com.au">cbenham@adam.com.au</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div>
<p>It had crossed my mind that it might be possible to construct a
(probably) complicated and implausible example where<br>
the IRV winner wins but there is a more approved candidate that
pairwise beats the IRV winner but is not in the Smith set.<br>
<br>
That would be a very embarrassing failure of Double Defeat. <br>
<br>
Your suggestion avoids that problem, but on the other hand to me
it sounds a bit more arbitrary.<br>
<br>
Why only "short" beatpaths? Why not any beatpath?<br>
<br>
Chris<br>
<br>
</p>
<div>On 19/09/2023 7:57 am, Forest Simmons
wrote:<br>
</div>
<blockquote type="cite">
<div dir="auto">How about simply restricting Approval to the
candidates with short beatpaths to the IRV winner (including the
IRV winner itself)?
<div dir="auto"><br>
</div>
<div dir="auto">The main advantage of this version is that it
doesn't require any explanation of Smith.</div>
<div dir="auto"><br>
</div>
<div dir="auto">fws</div>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Sun, Sep 17, 2023, 8:52 AM
C.Benham <<a href="mailto:cbenham@adam.com.au" target="_blank" rel="noreferrer">cbenham@adam.com.au</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><br>
I've been thinking a bit why the Condorcet has so little
popular <br>
traction, why some quite intelligent people<br>
are wary of it and prefer IRV.<br>
<br>
Suppose we are talking about electing members of a parliament
(or <br>
legislature) in single-member seats.<br>
<br>
Typically the two largest parties, say one centre-left and and
one <br>
centre-right, will between them win nearly<br>
all the seats and with luck the one that is preferred by more
voters <br>
than the other will get more seats<br>
(and so in a Parliamentary system will form a government with
its leader <br>
becoming the Prime Minister).<br>
<br>
<br>
So in this limited sense the result is very very roughly <br>
"proportional". Assuming the small wing parties'<br>
supporters are normally spread out in lots of different
districts, they <br>
will get no seats.<br>
<br>
But suppose in a lot of the seats the contest looks like this:<br>
<br>
47 A>>>C>B<br>
43 B>>>C>A<br>
10 C>A>>B<br>
<br>
If this is IRV or FPP then A easily wins, but the CW is C.<br>
<br>
But A is clearly the highest "social utility" candidate, and
assuming <br>
that voting is voluntary and at<br>
least somewhat inconvenient or costly, then C has only been
voted the CW <br>
because both A and B<br>
are on the ballot. If one of those candidates wasn't, then
most of his <br>
or her supporters would stay<br>
home and allow the other to easily beat C.<br>
<br>
And if something similar (electing a weak centrist that most
of the <br>
voters don't like) happens in enough<br>
seats it could result in the "weak centrist party" being
grossly <br>
over-represented in the legislature.<br>
<br>
So to allay these fears I suggest this compromise with IRV: <br>
Smith+IRV//Approval:<br>
<br>
*Voters strictly rank from the top however many or few
candidates they <br>
wish. Default approval is only<br>
for the top-ranked candidate, but voters can extend approval
to one or <br>
more other candidates by marking<br>
the lowest-ranked candidate they approve.<br>
<br>
Elect the most approved candidate that is either in the Smith
set or is <br>
the IRV winner.*<br>
<br>
Allowing above-bottom equal-preferences (at least without a
lot of extra <br>
complexity) makes Push-over strategising<br>
easier.<br>
<br>
So in the type of example I just discussed the IRV winner
would normally <br>
have a much higher approval score<br>
than the CW, but the supporters of the IRV runner-up could
change that <br>
if they like by extending their approval<br>
to the CW (who then might win, especially if the CW's
supporters refrain <br>
from extending their approval to the IRV winner).<br>
<br>
Chris B.<br>
<br>
</blockquote>
</div>
</blockquote>
</div>
</blockquote></div>