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<p>Forest,<br>
<br>
I gather you envisage a high-turnout primary election with the
final being held as soon as practicable afterwards.<br>
<br>
On the issue of whether or not we sometimes dispense with the
final because one candidate was so dominant in the primary,<br>
we could have a rule about the winners final-two IRV count (or
maybe some alternative, like minimum pairwise support) as a
proportion<br>
of the total number of eligible voters.<br>
<br>
If that is too low, then maybe we can have a final anyway, say
between the IRV winner and the candidate with the most pairwise
opposition<br>
to the IRV winner (and maybe if that isn't the IRV last-2
runner-up that candidate also if that pairwise result was
"sufficiently", according to<br>
some rule we make up, close).<br>
<br>
There should be no simple rule that says we always have a final if
the turnout for the primary is below X%, because that could
sometimes cause <br>
some faction of voters to have a strategic incentive to abstain
from the primary. <br>
<br>
Chris B.<br>
<br>
</p>
<div class="moz-cite-prefix">On 1/09/2023 6:37 am, Forest Simmons
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CANUDvfqbA9cyd8-W-mmi1gd1ZYkbxdnUG3--4eOkt8Yzh922jg@mail.gmail.com">
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<div dir="auto">Say the finalists are the IRV winner together with
any and all of its "enemies" (defined as those candidates that
defeat it pairwise).
<div dir="auto"><br>
</div>
<div dir="auto">If the IRV winner has no enemies, no need for
any further runoff beyond the Instant Runoff that just popped
out the IRV winner.</div>
<div dir="auto"><br>
</div>
<div dir="auto">If the IRV winner has precisely one enemy, then
the two-candidate final runoff will be a no stress sincere
choice for the voters.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Otherwise, you have a potentially interesting
runoff with "around 3 to 5 candidates" to put the Condorcet
Meetng through its paces.</div>
<div dir="auto"><br>
</div>
<div dir="auto">fws</div>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Thu, Aug 31, 2023, 11:51 AM
Forest Simmons <<a href="mailto:forest.simmons21@gmail.com"
moz-do-not-send="true" class="moz-txt-link-freetext">forest.simmons21@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">Could the Implicit Approval winner ever be a
Condorcet loser?
<div dir="auto"><br>
</div>
<div dir="auto">Highly unlikely, especially in the context
of too many candidates, etc. But if so, every other
candidate would have a short beatpath to it ... so no
narrowing of the field would occur.</div>
<div dir="auto"><br>
</div>
<div dir="auto">So it would be better to use the IRV winner
or the MaxMax Pairwise Support winner as the short
beatpath target ... the winner of the simplest method that
satisfies the Condorcet Loser Criterion.</div>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Wed, Aug 30, 2023,
11:30 PM Forest Simmons <<a
href="mailto:forest.simmons21@gmail.com" target="_blank"
rel="noreferrer" moz-do-not-send="true"
class="moz-txt-link-freetext">forest.simmons21@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">Voters strictly rank as many candidates as
they care to.
<div dir="auto"><br>
</div>
<div dir="auto">The implicit it approval of a candidate
is the number of ballots on which it out ranks at
least one other candidate.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Let S be the set of candidates tied for
most implicit approval.</div>
<div dir="auto"><br>
</div>
<div dir="auto">A candidate will advance to the final
ballot if and only if it has a beatpath of two or
fewer steps to some member of S.</div>
<div dir="auto"><br>
</div>
<div dir="auto">fws</div>
<div dir="auto"><br>
</div>
<div dir="auto"><br>
</div>
</div>
</blockquote>
</div>
</blockquote>
</div>
</blockquote>
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