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<p><br>
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<p>Thank you, Forest,</p>
<p>Your example is the kind of example that Riker gave. <br>
</p>
<p>Here the quota equals 50 = 100/[1+1].</p>
<p>Original profile:<br>
</p>
<p>Election Keep value is quota/candidate vote:<br>
</p>
<p>for A 50/35 <br>
</p>
<p>B: 50/33<br>
</p>
<p>C: 50/32</p>
<p>Exclusion keep value = quota/candidate reverse vote:</p>
<p>for A: 50/33</p>
<p>B: 50/32</p>
<p>C: 50/35</p>
<p>Final (geometric mean) keep values, divide election keep value by
exclusion keep value. <br>
</p>
<p>(This is equivalent to multiplying by the inverse exclusion keep
value, as a make-shift second opinion election keep value.)<br>
</p>
<p>for A: 50/35 x 33/50. And take their square root ~ ,971<br>
</p>
<p>for B: 50/33 x 32/50. As above, gives ~ .9847<br>
</p>
<p>for C: 50/32 x 35/50. ... gives ~ 1.0458</p>
<p>Keep values below unity are technically electable. A wins, with
lowest keep value.</p>
<p>New profile:</p>
<p>Election divided by exclusion keep values:</p>
<p>A: 50/37 x 31/50. Take square root of 31/37, for ~ .9153</p>
<p>B: 50/31 x 32/50. As above, ~ 1.016</p>
<p>C: 50/32 x 37/50. As above, ~ 1,075</p>
<p>Again, A is elected as before, and with a yet lower keep value,
as the extra preferences for A warrant.</p>
<p>Regards,</p>
<p>Richard Lung.<br>
</p>
<p><br>
</p>
<div class="moz-cite-prefix">On 26/02/2022 01:30, Forest Simmons
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CANUDvfpSiAPwKAmnnCPGDaZB9CXTybtGvkHPohukqK6EwcG31A@mail.gmail.com">
<div dir="auto">Richard,
<div dir="auto"><br>
</div>
<div dir="auto">Here's an example of monotonicity failure in
conventional single winner STV as I understand it:</div>
<div dir="auto"><br>
</div>
<div dir="auto">Original profile of ballots:</div>
<div dir="auto"><br>
</div>
<div dir="auto">35 A>B>C</div>
<div dir="auto">33 B>C>A</div>
<div dir="auto">32 C>A>B</div>
<div dir="auto"><br>
</div>
<div dir="auto">C eliminated and A wins.</div>
<div dir="auto"><br>
</div>
<div dir="auto">New profile: two members of B faction defect to
A faction:</div>
<div dir="auto"><br>
</div>
<div dir="auto">
<div dir="auto">37 A>B>C</div>
<div dir="auto">31 B>C>A</div>
<div dir="auto">32 C>A>B</div>
</div>
<div dir="auto"> </div>
<div dir="auto">Now B is eliminated and C wins.</div>
<div dir="auto"><br>
</div>
<div dir="auto"><span>How does Binomial STV avoid this
monotonicity failure?</span><br>
</div>
<div dir="auto"><span><br>
</span></div>
<div dir="auto"><span>Thanks!</span></div>
<div dir="auto"><span><br>
</span></div>
<div dir="auto"><span>-Forest</span></div>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">El jue., 24 de feb. de 2022
10:36 a. m., Richard Lung <<a
href="mailto:voting@ukscientists.com" moz-do-not-send="true"
class="moz-txt-link-freetext">voting@ukscientists.com</a>>
escribió:<br>
</div>
<blockquote class="gmail_quote">
<div>
<p><br>
</p>
<p> </p>
<p class="MsoNormal"><span>“Monotonic” Binomial STV</span></p>
<p class="MsoNormal"><span> </span></p>
<p class="MsoNormal"><span>I was told (hello Kristofer) that
I could not say that binomial STV is “monotonic”</span><span>
unlike traditional or conventional STV. But I gave my
reasons why I could say this, and they were not
contradicted or even answered. It is not tabu or
forbidden to say, and say again, what there is good
reason to believe is true, whatever the prevailing view.</span>
</p>
<p class="MsoNormal"><span>In conventional STV, the transfer
of surpluses, over a quota, to next preferences is
monotonic. There is “later no harm” unlike the Borda
count. The intermediate Plant report quoted a
non-monotonic test example from Riker, to justify their
rejection of STV. This was based solely on the perverse
outcome of a different candidate being last past the
post, for elimination.</span></p>
<p class="MsoNormal"><span>Riker made the unsupported claim
that STV is “chaotic.” From a century of STV usage, he
did not provide a single real case of this. The record
is that STV counts well approximate STV votes, all
things considered.<br>
</span></p>
<p class="MsoNormal"><span>A paper that tried to provide
some doubt, of STV as a well-behaved system, drew not on
a conventional STV election of candidates, but on NASA
using STV for outer space engineers to vote on a set of
best trajectories (I forget where).</span></p>
<p class="MsoNormal"><span>Traditional STV is not “chaotic”.
It is not even wrong. It is just an initial or first
approximation of binomial STV, a zero order binomial
STV.</span></p>
<p class="MsoNormal"><span>Zero order STV is a uninomial
count that does not clearly distinguish between an
election count or an exclusion count. In 1912, HG Wells
said of FPTP, we no longer have elections we only have
Rejections. From first order Binomial STV, the two
counts, election and exclusion counts, are clearly
distinguished and both made operational.</span></p>
<p class="MsoNormal"><span>Binomial STV does not exclude
candidates during the count. It uses an exclusion count,
to help determine a final election. This exclusion count
is exactly the same or symmetrical to the (monotonic)
transfer of surplus votes in an election count.</span></p>
<p class="MsoNormal"><span>In both election and exclusion
counts, Gregory Method or the senatorial rules are
expressed in terms of keep values, which enable proper
book-keeping of all preferences. Keep values can keep
track of all the preference votes, including
abstentions. So, no perverse results are possible from
the chance exclusion of preferences from this or that
candidate last past the post. This is also why binomial
STV is one complete dimension of choice.</span></p>
<p class="MsoNormal"><span></span><span>Binomial STV has
“Independence of Irrelevant Alternatives.” For instance,
it makes no difference what level the quota is set, to
the order of the candidates keep values, their order of
election. It is just that bigger quotas raise the
threshold of election.</span><span></span></p>
<p class="MsoNormal"><span>Regards,</span></p>
<p class="MsoNormal"><span>Richard Lung.<br>
</span></p>
</div>
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