<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" style="font-family:sans-serif">37 A>B>C</div><div dir="auto" style="font-family:sans-serif">31 B>C>A</div><div dir="auto" style="font-family:sans-serif">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 style="font-family:sans-serif">How does Binomial STV avoid this monotonicity failure?</span><br></div><div dir="auto"><span style="font-family:sans-serif"><br></span></div><div dir="auto"><span style="font-family:sans-serif">Thanks!</span></div><div dir="auto"><span style="font-family:sans-serif"><br></span></div><div dir="auto"><span style="font-family:sans-serif">-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">voting@ukscientists.com</a>> escribió:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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<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 style="font-size:16.0pt"></span></p>
<p class="MsoNormal"><span>Regards,</span></p>
<p class="MsoNormal"><span>Richard Lung.<br>
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