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<p>When I happened to remark that divisor methods and quota methods
are sometimes distinguished, this is so. Robert Newland did so, in
his book on Comparitive Electoral Systems.</p>
<p>Indeed, I didn't say why party lists restrict personal choice.
(And you didn't deny it.) But Enid Lakeman did say why, in How
Democracies Vote. In so many words, It is because with
transferable voting, the voters decide how their votes will count
from first preferences onward, while with party lists, it is the
parties who more or less determine personal representation.</p>
<p>Richard Lung.<br>
</p>
<p><br>
</p>
<div class="moz-cite-prefix">On 07/09/2023 06:04, Michael Ossipoff
wrote:<br>
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<blockquote type="cite"
cite="mid:CAOKDY5AxOmr-0r5twXS1EN5i6cL+p2j4g7K_8E0DVEkADwMb0A@mail.gmail.com">
<div><br>
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<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Tue, Sep 5, 2023 at 23:59
Richard Lung <<a href="mailto:voting@ukscientists.com"
moz-do-not-send="true" class="moz-txt-link-freetext">voting@ukscientists.com</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote">
<div>
<p><br>
</p>
<p>Just a preliminary remark. Divisor methods and quotas
some times distinguished. </p>
</div>
</blockquote>
<div dir="auto"><br>
</div>
<div dir="auto">I don’t know what you mean by that.</div>
<div dir="auto"><br>
</div>
<div dir="auto">I didn’t say that the divisor methods are
quotas. I didn’t say that quotas are divisor methods.</div>
<div dir="auto"><br>
</div>
<div dir="auto">I defined “quota” for its use in what I was
saying. That use of that word isn’t new or unusual. It’s
found in divisor method discussion.</div>
<blockquote class="gmail_quote">
<div>
<p dir="auto">Thus there is the Droop quota and
corresponding D'Hont divisor method. </p>
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</blockquote>
<div dir="auto"><br>
</div>
<div dir="auto"><br>
</div>
<div dir="auto">I don’t know what you’ve heard of, but I’ve
never heard of Droop quota in a definition or discussion of
d’Hondt.</div>
<div dir="auto"><br>
</div>
<div dir="auto">But maybe someone has proposed a method that
he calls “d’Hondt”, & maybe his method uses the Droop
quota, which I’ve heard of being sometimes proposed, &
sometimes used, in STV.</div>
<blockquote class="gmail_quote">
<div>
<p dir="auto">Divisor methods regarded as belonging to
apportionment</p>
</div>
</blockquote>
<div dir="auto">That term was probably first applied to
apportionment proposals, but nonetheless d’Hondt is the
Jefferson divisor method, & Saints-Lague is the Webster
divisor method.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Those two list-PR methods are usually defined,
& at least partly implemented by a systematic procedure,
rather than the by the implementation often or usually
specified by the definitions of the divisor methods proposed
& used for apportionment. ..at least in earlier
apportionment discussion.</div>
<div dir="auto"><br>
</div>
<blockquote class="gmail_quote">
<div>
<p dir="auto">as by Jefferson and by Webster, not to carve
out party seats, which is too restrictive of personal
choice.</p>
</div>
</blockquote>
<div dir="auto"><br>
</div>
<div dir="auto">Carve out?</div>
<div dir="auto"><br>
</div>
<div dir="auto">I’m not sure, but you seem to be saying that
party-list PR restricts personal choice.</div>
<div dir="auto"><br>
</div>
<div dir="auto">But you didn’t say why you think so.</div>
<div dir="auto"><br>
</div>
<div dir="auto"><br>
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<blockquote class="gmail_quote">
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<p dir="auto"><br>
</p>
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<div> </div>
</blockquote>
<div dir="auto"><br>
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<div dir="auto"><br>
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<div dir="auto"><br>
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<div dir="auto"><br>
</div>
<blockquote class="gmail_quote">
<div>
<p><br>
</p>
<div>On 06/09/2023 05:05, Michael Ossipoff wrote:<br>
</div>
</div>
<div>
<blockquote type="cite">
<div dir="ltr">
<p class="MsoNormal"><span>Greetings list-members—<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>In 2006, I proposed an
allocation divisor-method that I called Bias-Free,
which eliminates bias. I’d like, in this message,
to better explain my derivation of Bias-Free (BF).<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>Instead of defining “bias”,
I’ll just let the derivation of BF tell what it
guarantees, and anyone can decide whether that’s
unbias.<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>Outline of derivation of
Bia-Free (BF):<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>First, to define the terms
in the explanation, I should say what a
divisor-method is:<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>Divide total votes by total
seats. That’s the Hare Quota.<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>Divide each party’s votes
by the Hare Quota, & round off to one of the
two closest integers. (Each divisor-method uses a
different round-up point.)<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>Allocate seats according to
those rounding-results.<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>If the number of seats thus
allocated equals the legally-ordained number of
seats, then that’s the final allocation.<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>Otherwise, try the
procedure using another number to replace the Hare
Quota, & call that new number the quota.
Repeat the above procedure, using that new quota
instead of the Hare Quota.<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>Find (by trial-&-error,
or by some systematic-procedure) a quota such that
the resulting number of seats allocated equals the
legally-ordained number of seats.<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>In the explanation below,
“quota” means “quota” as defined above, or a
number of seats equal to the quota.<span> </span>The
Hare Quote too is a “quota” as the term is used
below.<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>The object is for the
average seats per quota to be unity, averaged over
an interval between two integer numbers of quotas.<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>q = quotas.<span> </span>s
= seats.<span> </span>R = the round-up point
between a & b.<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>Above the round-up point,
s/q = b/q.<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>Below the round-up point,
s/q = a/q.<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>…because, below the
round-up point a party would have a seats, &
above the round-up point a party would have b
seats.<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>Integrate b/q from R, to b.<span>
</span><span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>Integrate a/q from a to R.<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>Add the two integrals
together.<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>To average over the
interval, divide by b – a, the total amount of
quota in the interval.<span></span></span></p>
<p class="MsoNormal"><span>… <span></span></span></p>
<p class="MsoNormal"><span>i.e. divide by 1.<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>Set that average s/q in the
interval equal to 1, because it’s desired for it
to be 1.<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>Solve for R.<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>R = (1/e)((b^b)/(a^a)).<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>That quantity is called (a
special case of) the identric-mean of a & b.<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>Someone expressed concern
that the unbias would be spoiled because the size
of parties has a nonuniform
probability-distribution. But he didn’t say why he
thinks so, I don’t know what that
probability-distribution has to do with anything
said in the derivation.<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>The identric-mean has been
much discussed by mathematicians. <span> </span>But,from
what was said in an academic paper (I’ll cite it
below), it wasn’t proposed as the round-up point
for an unbiased divisor-method before I proposed
it here in 2006.<span> </span>There were two
academic journal-papers about that proposa, in
versions starting in 2008.<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>Here are the two
academic-journal references:<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>“The Census and the Second
Law: An Entropic Approach to Optimal Apportionment
for the U.S. House of Representatives”.<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>By Andrew E. Charman<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>It was in _Physics and
Society__, or _Journal of Physics and Society_, in
2017. <span></span></span></p>
<p class="MsoNormal"><span>(The latest version of the
article was in 2017)<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>The citation said: <span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>Cite as arXiv.1712.09440v3
[<a href="http://physics.soc.ph" target="_blank"
moz-do-not-send="true">physics.soc.ph</a>]<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>I don’t know the page or
Journal-volume & the issue-numberr, or if that
information is encoded in the numbers above.<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>The other paper was:<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>“Optimal Congressional
Apportionment”<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>By Robert A. Agnew.<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>…in The American
Mathematical Monthly, for 2008, volume 115, number
4 (April 2008).<span></span></span></p>
<p class="MsoNormal"><span>…<span></span></span></p>
<p class="MsoNormal"><span>Pp 297-303<span> </span>(7
pages)<span></span></span></p>
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<pre>----
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