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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>
    </div>
    <blockquote type="cite"
cite="mid:CAOKDY5AxOmr-0r5twXS1EN5i6cL+p2j4g7K_8E0DVEkADwMb0A@mail.gmail.com">
      <div><br>
      </div>
      <div><br>
        <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>
            </div>
          </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>
          </div>
          <blockquote class="gmail_quote">
            <div>
              <p dir="auto"><br>
              </p>
            </div>
            <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>----
Election-Methods mailing list - see <a href="https://electorama.com/em" target="_blank" moz-do-not-send="true" class="moz-txt-link-freetext">https://electorama.com/em</a> for list info
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