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<![endif]--> </p>
    <p class="MsoNormal"><span
        style="font-size:16.0pt;font-family:"Arial Rounded MT
        Bold"">“still keeping some degree of local representation”</span></p>
    <p class="MsoNormal"><span
        style="font-size:16.0pt;font-family:"Arial Rounded MT
        Bold"">“Local representation” by National Members is the
        mantra of Safe-seat Man, feeding the populus, reformers and
        anti-reformers alike, with their mothers milk, in which the most
        elementary logic plays no part.</span></p>
    <p class="MsoNormal"><span
        style="font-size:16.0pt;font-family:"Arial Rounded MT
        Bold"">Local representation is the prerogative of local
        government. National representation is the prerogative of
        national government, and not local representation.</span></p>
    <p class="MsoNormal"><span
        style="font-size:16.0pt;font-family:"Arial Rounded MT
        Bold"">The outcome of this cross-wired politics is that
        British local government is moribund, and members of the
        national parliament grossly over-burdened with relatively petty
        local problems; “glorified social workers,” far beyond their
        numbers to efficiently cope. </span></p>
    <p class="MsoNormal"><span
        style="font-size:16.0pt;font-family:"Arial Rounded MT
        Bold"">While, there is no time for the issues of national
        politics, which are corralled by the national executive, and in
        which the public has virtually no say, and is not expected to
        have. Hence the Hailsham term for the </span><span
        style="font-size:16.0pt;font-family:"Arial Rounded MT
        Bold"">UK</span><span
        style="font-size:16.0pt;font-family:"Arial Rounded MT
        Bold""> government as “an elective dictatorship.”</span></p>
    <p class="MsoNormal"><span
        style="font-size:16.0pt;font-family:"Arial Rounded MT
        Bold"">Moreover the supposedly “local” representation of
        the single-member system is a euphemism for what actually takes
        place. In most cases, and as a matter of principle, these
        unstable constituencies do not serve any particular locality.
        Their boundaries are periodically smashed to give Members of
        Parliament an approximately equal workload and equal powers of
        patronage over their constituents. Neither democracy nor
        community is the purpose of the single-member system, but
        members monopolies on representation. The house of commons or
        communities should accurately be called the house of monopolies,
        departing from its historic role, late in the nineteenth
        century.</span></p>
    <p class="MsoNormal"><span
        style="font-size:16.0pt;font-family:"Arial Rounded MT
        Bold"">The assumption that the single-member constituency
        is the most local is the fallacy of scale. It is an extension of
        the confused idea that the only democracy is personal democracy,
        on the scale of the ancient Greek polis or city state.</span></p>
    <p class="MsoNormal"><span
        style="font-size:16.0pt;font-family:"Arial Rounded MT
        Bold"">In other words, democracy is not a function of
        representation by the fewest seats per constituency possible;
        one sole representative, democracy is, as Hare and Mill said it
        was, a function of many seats per constituency equally
        representative (by quota). This applies as much to the most
        local representation as to the most universal representation.</span></p>
    <p class="MsoNormal"><span
        style="font-size:16.0pt;font-family:"Arial Rounded MT
        Bold"">Regards, <br>
      </span></p>
    <p class="MsoNormal"><span
        style="font-size:16.0pt;font-family:"Arial Rounded MT
        Bold"">Richard Lung.<br>
      </span></p>
    <p class="MsoNormal"><span
        style="font-size:16.0pt;font-family:"Arial Rounded MT
        Bold""> </span></p>
    <p><br>
    </p>
    <div class="moz-cite-prefix">On 09/11/2023 16:25, Toby Pereira
      wrote:<br>
    </div>
    <blockquote type="cite"
      cite="mid:1347859608.2357077.1699547110253@mail.yahoo.com">
      <div class="ydp941989a1yahoo-style-wrap">
        <div dir="ltr" data-setdir="false">On non-deterministic methods,
          they can give potentially a better level of proportional
          representation than deterministic methods, while still keeping
          some degree of local representation. If you have
          constituencies with 5 or 6 representatives and use e.g. STV,
          then parties/ideologies with 10% of the support nationally
          would likely keep missing out and win far less than 10% of the
          seats. Non-deterministic methods can mean that on average
          things balance out.</div>
        <div dir="ltr" data-setdir="false"><br>
        </div>
        <div dir="ltr" data-setdir="false">If you use the simple random
          ballot method, things would still be pretty bad. With just one
          representative per constituency, quite a lot of people are
          likely to be represented only by a lunatic fringe candidate.
          But with 5 or 6 winning candidates, popular candidates will
          still generally win through, and there will be a balance of
          representation in each constituency.</div>
        <div dir="ltr" data-setdir="false"><br>
        </div>
        <div dir="ltr" data-setdir="false">Proportional methods can also
          get quite complex, but this can be massively reduced with a
          non-deterministic method. For example, COWPEA Lottery uses
          approval voting. To elect candidates you simply do this:</div>
        <div dir="ltr" data-setdir="false"><span><br>
          </span></div>
        <div dir="ltr" data-setdir="false"><span>Start with a list of
            all currently-unelected candidates. Pick a ballot at random
            and remove from the list all candidates not approved on this
            ballot. Pick another ballot at random, and continue with
            this process until one candidate is left. Elect this
            candidate. If the number of candidates ever goes from >1
            to 0 in one go, ignore that ballot and continue. If any tie
            cannot be broken, then elect the tied candidates with equal
            probability.</span></div>
        <div dir="ltr" data-setdir="false"><span><br>
          </span></div>
        <div dir="ltr" data-setdir="false"><span>It also has very good
            criterion compliance. If you accept non-determinism and
            ballots that aren't just ordinal, then probably the best of
            any known candidate-based proportional method. </span><a
            href="https://electowiki.org/wiki/COWPEA" rel="nofollow"
            target="_blank" moz-do-not-send="true"
            class="moz-txt-link-freetext">https://electowiki.org/wiki/COWPEA</a></div>
        <div dir="ltr" data-setdir="false"><br>
        </div>
        <div dir="ltr" data-setdir="false">Toby</div>
        <div><br>
        </div>
      </div>
      <div id="ydpcdaeb516yahoo_quoted_9991638099"
        class="ydpcdaeb516yahoo_quoted">
        <div>
          <div> On Wednesday, 8 November 2023 at 18:18:24 GMT, Richard
            Lung <a class="moz-txt-link-rfc2396E"
              href="mailto:voting@ukscientists.com"><voting@ukscientists.com></a>
            wrote: </div>
          <div><br>
          </div>
          <div><br>
          </div>
          <div>
            <div id="ydpcdaeb516yiv0491022789">
              <div>
                <p><br>
                </p>
                <p> </p>
                <p class="ydpcdaeb516yiv0491022789MsoNormal"><span>Why
                    has theorem Arrow gained so much traction over the
                    years?</span></p>
                <p class="ydpcdaeb516yiv0491022789MsoNormal"><span> </span></p>
                <p class="ydpcdaeb516yiv0491022789MsoNormal"><span>The
                    short answer, history is written by the victors.</span></p>
                <p class="ydpcdaeb516yiv0491022789MsoNormal"><span>The
                    history answer takes some explaining but is evident
                    enough.</span></p>
                <p class="ydpcdaeb516yiv0491022789MsoNormal"><span>New
                    York</span><span>, for instance, had a Personal
                    Representation society, by the late nineteenth
                    century. In fact the organised campaign writings, of
                    its early successes, over a century old, have been
                    bought-up, and are still subject to publishers pay
                    walls, of little if any commercial value and
                    contrary to the public interest.</span></p>
                <p class="ydpcdaeb516yiv0491022789MsoNormal"><span>By
                    the 1937 edition of Proportional Representation. The
                    key to democracy. Clarence Hoag and George Hallett
                    were introducing a single transferable vote to the
                    boroughs of </span><span>New York</span><span>.</span></p>
                <p class="ydpcdaeb516yiv0491022789MsoNormal"><span>These
                    two campaigning great men, both mathematicians in
                    their day job, did not get a mention in Wikipedia,
                    when I last looked.</span></p>
                <p class="ydpcdaeb516yiv0491022789MsoNormal"><span>As a
                    result of battering-ram referendums with the money
                    and publicity on their side, The Machine virtually
                    abolished the key to democracy.</span></p>
                <p class="ydpcdaeb516yiv0491022789MsoNormal"><span>Massachusetts</span><span>
                    legislature forbad other cities than </span><span>Cambridge</span><span>
                    to use their electoral reform. There are several
                    home-rule bills but they are bogged down in state
                    committee.</span></p>
                <p class="ydpcdaeb516yiv0491022789MsoNormal"><span>Kenneth
                    Arrow stepped in, in the nineteen fifties, to
                    effectively finish the job of The Machine. He took
                    the Kurt Godel Incompleteness theorem an extreme
                    step further by advertising an “Impossibility
                    theorem,” which he himself, cited in Scientific
                    American, belatedly admitted it did not amount to.</span></p>
                <p class="ydpcdaeb516yiv0491022789MsoNormal"><span>In
                    other words, he by-passed, nearly a century of
                    election method study, stemming from Thomas Hare and
                    John Stuart Mill. That tradition continues and so
                    does the naïve ignorance of it.</span></p>
                <p class="ydpcdaeb516yiv0491022789MsoNormal"><span>As a
                    Scottish STV programmer commented, theorem Arrow
                    does not even apply to proportional representation,
                    but merely to bare majority elections.</span></p>
                <p class="ydpcdaeb516yiv0491022789MsoNormal"><span>Any
                    theorem is only as good as its assumptions, and
                    those of the Impossibility theorem neglect the
                    possibility that statistical methods might be more
                    accurate than deterministic ones, as is indeed the
                    case in physics.</span></p>
                <p class="ydpcdaeb516yiv0491022789MsoNormal"><span>Regards,
                    <br>
                  </span></p>
                <p class="ydpcdaeb516yiv0491022789MsoNormal"><span>Richatrd
                    Lung.</span></p>
                <p class="ydpcdaeb516yiv0491022789MsoNormal"><span><br>
                  </span></p>
                <p class="ydpcdaeb516yiv0491022789MsoNormal"><span><br>
                  </span></p>
                <p><br>
                </p>
                <div class="ydpcdaeb516yiv0491022789moz-cite-prefix">On
                  07/11/2023 13:35, Toby Pereira wrote:<br>
                </div>
                <blockquote type="cite">
                  <div
                    class="ydpcdaeb516yiv0491022789ydpd48923f3yahoo-style-wrap">
                    <div dir="ltr">As is often the case, I think the
                      importance of Arrow's Theorem is overstated in
                      that article. Arrow's Theorem essentially says
                      "With a few reasonable background assumptions, no
                      ranked-ballot method passes Independence of
                      Irrelevant Alternatives." But this was already
                      known for centuries from the Condorcet Paradox. I
                      don't really know why it's gained so much traction
                      over the years, as it was nothing like the
                      paradigm shift people credit it as.</div>
                    <div dir="ltr"><br>
                    </div>
                    <div dir="ltr">Toby</div>
                    <div><br>
                    </div>
                  </div>
                  <div
                    id="ydpcdaeb516yiv0491022789ydpafe61227yahoo_quoted_9697965469"
class="ydpcdaeb516yiv0491022789ydpafe61227yahoo_quoted">
                    <div>
                      <div> On Tuesday, 7 November 2023 at 04:29:31 GMT,
                        Forest Simmons <a shape="rect"
                          href="mailto:forest.simmons21@gmail.com"
                          class="ydpcdaeb516yiv0491022789moz-txt-link-rfc2396E"
                          rel="nofollow" target="_blank"
                          moz-do-not-send="true"><forest.simmons21@gmail.com></a>
                        wrote: </div>
                      <div><br>
                      </div>
                      <div><br>
                      </div>
                      <div>
                        <div
                          id="ydpcdaeb516yiv0491022789ydpafe61227yiv0954465204">
                          <div>
                            <div>Rob,
                              <div><br>
                              </div>
                              <div>Thanks for clearing up a lot  of the
                                confusion... and for putting the current
                                status in perspective.</div>
                              <div><br>
                              </div>
                              <div>I like the comparison of the
                                "impossibilities of voting" with the
                                impossibilities of faster than light
                                travel, etc.  The 2nd law of
                                thermodynamics is especially relevant...
                                because as Prigogene showed in the 70's,
                                the impossibility of decreasing entropy
                                in closed systems still allows for local
                                pockets of possibility ... that make
                                life possible .... until the "heat
                                death" of our island space-time big bang
                                remnant ... while miriads of new
                                "inflationary bubbles" appear from
                                random virtual quantum fluctuations.</div>
                              <div><br>
                              </div>
                              <div>We used to "know" that the event
                                horizon was a boundary of no return ....
                                nut now evaporation of black holes
                                through quantum tunneling is taken for
                                granted.</div>
                              <div><br>
                              </div>
                              <div>In the early 1800's Gauss proved the
                                impossibility of trisecting an
                                arbitrarily given angle .... inside the
                                rules of classical geometric ruler and
                                compass constructions.</div>
                              <div><br>
                              </div>
                              <div>But it turns out that (as any first
                                year topology student can show) any
                                angle can be transformed into
                                atrisectable one by an arbitrarily small
                                perturbation.</div>
                              <div><br>
                              </div>
                              <div>I'm fact, once you learn the binary
                                point expansion of 1/3 ..., you can get
                                within a relative error tolerance of
                                1/2^n precision with n bisections...
                                bisections being the first constructions
                                you learn in geometty.</div>
                              <div><br>
                              </div>
                              <div>Pockets of possibility like these
                                .... adequate "For All Practical
                                Purposes" pervade mathematics ...
                                including the mathematics of voting
                                systems.</div>
                              <div><br>
                              </div>
                              <div>Sometimes you have to discover new
                                tools not included in the classical tool
                                kit. In  the case of angle trisections,
                                if you are allowed to make a few marks
                                on the ruler... hen the general ruler
                                and compass trisection suddenly resolves
                                itself.</div>
                              <div><br>
                              </div>
                              <div>Thanks,</div>
                              <div><br>
                              </div>
                              <div>Forest</div>
                            </div>
                            <br>
                            <div
                              class="ydpcdaeb516yiv0491022789ydpafe61227yiv0954465204gmail_quote">
                              <div
                                id="ydpcdaeb516yiv0491022789ydpafe61227yiv0954465204yqt91197"
class="ydpcdaeb516yiv0491022789ydpafe61227yiv0954465204yqt7468526250">
                                <div dir="ltr"
                                  class="ydpcdaeb516yiv0491022789ydpafe61227yiv0954465204gmail_attr">On
                                  Sun, Nov 5, 2023, 11:34 PM Rob
                                  Lanphier <<a shape="rect"
                                    href="mailto:roblan@gmail.com"
                                    class="ydpcdaeb516yiv0491022789moz-txt-link-freetext
                                    moz-txt-link-freetext"
                                    rel="nofollow" target="_blank"
                                    moz-do-not-send="true">roblan@gmail.com</a>>
                                  wrote:<br>
                                </div>
                                <blockquote
                                  class="ydpcdaeb516yiv0491022789ydpafe61227yiv0954465204gmail_quote">
                                  <div dir="ltr">
                                    <div>Hi folks,</div>
                                    <div><br>
                                    </div>
                                    <div>I just wrote a letter to the
                                      editor(s) of Scientific American,
                                      which I've included below.  My
                                      letter was in a response to the
                                      following article that was
                                      recently published on their
                                      website:<br>
                                    </div>
                                    <div>
                                      <div><a shape="rect"
href="https://www.scientificamerican.com/article/see-how-math-could-design-the-perfect-electoral-system/"
class="ydpcdaeb516yiv0491022789moz-txt-link-freetext
                                          moz-txt-link-freetext"
                                          rel="nofollow" target="_blank"
                                          moz-do-not-send="true">https://www.scientificamerican.com/article/see-how-math-could-design-the-perfect-electoral-system/</a></div>
                                      <div><br>
                                      </div>
                                      <div>Y'all may have other thoughts
                                        on the article.<br>
                                      </div>
                                      <div><br>
                                      </div>
                                    </div>
                                    <div>Rob<br>
                                      <div
                                        class="ydpcdaeb516yiv0491022789ydpafe61227yiv0954465204gmail_quote">
                                        <div dir="ltr"
                                          class="ydpcdaeb516yiv0491022789ydpafe61227yiv0954465204gmail_attr">----------
                                          Forwarded message ---------<br>
                                          From: <b
                                            class="ydpcdaeb516yiv0491022789ydpafe61227yiv0954465204gmail_sendername">Rob
                                            Lanphier</b> <span><<a
                                              shape="rect"
                                              href="mailto:roblan@gmail.com"
class="ydpcdaeb516yiv0491022789moz-txt-link-freetext
                                              moz-txt-link-freetext"
                                              rel="nofollow"
                                              target="_blank"
                                              moz-do-not-send="true">roblan@gmail.com</a>></span><br>
                                          Date: Sun, Nov 5, 2023 at
                                          11:22 PM<br>
                                          Subject: Regarding using math
                                          to create a "Perfect Electoral
                                          System"<br>
                                          To: Scientific American
                                          Editors <<a shape="rect"
                                            href="mailto:editors@sciam.com"
class="ydpcdaeb516yiv0491022789moz-txt-link-freetext
                                            moz-txt-link-freetext"
                                            rel="nofollow"
                                            target="_blank"
                                            moz-do-not-send="true">editors@sciam.com</a>><br>
                                        </div>
                                        <br>
                                        <br>
                                        <div dir="ltr">
                                          <div>To whom it may concern:</div>
                                          <div><br>
                                          </div>
                                          <div>I appreciate your article
                                            "Could Math Design the
                                            Perfect Electoral System?",
                                            since I agree that math is
                                            important for understanding
                                            electoral reform, and
                                            there's a lot of good
                                            information and great
                                            diagrams in your article:</div>
                                          <div><a shape="rect"
href="https://www.scientificamerican.com/article/see-how-math-could-design-the-perfect-electoral-system/"
class="ydpcdaeb516yiv0491022789moz-txt-link-freetext
                                              moz-txt-link-freetext"
                                              rel="nofollow"
                                              target="_blank"
                                              moz-do-not-send="true">https://www.scientificamerican.com/article/see-how-math-could-design-the-perfect-electoral-system/</a></div>
                                          <div><br>
                                          </div>
                                          <div>There's some things that
                                            the article gets wrong, but
                                            the good news is that the
                                            article title and its
                                            relation to <span>Betteridge</span><span>'s
                                              law.  This law states </span>"Any
                                            headline that ends in a
                                            question mark can be
                                            answered by the word <i>'</i>no<i>'</i>." 
                                            The bad news: the URL slug
                                            ("see-how-math-could-design-the-perfect-electoral-system")
                                            implies the answer is
                                            "yes".  The answer is "no";
                                            Kenneth Arrow and Allan
                                            Gibbard proved there is no
                                            perfect electoral system
                                            (using math).</div>
                                          <div><br>
                                          </div>
                                          <div>I appreciate that your
                                            article highlights the
                                            mayoral election in
                                            Burlington, Vermont in
                                            2009.  That is an important
                                            election for all voters
                                            considering FairVote's
                                            favorite single-winner
                                            system ("instant-runoff
                                            voting" or rather
                                            "ranked-choice voting, as
                                            they now call it).  When I
                                            volunteered with FairVote in
                                            the late 1990s, I remember
                                            when they introduced the
                                            term "instant-runoff
                                            voting".  I thought the name
                                            was fine.  After Burlington
                                            2009, it would seem that
                                            FairVote has abandoned the
                                            name.  Regardless, anyone
                                            considering instant-runoff
                                            needs to consider
                                            Burlington's experience.<br>
                                          </div>
                                          <div><br>
                                          </div>
                                          <div>Sadly, your article
                                            describes "cardinal methods"
                                            in a confusing manner.  It
                                            erroneously equates
                                            cardinal's counterpart
                                            ("ordinal voting") with
                                            "ranked-choice voting". 
                                            Intuitively, all "ordinal
                                            methods" should be called
                                            "ranked choice voting", but
                                            during this century, the
                                            term has been popularized by
                                            FairVote and the city of San
                                            Francisco to refer to a
                                            specific method formerly
                                            referred to as
                                            "instant-runoff voting". 
                                            These days, when Americans
                                            speak of "RCV", they're
                                            generally referring to the
                                            system known on English
                                            Wikipedia as "IRV" (or
                                            "Instant-runoff voting"):</div>
                                          <div><a shape="rect"
                                              href="https://en.wikipedia.org/wiki/Instant-runoff_voting"
class="ydpcdaeb516yiv0491022789moz-txt-link-freetext
                                              moz-txt-link-freetext"
                                              rel="nofollow"
                                              target="_blank"
                                              moz-do-not-send="true">https://en.wikipedia.org/wiki/Instant-runoff_voting</a><br>
                                          </div>
                                          <br>
                                          <div>There have been many
                                            methods that use ranked
                                            ballots, including the
                                            methods developed by Nicolas
                                            de Condorcet
                                            and Jean-Charles de Borda in
                                            the 1780s and the 1790s. I'm
                                            grateful that the Marquis de
                                            Condorcet's work is featured
                                            so prominently in your
                                            article.  Condorcet's work
                                            was brilliant, and I'm sure
                                            he would have become more
                                            prominent if he hadn't died
                                            in a French prison in the
                                            1790s.  Many single-winner
                                            methods that strictly comply
                                            with the "Condorcet winner
                                            criterion" are probably as
                                            close to "perfect" as any
                                            system (from a mathematical
                                            perspective).<br>
                                          </div>
                                          <div><br>
                                          </div>
                                          <div>Most methods that pass
                                            the "Condorcet winner
                                            criterion" typically use
                                            ranked ballots (and thus are
                                            "ordinal"), but it's
                                            important to note that
                                            almost all "ordinal" methods
                                            can use cardinal ballots. 
                                            Instant-runoff voting
                                            doesn't work very well with
                                            cardinal ballots (because
                                            tied scores cannot be
                                            allowed), but most other
                                            ordinal systems work
                                            perfectly well with tied
                                            ratings or rankings.  Even
                                            though passing the Condorcet
                                            winner criterion is very
                                            important, there are many
                                            methods that come very, very
                                            close in reasonable
                                            simulations.  I would
                                            strongly recommend that you
                                            contact Dr. Ka-Ping Yee, who
                                            is famous in electoral
                                            reform circles for "Yee
                                            diagrams":</div>
                                          <div><a shape="rect"
                                              href="https://electowiki.org/wiki/Yee_diagram"
class="ydpcdaeb516yiv0491022789moz-txt-link-freetext
                                              moz-txt-link-freetext"
                                              rel="nofollow"
                                              target="_blank"
                                              moz-do-not-send="true">https://electowiki.org/wiki/Yee_diagram</a></div>
                                          <div>(a direct link to Yee's
                                            2005 paper: <a shape="rect"
href="http://zesty.ca/voting/sim/"
                                              class="ydpcdaeb516yiv0491022789moz-txt-link-freetext
                                              moz-txt-link-freetext"
                                              rel="nofollow"
                                              target="_blank"
                                              moz-do-not-send="true">http://zesty.ca/voting/sim/</a>
                                            )</div>
                                          <div><br>
                                          </div>
                                          <div>Note that "approval
                                            voting" and "Condorcet"
                                            provide pretty much the same
                                            results in Yee's 2005
                                            paper.  "Instant-runoff
                                            voting" seems a little crazy
                                            in Yee's simulations.<br>
                                          </div>
                                          <div><br>
                                          </div>
                                          <div>Though Arrow and Gibbard
                                            disproved "perfection", I
                                            prefer to think of Arrow's
                                            and Gibbard's work as
                                            defining the physics of
                                            election methods.  To
                                            explain what I mean,
                                            consider the physics of
                                            personal transportation.  It
                                            is impossible to design the
                                            PERFECT vehicle (that is
                                            spacious, and comfortable,
                                            travels faster than the
                                            speed of light, fits in
                                            anyone's garage or personal
                                            handbag).  Newton and
                                            Einstein more-or-less proved
                                            it.  However, those esteemed
                                            scientists' work didn't
                                            cause us to stop working on
                                            improvements in personal
                                            transportation.  Buggy whips
                                            are now (more or less)
                                            recognized as obsolete, as
                                            is Ford's "Model T".<br>
                                          </div>
                                          <div><br>
                                          </div>
                                          <div>Now that Arrow and
                                            Gibbard have helped us
                                            understand the physics of
                                            election methods, we can
                                            hopefully start pursuing
                                            alternatives to the buggy
                                            whip (or rather,
                                            alternatives to "choose-one"
                                            voting systems, often
                                            referred to as "first past
                                            the post" systems).  <br>
                                          </div>
                                          <div><br>
                                          </div>
                                          <div>This gets me to the
                                            statement from your article
                                            that gets under my skin the
                                            most::</div>
                                          <blockquote
                                            class="ydpcdaeb516yiv0491022789ydpafe61227yiv0954465204gmail_quote">
                                            <div>This is called cardinal
                                              voting, or range voting,
                                              and although it’s no
                                              panacea and has its own
                                              shortcomings, it
                                              circumvents the
                                              limitations imposed by
                                              Arrow’s impossibility
                                              theorem, which only
                                              applies to ranked choice
                                              voting. <br>
                                            </div>
                                          </blockquote>
                                          <div> </div>
                                          <div>People who study election
                                            methods refer to "cardinal
                                            voting" as a <i>category</i>
                                            of voting methods, of which
                                            "range voting" is just one
                                            (which is called "score
                                            voting" on English
                                            Wikipedia):</div>
                                          <div><a shape="rect"
                                              href="https://en.wikipedia.org/wiki/Score_voting"
class="ydpcdaeb516yiv0491022789moz-txt-link-freetext
                                              moz-txt-link-freetext"
                                              rel="nofollow"
                                              target="_blank"
                                              moz-do-not-send="true">https://en.wikipedia.org/wiki/Score_voting</a><br>
                                          </div>
                                          <div><br>
                                          </div>
                                          <div>The conflation of "ranked
                                            choice voting" with all
                                            ordinal voting methods is
                                            also highly problematic
                                            (though I don't entirely
                                            blame you for this).  As I
                                            stated earlier, there are
                                            many methods that can use
                                            ranked ballots.  While this
                                            article may have been
                                            helpful for those of us that
                                            prefer ranking methods that
                                            are not "instant-runoff
                                            voting" back when FairVote
                                            switched to "ranked-choice
                                            voting" in the early 2010s. 
                                            Note that before the fiasco
                                            in Burlington in 2009,
                                            FairVote pretty consistently
                                            preferred "instant runoff
                                            voting":</div>
                                          <div><a shape="rect"
href="https://web.archive.org/web/20091111061523/http://www.fairvote.org/"
class="ydpcdaeb516yiv0491022789moz-txt-link-freetext
                                              moz-txt-link-freetext"
                                              rel="nofollow"
                                              target="_blank"
                                              moz-do-not-send="true">https://web.archive.org/web/20091111061523/http://www.fairvote.org/</a></div>
                                          <br>
                                          <div>I appreciate that you're
                                            trying to explain this
                                            insanely complicated topic
                                            to your readers.  When I
                                            edit English Wikipedia
                                            (which I've done for over
                                            twenty years), I would love
                                            to be able to cite
                                            Scientific American on this
                                            topic.  However, I'm not yet
                                            sure I'd feel good about
                                            citing this article.<br>
                                          </div>
                                          <div><br>
                                          </div>
                                          <div>Rob Lanphier</div>
                                          <div>Founder of
                                            election-methods mailing
                                            list and <a shape="rect"
                                              href="http://electowiki.org"
                                              rel="nofollow"
                                              target="_blank"
                                              moz-do-not-send="true">electowiki.org</a><br>
                                          </div>
                                          <div><a shape="rect"
                                              href="https://robla.net"
                                              class="ydpcdaeb516yiv0491022789moz-txt-link-freetext
                                              moz-txt-link-freetext"
                                              rel="nofollow"
                                              target="_blank"
                                              moz-do-not-send="true">https://robla.net</a></div>
                                          <div><a shape="rect"
                                              href="https://electowiki.org/wiki/User:RobLa"
class="ydpcdaeb516yiv0491022789moz-txt-link-freetext
                                              moz-txt-link-freetext"
                                              rel="nofollow"
                                              target="_blank"
                                              moz-do-not-send="true">https://electowiki.org/wiki/User:RobLa</a></div>
                                          <div><a shape="rect"
                                              href="https://en.wikipedia.org/wiki/User:RobLa"
class="ydpcdaeb516yiv0491022789moz-txt-link-freetext
                                              moz-txt-link-freetext"
                                              rel="nofollow"
                                              target="_blank"
                                              moz-do-not-send="true">https://en.wikipedia.org/wiki/User:RobLa</a><br>
                                          </div>
                                          <div><br>
                                          </div>
                                          <div>p.s. back in the late
                                            1990s, I wrote an article
                                            for a small tech journal
                                            called "The Perl Journal". 
                                            It's out of print, but I've
                                            reproduced my 1996 article
                                            about election methods which
                                            I think holds up pretty
                                            well:</div>
                                          <div><a shape="rect"
                                              href="https://robla.net/1996/TPJ"
class="ydpcdaeb516yiv0491022789moz-txt-link-freetext
                                              moz-txt-link-freetext"
                                              rel="nofollow"
                                              target="_blank"
                                              moz-do-not-send="true">https://robla.net/1996/TPJ</a><br>
                                          </div>
                                        </div>
                                      </div>
                                    </div>
                                  </div>
                                  ----<br>
                                  Election-Methods mailing list - see <a
                                    shape="rect"
                                    href="https://electorama.com/em"
                                    class="ydpcdaeb516yiv0491022789moz-txt-link-freetext
                                    moz-txt-link-freetext"
                                    rel="nofollow" target="_blank"
                                    moz-do-not-send="true">https://electorama.com/em</a>
                                  for list info
                                  <div
                                    id="ydpcdaeb516yiv0491022789yqtfd11320"
class="ydpcdaeb516yiv0491022789yqt5150919581"><br>
                                  </div>
                                </blockquote>
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class="ydpcdaeb516yiv0491022789yqt5150919581"> </div>
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class="ydpcdaeb516yiv0491022789yqt5150919581"> </div>
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class="ydpcdaeb516yiv0491022789yqt5150919581"> </div>
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                          <div
                            id="ydpcdaeb516yiv0491022789ydpafe61227yqt56102"
class="ydpcdaeb516yiv0491022789ydpafe61227yqt7468526250">----<br>
                            Election-Methods mailing list - see <a
                              shape="rect"
                              href="https://electorama.com/em"
                              class="ydpcdaeb516yiv0491022789moz-txt-link-freetext
                              moz-txt-link-freetext" rel="nofollow"
                              target="_blank" moz-do-not-send="true">https://electorama.com/em</a>
                            for list info<br>
                          </div>
                        </div>
                      </div>
                      <div id="ydpcdaeb516yiv0491022789yqtfd43619"
                        class="ydpcdaeb516yiv0491022789yqt5150919581"> </div>
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                    <pre class="ydpcdaeb516yiv0491022789moz-quote-pre">----
Election-Methods mailing list - see <a shape="rect" href="https://electorama.com/em" class="ydpcdaeb516yiv0491022789moz-txt-link-freetext moz-txt-link-freetext" rel="nofollow" target="_blank" moz-do-not-send="true">https://electorama.com/em</a> for list info
</pre>
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