<div dir="ltr">I might be missing something but since C is ranked above bottom in the last two factions, which add up to 54% of the electorate, candidate C would have more implicit approval than candidate B.<br></div><div class="gmail_extra"><br><div class="gmail_quote">On Tue, Nov 22, 2016 at 5:19 PM, Chris Benham <span dir="ltr"><<a href="mailto:cbenhamau@yahoo.com.au" target="_blank">cbenhamau@yahoo.com.au</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
  
    
  
  <div bgcolor="#FFFFFF" text="#000000">
    <div class="m_5161955729756582496moz-cite-prefix"><span class="">On 11/23/2016 8:22 AM, Forest Simmons
      wrote:<br>
      <blockquote type="cite">
        <p class="MsoNormal">If the 44 buriers were more conservative in
          their burial by
          not approving C …</p>
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new""><br>
          </span></p>
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new"">43:
            A</span></p>
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new"">03:
            A>B</span></p>
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new"">44:
            B>>C<span>  </span>(sincere is B or B>A)</span></p>
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new"">10:
            C</span></p>
        <p class="MsoNormal"> </p>
        <p class="MsoNormal">… then A would win without regard to the
          convention of the
          default approval cutoff.</p>
      </blockquote>
      <br></span>
      Forest,<br>
      <br>
      By my calculation B wins if the default approval cutoff is just
      above equal bottom. With the symmetric completion<br>
      at the bottom all three candidates have majority-strength defeats
      (A>B 51-49, B>C 68.5-31.5, C>A 54-46) and the<br>
      Approval scores are  B47 > A46 > C10.<br>
      <br>
      So as in Smith//Approval  B wins.  This is a good example of why
      Kevin Venzke wasn't in favour of allowing voters <br>
      to rank among unapproved candidates (at least under
      Smith//Approval). <br>
      <br>
      It's also a good advertisement for Approval Sorted Margins, which
      easily elects A.<br>
      <br>
      And it leads me to think that in MDDA(SC) the default approval
      should only be for the top-voted candidates.<br>
      <br>
      Chris Benham<div><div class="h5"><br>
      <br>
      <br>
      On 11/23/2016 8:22 AM, Forest Simmons wrote:<br>
    </div></div></div>
    <blockquote type="cite"><div><div class="h5">
      <div dir="ltr">
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new"">Chris,</span></p>
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new""> </span></p>
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new"">Here’s
            an example that you asked me to look at from last month.</span></p>
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new""> </span></p>
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new"">You
            wrote ….</span></p>
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new""> </span></p>
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new"">43:
            A</span></p>
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new"">03:
            A>B</span></p>
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new"">44:
            B>C<span>  </span>(sincere is B or B>A)</span></p>
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new"">10:
            C</span></p>
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new""> </span></p>
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new"">C>A<span> 
            </span>54-46,<span>   
            </span>A>B<span>  </span>46-44,<span>   </span>B>C
            47-10.</span></p>
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new""> </span></p>
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new"">Here
            A is the sincere CW and supported by the largest of the
            three </span></p>
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new"">factions
            of voters, but Winning Votes rewards the buriers by electing
            B.</span></p>
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new""> </span></p>
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new"">Benham
            and<span>  </span>LV(erw)SME<span>   </span>easily elect<span> 
            </span>A.<span>    </span>Smith//Approval (equivalent </span></p>
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new"">here
            to Max Covered Approval) and Approval Sorted Margins elect
            C.</span></p>
        <p class="MsoNormal"> </p>
        <p class="MsoNormal">[end quote]</p>
        <p class="MsoNormal"> </p>
        <p class="MsoNormal">Let’s look at this example from the point
          of view
          MDDA(symmetric completion):</p>
        <p class="MsoNormal"><br>
        </p>
        <p class="MsoNormal">With symmetric completion every candidate
          is 50% plus
          defeated, so nobody is disqualified, and the approval winner
          is elected.</p>
        <p class="MsoNormal"><br>
        </p>
        <p class="MsoNormal">If the default is to approve only top, then
          A is elected.<span>  </span>If the default is to approve all
          ranked
          candidates, then C is elected.</p>
        <p class="MsoNormal"><br>
        </p>
        <p class="MsoNormal">Neither case rewards the buriers.</p>
        <p class="MsoNormal"><br>
        </p>
        <p class="MsoNormal">If the 44 buriers were more conservative in
          their burial by
          not approving C …</p>
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new""><br>
          </span></p>
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new"">43:
            A</span></p>
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new"">03:
            A>B</span></p>
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new"">44:
            B>>C<span>  </span>(sincere is B or B>A)</span></p>
        <p style="margin-bottom:0.0001pt;line-height:normal" class="MsoNormal"><span style="font-size:10pt;font-family:"courier new"">10:
            C</span></p>
        <p class="MsoNormal"> </p>
        <p class="MsoNormal">… then A would win without regard to the
          convention of the
          default approval cutoff.</p>
        <p class="MsoNormal"><br>
        </p>
        <p class="MsoNormal">So far so good!</p>
        <p class="MsoNormal"><br>
        </p>
        <p class="MsoNormal">Forest</p>
        <p class="MsoNormal"><br>
        </p>
        <p class="MsoNormal">P.S.<br>
        </p>
        <p class="MsoNormal"><br>
        </p>
        <p class="MsoNormal">Monkey Puzzle,</p>
        <p class="MsoNormal"><br>
        </p>
        <p class="MsoNormal">I'll write a definition and brief
          explanation of MDDA(symmetric completion) and its relation to
          MDDTR, ICA, and ICT tomorrow.  It looks like I won't have
          enough time today.</p>
        <p class="MsoNormal"><br>
        </p>
        <p class="MsoNormal">But briefly it is a cross between ICA and
          ICT, where the voters can decide where the approval cutoff is
          on their ballot.  If they put it just under Top, then their
          ballot is counted as in ICT.  If they put it just above
          Bottom, then their ballot is counted as in ICA.</p>
        <p class="MsoNormal"><br>
        </p>
        <p class="MsoNormal">MDDTR(pt/2) and ICT are the same.</p>
        <p class="MsoNormal"><br>
        </p>
        <p class="MsoNormal">Gotta go!</p>
        <p class="MsoNormal"><br>
        </p>
        <p class="MsoNormal">Forest<br>
        </p>
      </div>
      <br>
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      <br>
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