<html>
  <head>
    <meta content="text/html; charset=utf-8" http-equiv="Content-Type">
  </head>
  <body bgcolor="#FFFFFF" text="#000000">
    <div class="moz-cite-prefix">Forest,<br>
      <br>
      Why do you want to give any points at all for middle ratings?<br>
      <br>
      What is wrong with  simply 3-slot  Smith//Top Ratings?   <br>
      <br>
      Or 3-slot TTR, Top Ratings (aka ICT)?<br>
      <br>
      Chris Benham<br>
      <br>
      <br>
      On 10/11/2016 9:22 AM, Forest Simmons wrote:<br>
    </div>
    <blockquote
cite="mid:CAP29onf+qZCXtq=EFg5GHRs8yvYaFvJ4LiMiKucKNNdYK-Je0w@mail.gmail.com"
      type="cite">
      <div dir="ltr">
        <div>
          <div>
            <div>
              <div>
                <div>
                  <div>
                    <div>AS Chris Benham and Michael Ossipoff pointed
                      out this Smith//3Score doesn't disappoint the
                      defecting faction (B) unless the plumping faction
                      (C) is fairly close to half of the electorate. It
                      only works when C is plumped on at least 43
                      percent of the ballots.<br>
                      <br>
                    </div>
                    To make it work for Mike's example below where C is
                    plumped on only 100 out of 297 ballots, the middle
                    ranks have to count much les than half of the equal
                    top ranks.  About 2 percent of the equal top value
                    would do.<br>
                    <br>
                  </div>
                  So with sincere ballots the point totals are ...<br>
                  <br>
                </div>
                99+.02(98) = 100.96 for A,<br>
              </div>
              98+ .02(99)= 99.98 for B, and <br>
            </div>
            100 for C.  In this case A is both the CW and the points
            winner.<br>
            <br>
          </div>
          The B faction's defection simultaneously promotes C to the
          Smith set and reduces A's point total to 99, making C (still
          with 100 points) the method winner.<br>
          <br>
        </div>
        <div>What makes this example hard is that the C faction is just
          over one third of the electorate, and that the A and B
          subfactions are very close in size.<br>
          <br>
        </div>
        <div>For a defection attempt to succeed under these conditions
          the B faction would have to possess very precise information. 
          If the A faction had the same information it would be easy for
          them to make a defensive move in the form of truncating B on a
          few ballots.<br>
        </div>
        <div><br>
        </div>
        <div>In practice, a point value substantially larger than .02
          for the middle ranks would be adequate.<br>
        </div>
        <div><br>
        </div>
        <div>What would be a reasonable compromise?  <br>
          <br>
        </div>
        <div>How about 1/4 or 25% ?<br>
          <br>
        </div>
        <div>In that case the A faction could say to the B faction, "You
          rank me on two ballots and I will rank you on seven."<br>
          <br>
        </div>
        <div>The resulting equilibrium would be<br>
          <br>
        </div>
        <div>92 A<br>
        </div>
        <div> 7 A>B<br>
        </div>
        <div>96 B<br>
        </div>
        <div> 2 B>A<br>
        </div>
        <div>100 C<br>
          <br>
        </div>
        <div>Candidate A is elected as the CW.<br>
          <br>
        </div>
        <div>If B defects from this equilibrium proposal ...<br>
          <br>
        </div>
        <div>92 A<br>
        </div>
        <div> 7 A>B<br>
        </div>
        <div>98 B<br>
        </div>
        <div>100 C<br>
          <br>
        </div>
        <div>then {A, B, C} forms Smith, and C wins with 100 points,
          while B gets only<br>
          <br>
        </div>
        <div>98+7/4 = 99.75 points.<br>
          <br>
          <br>
        </div>
        <div>If grade style ballots were in use, the A faction could say
          I will give you two B grades in exchange for two D's.<br>
          <br>
        </div>
        <div>Two B grade points add up to 1.5 which would bring the B
          candidate up to 99.5, still short of the 100 needed to tie the
          C candidate.<br>
          <br>
        </div>
        <div>On the other hand, the two D grades for the A candidate
          would make her the Condorcet Winner.<br>
          <br>
        </div>
        <div>When the plumping faction forms greater than 39 percent of
          the electorate, then no strategy would be needed other than
          for the larger subfaction to give D grades to the potential
          defection candidate.<br>
          <br>
        </div>
        <div>32 A(4), B(1)<br>
        </div>
        <div>31 B(4) (Sincere B>0)<br>
        </div>
        <div>39 C(4)<br>
        </div>
        <div><br>
        </div>
        <div>If eight or more of the B faction give A a positive rating,
          then A wins as the only member of the Smith set.<br>
          <br>
        </div>
        <div>If fewer than eight vote sincerely, then C and B are tied
          with 156 grade points each.<br>
          <br>
        </div>
        <div>So the method I am now proposing is <br>
          <br>
        </div>
        <div>Smith//GPA<br>
          <br>
        </div>
        <div>Elect the member of the Smith set with the largest Grade
          Point Average.<br>
        </div>
        <div><br>
          <br>
        </div>
        <div><br>
        </div>
        <div><br>
        </div>
        <br>
        <div>
          <div>
            <div>
              <div>
                <div>
                  <div>
                    <div>
                      <div>
                        <div>
                          <div>
                            <div class="gmail_extra"><br>
                              <div class="gmail_quote"><br>
                                <blockquote class="gmail_quote"
                                  style="margin:0 0 0
                                  .8ex;border-left:1px #ccc
                                  solid;padding-left:1ex">
                                  From: Michael Ossipoff <br>
                                  Yes, the method still allows chicken
                                  dilemma defection to succeed.<br>
                                  <br>
                                  I tried an example in which the B
                                  faction is about as large as possible
                                  in<br>
                                  comparison to the C faction.<br>
                                  <br>
                                  99: A>B<br>
                                  98: B (sincere is B>A)<br>
                                  100: C<br>
                                  <br>
                                  This results in a cycle, so everyone
                                  is in the Smith-set.<br>
                                  <br>
                                  B has more Borda points than anyone
                                  else.<br>
                                  <br>
                                  It looks as if it isn't possible to
                                  have CD in a strategically good,<br>
                                  reliable, uncriticizable.  rank
                                  method.<br>
                                  <br>
                                  ICT isn't good as a ranking method.
                                  Only as a 3-slot method in which the<br>
                                  middle rating is used only in
                                  Chicken-Dilemma situations.<br>
                                  <br>
                                  In ICT, a candidate you rank middle
                                  doesn't get much protection from you.<br>
                                  <br>
                                  But, in a chicken dilemma situation
                                  you don't expect B to be a CWs anyway.<br>
                                  <br>
                                  3-Slot ICT is still my favorite, to be
                                  used as an Approval version rather<br>
                                  than a ranking method, with the middle
                                  rating only for chicken dilemma.<br>
                                  <br>
                                  Plain MMPO meets Weak CD, FBC, LNHa,
                                  and has wv-like strategy.<br>
                                  <br>
                                  Though it fails CD's strong original
                                  version, if the defection is a<br>
                                  burial--The method's wv burial
                                  defensive advice would warn the A
                                  voters to<br>
                                  not rank B, if A is likely to be CWs.<br>
                                  <br>
                                  That's a unique, impressive &
                                  amazing set of advantages.<br>
                                  <br>
                                  But there are some strongly-felt
                                  criticisms to it. I've answered them,
                                  and<br>
                                  it seems to me that only one of them
                                  is a genuine problem:<br>
                                  <br>
                                  ...the possibility of the perpetual
                                  burial fiasco.<br>
                                  <br>
                                  But I've told here why there's
                                  something a bit mutually contradictory
                                  about<br>
                                  that fiasco's requirements.<br>
                                  <br>
                                  So I suggest that it doesn't rule out
                                  MMPO or MAM, though it makes them<br>
                                  just a little questionable &
                                  unreliable.<br>
                                  <br>
                                  ...but still worth a try because of
                                  big advantages.<br>
                                  <br>
                                  I'd hoped that Bucklin with
                                  conditional votes would be a good CD
                                  method.<br>
                                  But it's not as good as I'd hoped,
                                  because the conditional votes option
                                  can<br>
                                  be strategically taken advantage of,
                                  resulting in another chicken dilemma,<br>
                                  differently-caused.<br>
                                  <br>
                                  I don't know if that rules out the
                                  conditional option, but it supports
                                  the<br>
                                  conclusion that a CD rank method
                                  always costs.<br>
                                  <br>
                                  Michael Ossipoff<br>
                                  <br>
                                  <br>
                                  On Oct 9, 2016 3:19 PM, "Forest
                                  Simmons" <<a moz-do-not-send="true"
                                    href="mailto:fsimmons@pcc.edu"
                                    target="_blank">fsimmons@pcc.edu</a>>
                                  wrote:<br>
                                  <br>
                                  ><br>
                                  ><br>
                                  > (Continued below)<br>
                                  ><br>
                                  ><br>
                                  >> Now, how do we adapt this to
                                  general rankings? We assume that equal
                                  top<br>
                                  >> rankings and equal bottom or
                                  multiple truncations are allowed.<br>
                                  >><br>
                                  >> For each ballot on which a
                                  candidate is ranked above bottom but
                                  below top<br>
                                  >> that candidate receives one
                                  point.  For each ballot on which the
                                  candidate<br>
                                  >> is ranked top or equal top
                                  that candidate receives two points.<br>
                                  >><br>
                                  >> The Smith candidate with the
                                  greatest number of points wins.<br>
                                  >><br>
                                  >> [End of definition]<br>
                                  >><br>
                                  >> Note that the method does
                                  satisfy CD unlike
                                  Smith//ImplicitApproval.<br>
                                  >> Jameson's idea of three slot
                                  scores makes it work.<br>
                                  >><br>
                                  >> How does it do on burial?<br>
                                </blockquote>
                              </div>
                              <br>
                            </div>
                          </div>
                        </div>
                      </div>
                    </div>
                  </div>
                </div>
              </div>
            </div>
          </div>
        </div>
      </div>
      <br>
      <fieldset class="mimeAttachmentHeader"></fieldset>
      <br>
      <pre wrap="">----
Election-Methods mailing list - see <a class="moz-txt-link-freetext" href="http://electorama.com/em">http://electorama.com/em</a> for list info
</pre>
      <br>
      <fieldset class="mimeAttachmentHeader"></fieldset>
      <br>
      <p class="" avgcert""="" color="#000000" align="left">No virus
        found in this message.<br>
        Checked by AVG - <a moz-do-not-send="true"
          href="http://www.avg.com">www.avg.com</a><br>
        Version: 2016.0.7797 / Virus Database: 4664/13183 - Release
        Date: 10/10/16</p>
    </blockquote>
    <p><br>
    </p>
  </body>
</html>