<div dir="ltr"><div>I've suggested larger electoral systems for this.</div><div><br></div><div>If you use Single Transferable Vote for a nonpartisan blanket Primary Election to get down to somewhere between 5 and 9 (I think 7 may be better than 5), then Tideman's Alternative as a Condorcet system, you get a pretty reliable result.</div><div><br></div><div>Consider the two-party oligarchy problem:  30% of voters vote D, 24% vote C, the parties are {A,B} and {C,D}.  If A>B>C>D for an {A} voter, then C is your Condorcet winner:<br><br>30%:  D>C>B>A</div><div>24%: C>D>B>A</div><div>46%:  {A,B}>C>D</div><div><br></div><div>24% + 46% consider C>D.  There's no marginal utility for C voters to vote D>C as a way to band together and prevent a loss.</div><div><br></div><div>Now, the 30% can vote D>A>C>B, under the theory that A is the Condorcet loser.  A few outcomes:</div><div><br></div><div>1.  An A vs. C pair where A defeats C creates a full cycle (A>C>{D,B}, D>A, Smith set is all candidates).  We're looking at 23% give or take for each of A and B, so the cycle will break in the runoff iteration, and C still wins even with all 30% voting D>C.</div><div>2.  If 32% and 22% instead of 30% and 24% for {C,D} voters, then this huge 32% plurality can indeed defeat C.  If just 4% of C voters defect and decide that D is f*$%ing crazy and their vote is C>B>D>A (because A is worse, to them)—and this is highly-likely, as we all well know and have seen in real elections—then D voters just elected B, who is worse from their perspective.</div><div><br></div><div>This tampering doesn't likely elect D, but rather pushes the winner farther toward A.  The distortion from the other side also doesn't work, although it might be possible for 21% A>B>C>D voters to rank A>D>B>C and elect D (also a worse outcome).</div><div><br></div><div>Pretty much only D and A have any utility voting as such.  C and B voters would be best off voting honestly, e.g. C>D>B or C>B>D.  Changing your first choice is always weakening your first choice.</div><div><br></div><div>With a span of 7, you have {A,B,C,D,E,F,G} at roughly 14% of the vote.  The impact of these groups and the usefulness or utility of tactical voting falls away, so these failures simply stop happening.  Don't use group voting tickets.</div><div><br></div><div>This proportional NPBP, Condorcet Election has a few other interesting properties, notably due to vote impact.</div><div><br></div><div>Imagine of the 7, {C,D,E} being centered around {D} (the natural Condorcet candidate), D defeats all other candidates, while E defeats all candidates except D.  E loses to D by 10%.  If E can get out 10% more voters—out of the whole election, not just 10% more E voters—then E can win.  That's pretty heavy.</div><div><br></div><div>Likewise, social media propaganda has to make some major shifts.  It can't change the winner to A or G or even E.  The change in ballots is immense and complex and nonsense.  This system resists such propaganda.</div><div><br></div><div>On the other hand, CHANGING a vote is two votes.  If D offends A voters who vote A>B>C>D>E, then A voters will change their vote to A>B>C>E>D.  That's -1 D, +1 E—it's 2 votes.  Just a 5% movement here will switch the winner from D to the substantially-similar E, even though the only people who switched their votes were fringe voters who are nowhere near the base for D and E.</div><div><br></div><div>This is more-sensitive with 7 candidates.  It does require voters to rank so many candidates, and voters typically rank to six in practice (according to Fair Vote).  If they tend to rank to three, then e.g. B>C>D and F>E>D votes form the edges, and we have likely enough of those (A and G voters are 2/7, then half of B and F voters makes 3/7, leaving 71% of voters who likely explicitly rank the Condorcet candidate) to accurately locate the Condorcet candidate.  I worry about 9 or 11 or 15 because it'll break.</div><div><br></div><div>Think in terms of larger electoral systems.  Think in terms of how many candidates and the distribution of first-choice voters, and in terms of engineering an election cycle to create the conditions which protect your election from such failures.  You will not find one voting rule to rule them all:  when 9 people show up from one party, 5 show up from another, 3 small parties send a candidate, and you have 2 independents, any single-winner method will bluntly fail.  You need a primary election.</div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Sun, Jun 9, 2019 at 10:20 PM C.Benham <<a href="mailto:cbenham@adam.com.au">cbenham@adam.com.au</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
  
    
  
  <div bgcolor="#FFFFFF">
    <p>Kevin,<br>
      <br>
      So to be clear the possible "complaint" some voters might have
      (and you think we should take seriously) is "We lied and the
      voting method<br>
      (instead of somehow reading our minds) believed us".<br>
      <br>
      So therefore it is good to have a less expressive ballot because
      that reduces the voter's opportunities to tell stupid lies and if
      the method<br>
      is simple enough then maybe also the temptation for them to do so.<br>
      <br>
      To me that is absurd. If I agreed with that idea I would forget
      about the Condorcet criterion and instead demand a method that
      meets <br>
      Later-no-Help,  such as  IRV or Bucklin or Approval.<br>
      <br>
      But I've thought of a patch to address your issue.  We could have
      a rule which says that if the winner's approval score is below
      some fixed <br>
      fraction of that of the most approved candidate, then a
      second-round runoff is triggered between those two candidates. 
      What do you<br>
      think of that?  What do you think that fraction should be?<br>
      <br>
      Chris <br>
      <br>
      <br>
    </p>
    <div class="gmail-m_-2507526158578233008moz-cite-prefix">On 10/06/2019 9:57 am, Kevin Venzke
      wrote:<br>
    </div>
    <blockquote type="cite">
      
      <div class="gmail-m_-2507526158578233008ydp8f615ceyahoo-style-wrap" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:16px">
        <div>Hi Chris,</div>
        <div><br>
        </div>
        <div>
          <div>
            <div>
              <blockquote type="cite" style="margin:0px;padding:8px;color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">>>I don't think
                it's ideal if burying X under Y (both disapproved) can
                only backfire when Y is made the CW.
                <div>>></div>
              </blockquote>
              <span style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">>Why
                is that?  </span></div>
            <div><span style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><br>
              </span></div>
            <div><span style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">Because I
                think if voters decide to attempt to prevent another
                candidate from being CW, via insincerity, there should
                be risks to doing that. Of course there is already some
                risk. But if you "knew" that a given candidate had no
                chance of being CW then there would be nothing to lose
                in using that candidate in a burial strategy.</span></div>
            <div><span style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><br>
              </span></div>
            <div><span style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">>The
                post-election complaint (by any of the voters) would be
                .. what?</span></div>
            <div><br>
            </div>
            <div>For either a successful burial strategy, or one that
              backfires and elects an arbitrary candidate, I think the
              possible complaints are clear. Maybe someone would argue
              that a backfiring strategy proves the method's incentives
              are just fine. But that wouldn't be how I see it. I think
              if, in actual practice, it ever happens that voters
              calculate that a strategy is worthwhile, and it completely
              backfires to the point that everyone would like the
              results discarded, then that method will probably get
              repealed.</div>
            <div><br>
            </div>
            <div>><br style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif" clear="none">
              <span style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">>If
                you don't allow voters to rank among their unapproved
                candidates then arguably you are not even trying to
                elect the sincere CW.</span><br style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif" clear="none">
              <span style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">>Instead
                you are just modifying Approval to make it a lot more
                Condorcet-ish.  </span></div>
            <div><br>
            </div>
            <div>Not an unfair statement. If you require voters to have
              that much expressiveness then you can't use implicit.</div>
            <div><br>
            </div>
            <div>To me, the motivation for three-slot C//A(implicit) is
              partly about burial, partly about method simplicity,
              partly about ballot simplicity. C//A(explicit) retains 1
              of 3. (Arguably slightly less for the Smith version.)
              Possibly it has its own merits, but they will largely be
              different ones.</div>
            <div><br style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif" clear="none">
              ><br style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif" clear="none">
              <span style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">>A lot
                of voters like relatively expressive ballots. I think
                that is one of the reasons why Approval seems to be a
                lot less popular than IRV.</span><br style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif" clear="none">
            </div>
          </div>
          <div><span style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><br>
            </span></div>
          <div><span style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">I have no
              *inherent* complaints about the ballot format of explicit
              approval plus full ranking.</span></div>
          <div><span style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif"><br>
            </span></div>
          <div><span style="color:rgb(38,40,42);font-family:"Helvetica Neue",Helvetica,Arial,sans-serif">Kevin</span></div>
          <br>
        </div>
        <div><br>
        </div>
        <div><br>
        </div>
        <div><br>
        </div>
      </div>
      <div id="gmail-m_-2507526158578233008ydpb6a32dd9yahoo_quoted_0445501564" class="gmail-m_-2507526158578233008ydpb6a32dd9yahoo_quoted">
        <div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:13px;color:rgb(38,40,42)">
          <div> Le jeudi 6 juin 2019 à 21:03:19 UTC−5, C.Benham
            <a class="gmail-m_-2507526158578233008moz-txt-link-rfc2396E" href="mailto:cbenham@adam.com.au" target="_blank"><cbenham@adam.com.au></a> a écrit : </div>
          <div><br>
          </div>
          <div><br>
          </div>
          <div>
            <div id="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751">
              <div>
                <p>Kevin,<br clear="none">
                </p>
                <blockquote type="cite">Specifically should "positional
                  dominance" have the same meaning whether or not the
                  method has approval in it?</blockquote>
                <br clear="none">
                If the voters all choose to approve all the candidates
                they rank, then yes.  (For a while I was wrongly
                assuming that Forest's suggested<br clear="none">
                default approval was for all ranked-above-bottom
                candidates, but then I noticed that he specified that it
                was only for top voted candidates).<br clear="none">
                <br clear="none">
                One of my tired examples:<br clear="none">
                <br clear="none">
                25: A>B<br clear="none">
                26: B>C<br clear="none">
                23: C>A<br clear="none">
                26: C<br clear="none">
                <br clear="none">
                Assuming all the ranked candidates are approved, C is by
                far the most approved and the most top-voted candidate.
                <br clear="none">
                Normal Winning Votes (and your idea 2 in this example)
                elect B.<br clear="none">
                <br clear="none">
                <blockquote type="cite">I will go easy on these methods
                  over failing MD, because it happens when some of the
                  majority don't approve their common candidate.</blockquote>
                <br clear="none">
                For me this this type of ballot avoids the Minimal
                Defense versus Chicken Dilemma dilemma, rendering those
                criteria inapplicable.<br clear="none">
                <p>48: A<br clear="none">
                  27: B>C<br clear="none">
                  25: C<br clear="none">
                  <br clear="none">
                  The problem has been that we don't know whether the
                  B>C voters are thinking "I am ranking C because
                  above all I don't want that evil A<br clear="none">
                  to win" or  "My C>A preference isn't all that
                  strong, and I think that my favourite could well be
                  the sincere CW, and if  C's supporters rank<br clear="none">
                  B above A then B has a good chance to win. But if they
                  if they create a cycle by truncating I'm not having
                  them steal it".<br clear="none">
                  <br clear="none">
                  With the voters able to express explicit approval we
                  no longer have to guess which it is.<br clear="none">
                  <br clear="none">
                </p>
                <blockquote type="cite"> I don't think it's ideal if
                  burying X under Y (both disapproved) can only backfire
                  when Y is made the CW.
                  <div><br clear="none">
                  </div>
                </blockquote>
                Why is that?  The post-election complaint (by any of the
                voters) would be .. what?<br clear="none">
                <br clear="none">
                If you don't allow voters to rank among their unapproved
                candidates then arguably you are not even trying to
                elect the sincere CW.<br clear="none">
                Instead you are just modifying Approval to make it a lot
                more Condorcet-ish.  <br clear="none">
                <br clear="none">
                A lot of voters like relatively expressive ballots. I
                think that is one of the reasons why Approval seems to
                be a lot less popular than IRV.<br clear="none">
                <br clear="none">
                Chris Benham<br clear="none">
                <br clear="none">
                <div class="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751yqt8593146214" id="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751yqt96283">
                  <div class="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751moz-cite-prefix">On
                    6/06/2019 5:34 pm, Kevin Venzke wrote:<br clear="none">
                  </div>
                  <blockquote type="cite"> </blockquote>
                </div>
              </div>
              <div class="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751yqt8593146214" id="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751yqt32286">
                <div>
                  <div class="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751ydpe4c7db39yahoo-style-wrap" style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:16px">
                    <div>Hi Chris,</div>
                    <div><br clear="none">
                    </div>
                    <div>I've been short on time so I don't actually
                      have much thought on any of the methods, even my
                      own.</div>
                    <div><br clear="none">
                    </div>
                    <div>I suppose Idea 2 is the same as
                      Schwartz-limited MinMax(WV) if nobody submits
                      disapproved rankings. I'm not sure if it makes
                      sense to reject the method over that. Specifically
                      should "positional dominance" have the same
                      meaning whether or not the method has approval in
                      it? As a comparison, I will go easy on these
                      methods over failing MD, because it happens when
                      some of the majority don't approve their common
                      candidate.</div>
                    <div><br clear="none">
                    </div>
                    <div>I would have liked to simplify Idea 2, but
                      actually Forest's eventual proposal wasn't all
                      that simple either. As I wrote, if you add "elect
                      a CW if there is one" it can become much simpler,
                      so that it isn't really distinct from Idea 1. I
                      actually tried pretty hard to present three
                      "Ideas" in that post, but kept having that
                      problem.</div>
                    <div><br clear="none">
                    </div>
                    <div>I posted those ideas because I thought Forest
                      posed an interesting challenge, and I thought I
                      perceived that he was trying to fix a problem with
                      CD. That said, I am not a fan of
                      Smith//Approval(explicit). If all these methods
                      are basically the same then I probably won't end
                      up liking any of them. I don't think it's ideal if
                      burying X under Y (both disapproved) can only
                      backfire when Y is made the CW.</div>
                    <div><br clear="none">
                    </div>
                    <div>Kevin</div>
                    <div><br clear="none">
                    </div>
                    <div><br clear="none">
                    </div>
                  </div>
                  <div class="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751ydp50d5cd69yahoo_quoted" id="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751ydp50d5cd69yahoo_quoted_0454840046">
                    <div style="font-family:"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:13px;color:rgb(38,40,42)">
                      <div> Le mercredi 5 juin 2019 à 21:26:23 UTC−5,
                        C.Benham <a shape="rect" class="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751moz-txt-link-rfc2396E" href="mailto:cbenham@adam.com.au" rel="nofollow" target="_blank"><cbenham@adam.com.au></a>
                        a écrit : </div>
                      <div><br clear="none">
                      </div>
                      <div>Kevin,<br clear="none">
                      </div>
                      <div>
                        <div id="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751ydp50d5cd69yiv9085021920">
                          <div>
                            <p>I didn't comment earlier on your "idea
                              2".  <br clear="none">
                              <br clear="none">
                              If there no "disapproved rankings" (i.e.
                              if the voters all approve the candidates
                              they rank above bottom),<br clear="none">
                              then your suggested method is simply
                              normal  Winning Votes, which I don't like
                              because the winner can<br clear="none">
                              be uncovered and positionally dominant or
                              pairwise-beaten and positionally dominated
                              by a single other<br clear="none">
                              candidate.<br clear="none">
                              <br clear="none">
                              On top of that I don't think it really
                              fills the bill as "simple".  Approval
                              Margins (using Sort or Smith//MinMax<br clear="none">
                              or equivalent or almost equivalent
                              algorithm) would be no more complex and in
                              my opinion would be better.<br clear="none">
                              <br clear="none">
                              I would also prefer the still more simple
                              Smith//Approval.<br clear="none">
                              <br clear="none">
                              What did you think of my suggestion for a
                              way to implement your idea 1?  </p>
                            <div class="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751ydp50d5cd69yiv9085021920yqt3873327189" id="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751ydp50d5cd69yiv9085021920yqtfd25173"><br clear="none">
                              Chris <br clear="none">
                            </div>
                            <div class="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751ydp50d5cd69yiv9085021920yqt3873327189" id="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751ydp50d5cd69yiv9085021920yqtfd71007">
                              <div class="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751ydp50d5cd69yiv9085021920moz-forward-container"><br clear="none">
                                <br clear="none">
                                <br clear="none">
                                <blockquote type="cite">
                                  <p><b>Kevin Venzke</b> <a shape="rect" title="[EM] What are
                                      some simple methods that
                                      accomplish the following
                                      conditions?" href="mailto:election-methods%40lists.electorama.com?Subject=Re%3A%20%5BEM%5D%20What%20are%20some%20simple%20methods%20that%20accomplish%20the%20following%0A%20conditions%3F&In-Reply-To=%3C1931864740.14928463.1559418507456%40mail.yahoo.com%3E" rel="nofollow" target="_blank">stepjak at
                                      yahoo.fr </a><br clear="none">
                                    Sat Jun 1 12:48:27 PDT 2019 </p>
                                  <p><br clear="none">
                                    Hi Forest,<br clear="none">
                                    <br clear="none">
                                    I had two ideas.<br clear="none">
                                    <br clear="none">
                                    Idea 1:<br clear="none">
                                    1. If there is a CW using all
                                    rankings, elect the CW.<br clear="none">
                                    2. Otherwise flatten/discard all
                                    disapproved rankings.<br clear="none">
                                    3. Use any method that would elect C
                                    in scenario 2. (Approval, Bucklin,
                                    MinMax(WV).)<br clear="none">
                                    <br clear="none">
                                    So scenario 1 has no CW. The
                                    disapproved C>A rankings are
                                    dropped. A wins any method.<br clear="none">
                                    In scenario 2 there is no CW but
                                    nothing is dropped, so use a method
                                    that picks C.<br clear="none">
                                    In both versions of scenario 3 there
                                    is a CW, B.<br clear="none">
                                    <br clear="none">
                                    If step 3 is Approval then of course
                                    step 2 is unnecessary.<br clear="none">
                                    <br clear="none">
                                    In place of step 1 you could find
                                    and apply the majority-strength
                                    solid coalitions (using all
                                    rankings)<br clear="none">
                                    to disqualify A, instead of acting
                                    based on B being a CW. I'm not sure
                                    if there's another elegant way<br clear="none">
                                    to identify the majority coalition.<br clear="none">
                                    <br clear="none">
                                    Idea 2:<br clear="none">
                                    1. Using all rankings, find the
                                    strength of everyone's worst WV
                                    defeat. (A CW scores 0.)<br clear="none">
                                    2. Say that candidate X has a
                                    "double beatpath" to Y if X has a
                                    standard beatpath to Y regardless<br clear="none">
                                    of whether the disapproved rankings
                                    are counted. (I don't know if it
                                    needs to be the *same* beatpath,<br clear="none">
                                    but it shouldn't come into play with
                                    these scenarios.)<br clear="none">
                                    3. Disqualify from winning any
                                    candidate who is not in the Schwartz
                                    set calculated using double<br clear="none">
                                    beatpaths. In other words, for every
                                    candidate Y where there exists a
                                    candidate X such that X has a<br clear="none">
                                    double beatpath to Y and Y does not
                                    have a double beatpath to X, then Y
                                    is disqualified.<br clear="none">
                                    4. Elect the remaining candidate
                                    with the mildest WV defeat
                                    calculated earlier.<br clear="none">
                                    <br clear="none">
                                    So in scenario 1, A always has a
                                    beatpath to the other candidates, no
                                    matter whether disapproved<br clear="none">
                                    rankings are counted. The other
                                    candidates only have a beatpath to A
                                    when the C>A win exists. So<br clear="none">
                                    A has a double beatpath to B and C,
                                    and they have no path butt. This
                                    leaves A as the only candidate<br clear="none">
                                    not disqualified.<br clear="none">
                                    <br clear="none">
                                    In scenario 2, the defeat scores
                                    from weakest to strongest are
                                    B>C, A>B, C>A. Every
                                    candidate has<br clear="none">
                                    a beatpath to every other candidate
                                    no matter whether the (nonexistent)
                                    disapproved rankings are<br clear="none">
                                    counted. So no candidate is
                                    disqualified. C has the best defeat
                                    score and wins.<br clear="none">
                                    <br clear="none">
                                    In scenario 3, the first version: B
                                    has no losses. C's loss to B is
                                    weaker than both of A's losses. B<br clear="none">
                                    beats C pairwise no matter what, so
                                    B has a double beatpath to C.
                                    However C has no such beatpath<br clear="none">
                                    to A, nor has A one to B, nor has B
                                    one to A. The resulting Schwartz set
                                    disqualifies only C. (C needs<br clear="none">
                                    to return B's double beatpath but
                                    can't, and neither A nor B has a
                                    double beatpath to the other.)<br clear="none">
                                    Between A and B, B's score (as CW)
                                    is 0, so he wins.  <br clear="none">
                                    <br clear="none">
                                    Scenario 3, second version: B again
                                    has no losses, and also has double
                                    beatpaths to both of A and<br clear="none">
                                    C, neither of whom have double
                                    beatpaths butt. So A and C are
                                    disqualified and B wins.<br clear="none">
                                    <br clear="none">
                                    I must note that this is actually a
                                    Condorcet method, since a CW could
                                    never get disqualified and<br clear="none">
                                    would always have the best worst
                                    defeat. That observation would
                                    simplify the explanation of<br clear="none">
                                    scenario 3.<br clear="none">
                                    <br clear="none">
                                    I needed the defeat strength rule
                                    because I had no way to give the win
                                    to B over A in scenario 3<br clear="none">
                                    version 1. But I guess if it's a
                                    Condorcet rule in any case, we can
                                    just add that as a rule, and greatly<br clear="none">
                                    simplify it to the point where it's
                                    going to look very much like idea 1.
                                    I guess all my ideas lead me to<br clear="none">
                                    the same place with this question.<br clear="none">
                                    <br clear="none">
                                    Oh well, I think the ideas are
                                    interesting enough to post.<br clear="none">
                                    <br clear="none">
                                    Kevin<br clear="none">
                                    <br clear="none">
                                    >Le jeudi 30 mai 2019 à 17:32:42
                                    UTC−5, Forest Simmons <fsimmons
                                    at <a href="http://pcc.edu" target="_blank">pcc.edu</a>> a écrit : <br clear="none">
                                    ><br clear="none">
                                    >In the example profiles below
                                    100 = P+Q+R, and 
                                    50>P>Q>R>0.  One
                                    consequence of these constraints is
                                    that in all three profiles below the
                                    cycle >A>B>C>A will
                                    obtain.<br clear="none">
                                    ><br clear="none">
                                    >I am interested in simple
                                    methods that always ...<br clear="none">
                                    ><br clear="none">
                                    >(1) elect candidate A given the
                                    following profile:<br clear="none">
                                    ><br clear="none">
                                    >P: A<br clear="none">
                                    >Q: B>>C<br clear="none">
                                    >R: C,<br clear="none">
                                    >and <br clear="none">
                                    >(2) elect candidate C given<br clear="none">
                                    >P: A<br clear="none">
                                    >Q: B>C>><br clear="none">
                                    >R: C,<br clear="none">
                                    >and <br clear="none">
                                    >(3) elect candidate B given<br clear="none">
                                    <br clear="none">
                                    ><br clear="none">
                                    >P: A<br clear="none">
                                    >Q: B>>C  (or B>C)<br clear="none">
                                    >R: C>>B. (or C>B)<br clear="none">
                                    ><br clear="none">
                                    >I have two such methods in mind,
                                    and I'll tell you one of them below,
                                    but I don't want to prejudice your
                                    creative efforts with too many
                                    ideas.<br clear="none">
                                    ><br clear="none">
                                    >Here's the rationale for the
                                    requirements:<br clear="none">
                                    ><br clear="none">
                                    >Condition (1) is needed so that
                                    when the sincere preferences are<br clear="none">
                                    <br clear="none">
                                    ><br clear="none">
                                    >P: A<br clear="none">
                                    >Q: B>C<br clear="none">
                                    >R: C>B,<br clear="none">
                                    >the B faction (by merely
                                    disapproving C without truncation)
                                    can defend itself against a
                                    "chicken" attack (truncation of B)
                                    from the C faction.<br clear="none">
                                    ><br clear="none">
                                    >Condition (3) is needed so that
                                    when the C faction realizes that the
                                    game of Chicken is not going to work
                                    for them, the sincere CW is elected.<br clear="none">
                                    ><br clear="none">
                                    >Condition (2) is needed so that
                                    when  sincere preferences are<br clear="none">
                                    <br clear="none">
                                    ><br clear="none">
                                    >P: A>C<br clear="none">
                                    >Q: B>C<br clear="none">
                                    >R: C>A,<br clear="none">
                                    >then the C faction (by
                                    proactively truncating A) can defend
                                    the CW against the A faction's
                                    potential truncation attack.<br clear="none">
                                    ><br clear="none">
                                    >Like I said, I have a couple of
                                    fairly simple methods in mind. The
                                    most obvious one is Smith\\Approval
                                    where the voters have <br clear="none">
                                    >control over their own approval
                                    cutoffs (as opposed to implicit
                                    approval) with default approval as
                                    top rank only. The other <br clear="none">
                                    >method I have in mind is not
                                    quite as <br clear="none">
                                    >simple, but it has the added
                                    advantage of satisfying the FBC,
                                    while almost always electing from
                                    Smith.<br clear="none">
                                    <br clear="none">
                                    <br clear="none">
                                    <br clear="none">
                                    <br clear="none">
                                    <br clear="none">
                                    <br clear="none">
                                  </p>
                                </blockquote>
                                <i><br clear="none">
                                </i> </div>
                              <div id="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751ydp50d5cd69yiv9085021920DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2"><br clear="none">
                                <table style="border-top:1px solid rgb(211,212,222)">
                                  <tbody>
                                    <tr>
                                      <td colspan="1" rowspan="1" style="width:55px;padding-top:13px"><a shape="rect" href="http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient" rel="nofollow" target="_blank"><img src="https://ipmcdn.avast.com/images/icons/icon-envelope-tick-green-avg-v1.png" alt="" style="width: 46px; min-height: 29px;" width="46" height="29"></a></td>
                                      <td colspan="1" rowspan="1" style="width:470px;padding-top:12px;color:rgb(65,66,78);font-size:13px;font-family:Arial,Helvetica,sans-serif;line-height:18px">Virus-free.
                                        <a shape="rect" href="http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient" style="color:rgb(68,83,234)" rel="nofollow" target="_blank">www.avg.com</a>
                                      </td>
                                    </tr>
                                  </tbody>
                                </table>
                                <a shape="rect" href="#m_-2507526158578233008_DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2" rel="nofollow"> </a></div>
                            </div>
                          </div>
                        </div>
                        <div class="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751ydp50d5cd69yqt3873327189" id="gmail-m_-2507526158578233008ydpb6a32dd9yiv8583323751ydp50d5cd69yqtfd87137">----<br clear="none">
                          Election-Methods mailing list - see <a shape="rect" href="https://electorama.com/em" rel="nofollow" target="_blank">https://electorama.com/em
                          </a>for list info<br clear="none">
                        </div>
                      </div>
                    </div>
                  </div>
                </div>
              </div>
            </div>
          </div>
        </div>
      </div>
    </blockquote>
  </div>

</blockquote></div></div>