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    <div class="moz-cite-prefix">On 11/14/2016 1:48 AM, Jameson Quinn
      wrote:<br>
      <br>
      <blockquote type="cite">
        <div>Suppose you have a scenario like the following:</div>
        <div>19: A>B</div>
        <div>11: ??? A or A>B ??? (more generally: either a bullet
          vote for A, or a vote with A top, B second-to-bottom, and all
          else bottom. In approval, then, this would be A or AB)</div>
        <div>25: (ego faction; true preferences B>A)</div>
        <div>45: C</div>
        <div><br>
        </div>
        <div>You are in the ego faction, and deciding whether to vote
          B>A or just B (or in approval, BA or B). If there is some
          combination of votes that the ego faction can give such that B
          wins in the case where the 11 votes are B>A, but A wins in
          the case where the 11 votes are A, then there is a slippery
          slope; the ego faction can safely and profitably use a small
          amount of offensive strategy, which means that A voters should
          use slightly more defensive strategy, and then there's a cycle
          of escalation until both factions fall off the cliff and end
          up electing C. </div>
        <div><br>
        </div>
        <div>Is that clear now?</div>
      </blockquote>
      <br>
      <br>
      Jameson,<br>
      <br>
      Much more than it was, thanks.  In the example you give, if the
      ??? cohort vote A>> B=C then under PAR if the "ego" faction
      gives Rejects to A then C will win<br>
      and if they give Accepts or Prefers to A then A will win.<br>
      <br>
      But is there a precisely worded criterion about this "slippery
      slope" problem?  Is there anything non-arbitrary about the numbers
      you chose for your example?<br>
      <br>
      In your example there doesn't seem to be any problem if the method
      meets Condorcet  or is IRV.<br>
      <br>
      <blockquote type="cite">MJ passes IIA.</blockquote>
      <br>
      I suppose if a losing "irrelevant" candidate is removed and the
      number of ballots remain unchanged and no voters react by changing
      any of their ratings <br>
      of any of the remaining candidates, then I suppose it might (in a
      useless and abstract way).  <br>
      <br>
      The claim I've seen made that it also meets some version of
      Majority involves a bit of goal-post shifting.<br>
      <br>
      Chris Benham<br>
      <br>
      <br>
      On 11/14/2016 1:48 AM, Jameson Quinn wrote:<br>
    </div>
    <blockquote
cite="mid:CAO82iZzH4S=zPz_cMvLgFrdf5ENjBv=8dHnUCOP6qgw3S2geXQ@mail.gmail.com"
      type="cite">
      <div dir="ltr"><br>
        <div class="gmail_extra"><br>
          <div class="gmail_quote">2016-11-13 6:34 GMT-05:00 C.Benham <span
              dir="ltr"><<a moz-do-not-send="true"
                href="mailto:cbenham@adam.com.au" target="_blank">cbenham@adam.com.au</a>></span>:<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_-1237047743598476909m_4460909035235871631moz-cite-prefix"><span>On
                    11/13/2016 3:35 AM, Jameson Quinn wrote:<br>
                    <br>
                    <blockquote type="cite">
                      <div>What I mean is that if you take a
                        non-election-theorist, present an election
                        scenario to them, explain who won and why, and
                        ask how they would strategize in the place of
                        voter X, they are more likely to suggest
                        counterproductive strategies, and less likely to
                        see any strategies that actually might work, in
                        Condorcet than in Bucklin-like systems.</div>
                      <div><br>
                      </div>
                    </blockquote>
                    <br>
                  </span> The strategy incentives for Condorcet voting
                  methods vary widely.  Some have a random-fill
                  incentive while others have a truncation incentive.
                  Some have<br>
                  a stronger or weaker incentive to equal-top rank than
                  others, and some are more vulnerable to Burial than
                  others.<br>
                  <br>
                  Smith//Approval has a truncation incentive like
                  Bucklin's, only less strong. In addition Bucklin has
                  an equal-top rank/rate incentive.  I don't see the
                  problem.<br>
                  <br>
                  BTW, why does it matter if "non-election-theorists"
                  when asked suggest "counter-productive strategies"? 
                  Shouldn't we be encouraging sincere voting?<br>
                  If they don't want to do that, why can't they just
                  take the strategy advice of their favourites?</div>
              </div>
            </blockquote>
            <div><br>
            </div>
            <div>My concern here is that people will misuse strategy. I
              think that FBC and IIA are good guarantees to be able to
              give, but also that these guarantees are related to O(N)
              summability, which is basically saying "you can think
              about what's going on in an election, it fits inside your
              head." PAR does not have O(N) summability, but it can be
              done in 2 steps, each of them O(N) summable, and each of
              them considered separately meeting FBC and IIA. </div>
            <div><br>
            </div>
            <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_-1237047743598476909m_4460909035235871631moz-cite-prefix"><span><br>
                    <br>
                    <span>35: C >> A=B<br>
                      33: A>B >> C<br>
                      32: B>A >> C<br>
                      <br>
                    </span> </span><span>
                    <blockquote type="cite"><span>In Smith//approval,
                        one vote alone would shift the above honest
                        election; so the fact that it does not in PAR is
                        indeed notable.</span></blockquote>
                    <br>
                  </span><span>I don't see why.  The example I gave just
                    happened to have a close CW.  PAR seems to give an
                    A=B tie unless (as I assume) it breaks tied final<br>
                    scores in favour of the "leader" (A).<br>
                    <br>
                  </span><span>
                    <blockquote type="cite"><span>In particular: in PAR,
                        there is no way for the B voters to strategize
                        such that they win the above election, while
                        still ensuring that C does not win no matter
                        what the A voters do.<br>
                      </span></blockquote>
                    <br>
                  </span><span>Of course, that is why it's called a
                    "chicken dilemma".  In what method <i>can</i> "</span><span>the
                    B voters to strategize such that they win the above
                    election, while still ensuring that C does not win
                    no matter what the A voters do" ??<br>
                  </span></div>
              </div>
            </blockquote>
            <div><br>
            </div>
            <div>I think that you still don't understand what I mean by
              "slippery slope". (Of course, once you do understand it,
              you're still free to disagree that it's important.)</div>
            <div><br>
            </div>
            <div>Suppose you have a scenario like the following:</div>
            <div>19: A>B</div>
            <div>11: ??? A or A>B ??? (more generally: either a
              bullet vote for A, or a vote with A top, B
              second-to-bottom, and all else bottom. In approval, then,
              this would be A or AB)</div>
            <div>25: (ego faction; true preferences B>A)</div>
            <div>45: C</div>
            <div><br>
            </div>
            <div>You are in the ego faction, and deciding whether to
              vote B>A or just B (or in approval, BA or B). If there
              is some combination of votes that the ego faction can give
              such that B wins in the case where the 11 votes are
              B>A, but A wins in the case where the 11 votes are A,
              then there is a slippery slope; the ego faction can safely
              and profitably use a small amount of offensive strategy,
              which means that A voters should use slightly more
              defensive strategy, and then there's a cycle of escalation
              until both factions fall off the cliff and end up electing
              C. </div>
            <div><br>
            </div>
            <div>Is that clear now?</div>
            <div> </div>
            <blockquote class="gmail_quote" style="margin:0 0 0
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                <div
                  class="m_-1237047743598476909m_4460909035235871631moz-cite-prefix"><span>
                    <br>
                  </span><span>
                    <blockquote type="cite">MJ passes IIA. PAR fails it,
                      as you say, but passes LIIA. <br>
                    </blockquote>
                    <br>
                  </span> As do some Condorcet methods. It isn't one of
                  the criteria I care much about.<br>
                  <br>
                  As I understand it, IIA can only be met by methods
                  that fail Majority (like positional methods that
                  pretend that the voters' ratings are on some scale
                  independent of the<br>
                  candidates).   MJ  is a variety of Median Ratings
                  which is normally claimed to meet Majority. <br>
                </div>
              </div>
            </blockquote>
            <div><br>
            </div>
            <div>IIA, when applied to a cardinal or categorical method,
              assumes that when you remove a candidate, you simply
              delete that candidate from all ballots and leave them
              otherwise unchanged.</div>
            <div><br>
            </div>
            <div>The definition of majority used in the proof that IIA
              and Majority are incompatible assumes otherwise. Thus,
              this proof does not apply to non-ranked methods. Or
              perhaps one could say: it shows that a method cannot pass
              IIA and ranked-majority. MJ does not pass ranked-majority,
              but it does pass majority, so that's fine.</div>
            <div><br>
            </div>
            <div>MJ does pass IIA.</div>
            <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_-1237047743598476909m_4460909035235871631moz-cite-prefix">
                  <br>
                  I would be a bit surprised if IIA can be met by a
                  method (such as MJ and Bucklin) by a method that fails
                  Irrelevant Ballots Independence.<br>
                  <br>
                  There is some rubbish about Independence of Irrelevant
                  Alternatives (IIA) on Electowiki.  I'll address that
                  in a later post.<br>
                  <br>
                  Chris Benham
                  <div>
                    <div class="m_-1237047743598476909h5"><br>
                      <br>
                      <br>
                      On 11/13/2016 3:35 AM, Jameson Quinn wrote:<br>
                    </div>
                  </div>
                </div>
                <div>
                  <div class="m_-1237047743598476909h5">
                    <blockquote type="cite">
                      <div dir="ltr"><br>
                        <div class="gmail_extra"><br>
                          <div class="gmail_quote">2016-11-12 10:45
                            GMT-05:00 C.Benham <span dir="ltr"><<a
                                moz-do-not-send="true"
                                href="mailto:cbenham@adam.com.au"
                                target="_blank">cbenham@adam.com.au</a>></span>:<br>
                            <blockquote class="gmail_quote"
                              style="margin:0 0 0 .8ex;border-left:1px
                              #ccc solid;padding-left:1ex">
                              <div bgcolor="#FFFFFF" text="#000000"><span>
                                  <div
class="m_-1237047743598476909m_4460909035235871631m_-680782387900465520moz-cite-prefix">On
                                    11/12/2016 7:53 AM, Jameson Quinn
                                    wrote:<br>
                                  </div>
                                </span><span>
                                  <blockquote type="cite">
                                    <div dir="ltr"><br>
                                      <div class="gmail_extra"><br>
                                        <div class="gmail_quote">2016-11-11
                                          12:50 GMT-05:00 C.Benham <span
                                            dir="ltr"><<a
                                              moz-do-not-send="true"
                                              href="mailto:cbenham@adam.com.au"
                                              target="_blank">cbenham@adam.com.au</a>></span>:<br>
                                          <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">
                                              <div
class="m_-1237047743598476909m_4460909035235871631m_-680782387900465520m_-8048598155404746332gmail-m_-2730114550739300614moz-cite-prefix"><span
class="m_-1237047743598476909m_4460909035235871631m_-680782387900465520m_-8048598155404746332gmail-">On
                                                  11/11/2016 10:14 PM,
                                                  Jameson Quinn wrote:<br>
                                                  <br>
                                                  <blockquote
                                                    type="cite"> I think
                                                    that simple PAR is
                                                    close enough to FBC
                                                    compliance to be an
                                                    acceptable proposal.</blockquote>
                                                  <br>
                                                </span> I'm afraid I
                                                can't see any value in
                                                "close enough" to FBC
                                                compliance.  The point
                                                of FBC is to give an
                                                absolute guarantee to
                                                (possibly uninformed<br>
                                                and not strategically
                                                savvy)  greater-evil
                                                fearing voters.</div>
                                            </div>
                                          </blockquote>
                                          <div><br>
                                          </div>
                                          <div>Yes. The guarantee you
                                            can give is "as long as the
                                            world is somewhere in this
                                            restricted domain — that is,
                                            essentially, as long as
                                            there are no Condorcet
                                            cycles and each voter
                                            naturally rejects at least
                                            one of the 3 frontrunners —
                                            this method meets FBC". This
                                            is much broader than any
                                            guarantee you could give for
                                            a typical non-FBC method.
                                            For instance, with IRV, the
                                            best you could say would be
                                            "as long as your favorite is
                                            eliminated early or wins
                                            overall, you don't have to
                                            betray them", which unlike
                                            PAR's guarantee is not
                                            something which could ever
                                            be generally true about all
                                            real elections for all
                                            factions.<br>
                                            <br>
                                          </div>
                                        </div>
                                      </div>
                                    </div>
                                  </blockquote>
                                </span> C: I have in mind voters who are
                                inclined to Compromise, and so it's <i>
                                  absolute guarantee</i> or it's
                                nothing.   Smith//Approval also has a
                                much lower Compromise incentive<br>
                                than does IRV  (which in turn has a much
                                much lower Compromise incentive then
                                FPP).<span><br>
                                  <br>
                                  <br>
                                  <blockquote type="cite">
                                    <div dir="ltr">
                                      <div class="gmail_extra">
                                        <div class="gmail_quote">
                                          <div><br>
                                          </div>
                                          <blockquote
                                            class="gmail_quote"
                                            style="margin:0px 0px 0px
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rgb(204,204,204);padding-left:1ex">
                                            <div bgcolor="#FFFFFF">
                                              <div
class="m_-1237047743598476909m_4460909035235871631m_-680782387900465520m_-8048598155404746332gmail-m_-2730114550739300614moz-cite-prefix"><span
class="m_-1237047743598476909m_4460909035235871631m_-680782387900465520m_-8048598155404746332gmail-"><br>
                                                  <br>
                                                  <blockquote
                                                    type="cite">It
                                                    elects the "correct"
                                                    winner in a chicken
                                                    dilemma scenario,
                                                    naive/honest/strategyless
                                                    ballots, without a
                                                    "slippery slope"
                                                    (though of course,
                                                    this is no longer a
                                                    strong Nash
                                                    equilibrium). </blockquote>
                                                  <br>
                                                </span> How do you have
                                                a "chicken dilemma
                                                scenario" with
                                                "naive/honest/strategyless
                                                ballots" ?<br>
                                                <br>
                                                35: C >> A=B<br>
                                                33: A>B >> C<br>
                                                32: B >> A=C 
                                                (sincere is B>A
                                                >> C)<br>
                                                <br>
                                                In this CD scenario your
                                                method elects B  in
                                                violation of the CD
                                                criterion.<br>
                                              </div>
                                            </div>
                                          </blockquote>
                                          <div><br>
                                          </div>
                                          <div>You're suggesting that
                                            the sincere preferences are
                                             <br>
                                          </div>
                                          <div><br>
                                            35: C >> A=B<br>
                                            33: A>B >> C<br>
                                            32: B>A >> C<br>
                                            <br>
                                            <br>
                                          </div>
                                        </div>
                                      </div>
                                    </div>
                                  </blockquote>
                                </span> C:  I'm not "suggesting". I'm
                                stating.<span><br>
                                  <blockquote type="cite">
                                    <div dir="ltr">
                                      <div class="gmail_extra">
                                        <div class="gmail_quote">
                                          <div><br>
                                          </div>
                                          <div>If you are 1 of the
                                            B>A>>C voters
                                            considering whether to
                                            strategically vote
                                            B>>A=C, you have no
                                            strong motivation to do so,
                                            because your vote alone is
                                            not enough to shift the
                                            winner to B. This is what I
                                            mean by "no slippery slope".<br>
                                            <br>
                                            <br>
                                          </div>
                                        </div>
                                      </div>
                                    </div>
                                  </blockquote>
                                </span> C: One "vote alone" is very
                                rarely enough to do anything, so I
                                suppose no-one has a "strong motivation"
                                to vote.</div>
                            </blockquote>
                            <div><br>
                            </div>
                            <div>In Smith//approval, one vote alone
                              would shift the above honest election; so
                              the fact that it does not in PAR is indeed
                              notable.</div>
                            <div><br>
                            </div>
                            <div>In particular: in PAR, there is no way
                              for the B voters to strategize such that
                              they win the above election, while still
                              ensuring that C does not win no matter
                              what the A voters do. This "safe"
                              strategizing is grease on the slippery
                              slope.</div>
                            <div><br>
                            </div>
                            <blockquote class="gmail_quote"
                              style="margin:0 0 0 .8ex;border-left:1px
                              #ccc solid;padding-left:1ex">
                              <div bgcolor="#FFFFFF" text="#000000"><span><br>
                                  <blockquote type="cite">
                                    <div dir="ltr">
                                      <div class="gmail_extra">
                                        <div class="gmail_quote">
                                          <div><br>
                                          </div>
                                          <div><br>
                                          </div>
                                          <div>I believe that in the
                                            election you gave, there is
                                            no way to tell what the
                                            sincere preferences are. <br>
                                            <br>
                                            <br>
                                          </div>
                                        </div>
                                      </div>
                                    </div>
                                  </blockquote>
                                  <br>
                                </span> C: From just the information on
                                the ballots, of course not (like any
                                election).<span><br>
                                  <blockquote type="cite">
                                    <div dir="ltr">
                                      <div class="gmail_extra">
                                        <div class="gmail_quote">
                                          <div><br>
                                            Perhaps the B voters are
                                            strategically truncating A;
                                            perhaps the C voters are
                                            strategically truncating B.
                                            So the "correct winner"
                                            could be either A or B, but
                                            is almost certainly not C. <br>
                                          </div>
                                        </div>
                                      </div>
                                    </div>
                                  </blockquote>
                                  <br>
                                </span> C: By "correct winner" I assume
                                you mean the sincere CW. But there is
                                reason to assume there is one. And if
                                the B voters are actively Burying C, it
                                could be C.<span><br>
                                  <br>
                                  <blockquote type="cite">
                                    <div dir="ltr">
                                      <div class="gmail_extra">
                                        <div class="gmail_quote">
                                          <div>The "CD criterion"
                                            requires the system to elect
                                            C, merely to punish the B
                                            voters; I think that's
                                            perverse, because, among
                                            other things, it means that
                                            a system does badly with
                                            center squeeze, allowing the
                                            C faction to strategize and
                                            win.<br>
                                            <br>
                                          </div>
                                        </div>
                                      </div>
                                    </div>
                                  </blockquote>
                                </span> C: No, it merely says "not B". 
                                But CD + Plurality say that it must be
                                C.<span><br>
                                  <blockquote type="cite">
                                    <div dir="ltr">
                                      <div class="gmail_extra">
                                        <div class="gmail_quote">
                                          <div> </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">
                                              <div
class="m_-1237047743598476909m_4460909035235871631m_-680782387900465520m_-8048598155404746332gmail-m_-2730114550739300614moz-cite-prefix">
                                                <br>
                                                Since you are apparently
                                                now content to do
                                                without FBC  compliance 
                                                and you imply that
                                                electing the CW is a
                                                good thing,<br>
                                                why don't you advocate a
                                                method that meets the
                                                Condorcet criterion?<br>
                                                <br>
                                                What is wrong with
                                                Smith//Approval?  Or
                                                Forest's nearly
                                                equivalent Max Covered
                                                Approval? <br>
                                              </div>
                                            </div>
                                          </blockquote>
                                          <div><br>
                                          </div>
                                          <div>Largely, it's because I
                                            think that Condorcet systems
                                            are strategically
                                            counterintuitive, and hard
                                            to present results in. I
                                            think that will lead to more
                                            strategy than a system like
                                            PAR. That's because PAR can
                                            make guarantees that
                                            Condorcet systems can't.<br>
                                            <br>
                                          </div>
                                        </div>
                                      </div>
                                    </div>
                                  </blockquote>
                                </span> C: Such as?  What exactly does
                                "strategically counter-intuitive" mean? 
                                An example?</div>
                            </blockquote>
                            <div><br>
                            </div>
                            <div>What I mean is that if you take a
                              non-election-theorist, present an election
                              scenario to them, explain who won and why,
                              and ask how they would strategize in the
                              place of voter X, they are more likely to
                              suggest counterproductive strategies, and
                              less likely to see any strategies that
                              actually might work, in Condorcet than in
                              Bucklin-like systems.</div>
                            <div><br>
                            </div>
                            <blockquote class="gmail_quote"
                              style="margin:0 0 0 .8ex;border-left:1px
                              #ccc solid;padding-left:1ex">
                              <div bgcolor="#FFFFFF" text="#000000"><span><br>
                                  <blockquote type="cite">
                                    <div dir="ltr">
                                      <div class="gmail_extra">
                                        <div class="gmail_quote">
                                          <div><br>
                                          </div>
                                          <div>In a system like MJ or
                                            Score, you can give a number
                                            to each candidate, based on
                                            their own ratings alone, and
                                            the higher number wins. That
                                            is an easy way to get
                                            monotonicity, FBC, and IIA.</div>
                                          <div><br>
                                          </div>
                                          <div>In Condorcet, no
                                            candidate has any number
                                            except in relation to all
                                            other candidates. That's
                                            good for passing the
                                            Condorcet criterion
                                            (obviously) but it breaks
                                            FBC and IIA.<br>
                                            <br>
                                          </div>
                                        </div>
                                      </div>
                                    </div>
                                  </blockquote>
                                </span> C:  Your method and MJ fail IIA.</div>
                            </blockquote>
                            <div><br>
                            </div>
                            <div>MJ passes IIA. PAR fails it, as you
                              say, but passes LIIA. </div>
                          </div>
                          <br>
                        </div>
                      </div>
                      <p color="#000000" align="left"><br>
                      </p>
                    </blockquote>
                  </div>
                </div>
                <p> </p>
                <blockquote type="cite">
                  <p>Prefer Accept Reject (PAR) voting works as follows:
                  </p>
                  <ol>
                    <li><b>Voters can Prefer, Accept, or Reject each
                        candidate.</b> Blanks count as "Reject" if no
                      rival is explicitly rejected; otherwise, blank is
                      "Accept".</li>
                    <li><b>Candidates with at least 25% Prefer, and no
                        more than 50% reject, are "viable"</b>. The
                      most-preferred viable candidate (if any) is the
                      leader.</li>
                    <li> Each "prefer" is worth 1 point. For viable
                      candidates, each "accept" on a ballot which
                      doesn't prefer the leader is also worth 1 point. <b>Most
                        points wins.</b></li>
                  </ol>
                </blockquote>
                <br>
              </div>
            </blockquote>
          </div>
          <br>
        </div>
      </div>
    </blockquote>
    <br>
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