<div dir="ltr"><div class="gmail_quote"><div dir="ltr">Whoops. I sent the below just to Chris, not to EM. Here it is:<br><div class="gmail_extra"><br><div class="gmail_quote"><span class="">2016-11-11 12:50 GMT-05:00 C.Benham <span dir="ltr"><<a 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_6604000314347844335m_-8048598155404746332gmail-m_-2730114550739300614moz-cite-prefix"><span class="m_6604000314347844335m_-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></span><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.</div><span class=""><div><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"><div class="m_6604000314347844335m_-8048598155404746332gmail-m_-2730114550739300614moz-cite-prefix"><span class="m_6604000314347844335m_-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></span><div>You're suggesting that the sincere preferences are <br></div><div><span class=""><br>35: C >> A=B<br>33: A>B >> C<br></span>32: B>A >> C<br></div><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".</div><div><br></div><div>I believe that in the election you gave, there is no way to tell what the sincere preferences are. 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. 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.</div><span class=""><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_6604000314347844335m_-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></span><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.</div><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.</div><div><br></div><div>In PAR, candidates are compared to absolute thresholds, and then to the other candidates that failed to meet those absolute thresholds. It doesn't have the cleanness of MJ or Score, but it also doesn't have the infinite recursive depth that Condorcet has. At the end of the day, each candidate gets a number, and cycles simply never happen.</div><div><br></div><div>I understand that the neither-fish-nor-fowl nature of PAR makes it worse for criteria compliance (though it's still better than something like IRV); but its performance in realistic scenarios is excellent.</div><div><div class="h5"><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_6604000314347844335m_-8048598155404746332gmail-m_-2730114550739300614moz-cite-prefix">
<br>
Chris Benham<div><div class="m_6604000314347844335m_-8048598155404746332gmail-h5"><br>
<br>
<br>
<br>
On 11/11/2016 10:14 PM, Jameson Quinn wrote:<br>
</div></div></div>
<blockquote type="cite"><div><div class="m_6604000314347844335m_-8048598155404746332gmail-h5">
<div dir="ltr">Here's the <a href="http://wiki.electorama.com/wiki/Prefer_Accept_Reject_voting" target="_blank">definition
of PAR</a> again:
<div><br>
</div>
<div>
<ol style="margin:0.3em 0px 0px 3.2em;padding:0px;color:rgb(37,37,37);font-family:sans-serif;font-size:14px">
<li style="margin-bottom:0.1em"><b>Voters can Prefer,
Accept, or Reject each candidate.</b> Default is
"Reject" for voters who do not explicitly reject any
candidates, and "Accept" otherwise.</li>
<li style="margin-bottom:0.1em"><b>Candidates with a
majority of Reject, or with under 25% Prefer, are
disqualified</b>, unless that would disqualify all
candidates.</li>
<li style="margin-bottom:0.1em">Each voter gives 1 point to
each non-eliminated candidate they prefer; and any voter
who gave no such points (because their preferred
candidates were all eliminated) gives 1 point to each
non-eliminated candidate they accept. <b>The winner is the
candidate with the most points.</b></li>
</ol>
</div>
<div><br>
</div>
<div>Note that since originally proposing this method, the only
substantive change to the process above has been a slight
adjustment in the default rule: the part where default is
"Reject" for voters who do not explicitly reject any
candidates.</div>
<div><br>
</div>
<div>As previously discussed, this method does not meet FBC. For
instance, consider the following "non-disqualifying
center-squeeze" scenario:</div>
<div><br>
</div>
<div>35: AX>B</div>
<div>10: B>A</div>
<div>10: B>AC</div>
<div>5: B>C</div>
<div>40: C>B</div>
<div><br>
</div>
<div>None are eliminated, so C wins with 40 points (against 35,
25, 35 for A, B, and X). However, if 6 of the first group of
voters strategically betrayed their true favorite A, the
situation would be as follows:</div>
<div><br>
</div>
<div>
<div>29: AX>B</div>
<div>6: X>B</div>
<div>10: B>A</div>
<div>10: B>AC</div>
<div>5: B>C</div>
<div>40: C>B</div>
</div>
<div><br>
</div>
<div>Now, A is eliminated with 51% rejection; so B (the CW)
wins.</div>
<div><br>
</div>
<div>Is this violation of FBC a serious defect in the system? I
would argue it isn't. In the above scenario pair, candidates
A, B, and C are the clear frontrunners, with X being merely a
distraction. In that context, the 10 B>AC voters are
clearly not using their full voting power. If they voted their
true preferences, whether those are B>A>C or
B>C>A, then either A or C would have to be eliminated,
and B would win.</div>
<div><br>
</div>
<div>More generally, one can "rescue" FBC-like behavior for this
system by restricting the domain to voting scenarios which
meet the following three restrictions:</div>
<br>
Each candidate either comes from one of no more than 3
"ideological categories", or is "nonviable".<br>
No "nonviable" candidate is preferred by more than 25%.<br>
Each voter rejects at least one of the 3 "ideological
categories" (that is, rejects all candidates in that category).<br>
<br>
If the above restrictions hold, then PAR voting would meet FBC.
It is arguably likely that real-world voting scenarios will meet
the above restrictions, except for a negligible fraction of
"ideologically atypical" voters. For instance, in the first
scenario above, the three categories would be {AX}, {B}, and
{C}, and the B>AC voters, who violate the third restriction,
would probably actually vote either B>A or B>C, which
wouldn't violate that restriction.
<div><br>
<div>Also, note that in any scenario where PAR fails FBC for
some small group, there is a rational strategy for some
superset of that group which does not involve betrayal. For
instance, in first scenario above, if 11 of the AX>B
voters switch to >AXB, then A is eliminated without any
betrayal.</div>
<div><br>
</div>
<div>If you're really concerned about FBC failure, then you
can always use <a href="http://wiki.electorama.com/wiki/FBPPAR" target="_blank">FBPPAR</a>
instead:</div>
<div><br>
<ol style="margin:0.3em 0px 0px 3.2em;padding:0px;color:rgb(37,37,37);font-family:sans-serif;font-size:14px">
<li style="margin-bottom:0.1em">Voters can Prefer, Accept,
or Reject each candidate. Default is "Accept"; except
that for voters who do not explicitly reject any
candidates, default is "Reject". Voters can also mark a
global option that says: "I believe that voters like me
should be the first to compromise."</li>
<li style="margin-bottom:0.1em">Candidates with a majority
of Reject, or with under 25% Prefer, are eliminated,
unless that would eliminate all candidates. If a
candidate would have been eliminatable considering all
the "prefer" votes they got on "compromise" ballots as
"rejects", then they are considered "eager to
compromise"</li>
<li style="margin-bottom:0.1em">The winner is the
non-eliminated candidate with the highest score. Voters
give 1 point to each candidate whom they prefer; and, if
all the candidates they gave points to are "eager to
compromise", they also give 1 point to each candidate
whom they accept.</li>
</ol>
<div><font face="sans-serif" color="#252525"><span style="font-size:14px"><br>
</span></font></div>
</div>
</div>
However, I think that FBPPAR is just a theoretical curiosity.
The "compromise" option adds significant extra complexity, and
would almost never be used. I think that simple PAR is close
enough to FBC compliance to be an acceptable proposal.
<div><br>
</div>
<div>Other than FBC, PAR has some pretty excellent properties.
It elects the CW in most realistic chicken dilemma scenarios,
giving a strong Nash equilibrium with
naive/honest/strategyless ballots, as shown in the Tennessee
example. 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). </div>
<div><br>
PAR voting passes the majority criterion, the mutual majority
criterion, Local independence of irrelevant alternatives
(under the assumption of fixed "honest" ratings for each voter
for each candidate), Independence of clone alternatives,
Monotonicity, polytime, and resolvability.<br>
<br>
There are a few criteria for which it does not pass as such,
but where it passes related but weaker criteria. These
include:</div>
<div>
<p style="margin:0.5em 0px;line-height:inherit"><br>
</p>
<ul>
<li>It fails Independence of irrelevant alternatives, but
passes Local independence of irrelevant alternatives.</li>
<li>It fails the Condorcet criterion, but for any set of
voters such that an honest majority Condorcet winner
exists, there always exists a strong equilibrium set of
strictly semi-honest ballots that elects that CW. (Note
that though this is in some sense a "weaker" criterion, it
is actually not met by most strictly-ranked Condorcet
systems!)</li>
<li>It fails the participation criterion but passes the
semi-honest participation criterion.</li>
<li>It fails O(N) summability, but can get that summability
with two-pass tallying (first determine who's eliminated,
then retally).</li>
<li>It may pass the majority Condorcet loser criterion (?).
If not, it certainly passes some weakened version.</li>
<li>It fails the later-no-help criterion, but passes if
there is at least one candidate above the elimination
thresholds (which is always true, for instance, if there
are some three candidates who get 3 different ratings on
every ballot).<br>
</li>
</ul>
<br>
It fails the consistency criterion, reversibility, the
majority loser criterion, the Strategy-free criterion, and
later-no-harm.<br>
<p style="margin:0.5em 0px;line-height:inherit">All-in-all, I
think it's a great method: reasonably simple and intuitive,
passes FBC on a restricted but essentially-realistic domain,
handles center-squeeze and CD with naive ballots, and
cloneproof.</p>
</div>
</div>
<br>
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