<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 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 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div bgcolor="#FFFFFF" text="#000000"><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 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 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 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-"><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>
<p></p>
</div>
</blockquote></div><br></div></div>