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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>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>
</blockquote>
<br>
Jameson,<br>
<br>
Maybe not entirely. When you refer to a "small amount" of
"offensive" or "defensive" strategy, presumably you are talking
about some members of a faction<br>
voting one way and the rest another. Is that right?<br>
<br>
I can see the problem in Approval, but under Smith//Approval in
your scenario A is simply the CW and the "ego faction" can't do
anything to get a result they prefer.<br>
<br>
I'm not sure that this problem is entirely avoided in PAR.
Presumably the C faction gives Rejects to both A and B. If six or
more of the ego faction give B a Reject<br>
and six or more of the ??? faction give B an Accept then both A
and C will be eliminated leaving B the winner.<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
.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
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
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>
</div>
</blockquote>
</div>
<br>
</div>
</div>
<p class="" avgcert""="" color="#000000" align="left"><br>
</p>
</blockquote>
<p><br>
</p>
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