<p dir="ltr">Ok, maybe you're right, & maybe, among Smith methods, Smith//Approval does the best, in terms of choosing from the most top-sets.</p>
<p dir="ltr">In fact maybe, compared to other rank methods in general, it does best by that standard.</p>
<p dir="ltr">I was comparing it to other rank-methods by a standard based on CWs (only indirectly related to top-sets), ignoring the Approval in Smith//Approval.</p>
<p dir="ltr">Thanks for pointing that out. ...pointing out something I'd missed.</p>
<p dir="ltr">Michael Ossipoff<br></p>
<div class="gmail_quote">On Oct 25, 2016 9:40 AM, "C.Benham" <<a href="mailto:cbenham@adam.com.au">cbenham@adam.com.au</a>> wrote:<br type="attribution"><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_-5175053362143103830moz-cite-prefix">On 10/25/2016 4:47 AM, Michael Ossipoff
wrote:<br>
<br>
<blockquote type="cite"> When sincerely-voted Approval chooses
differently from Condorcet, it's choosing socially better.</blockquote>
<blockquote type="cite">
<p dir="ltr">(Jameson wrote):</p>
<p dir="ltr">But even if they do win under honesty, they will
probably lose under "semi-honest offensive strategy" (SHOS) in
which the stronger wing truncates the CW to equal-bottom.</p>
<p dir="ltr">(endquote)</p>
<p dir="ltr">In rank methods, we've been calling that offensive
truncation.</p>
<p dir="ltr">In Approval, I don't regard it as an offensive
strategy at all. In Approval, the middle CWs doesn't need
support from both sides, as s/he does in general
pairwise-count methods.</p>
<p dir="ltr">The larger wing isn't the one that needs the CWs,
if you're after the best particular candidate you can get. But
you're talking about a strategy problem that shouldn't concern
voters in Approval.</p>
</blockquote>
<br>
Mike,<br>
<br>
Given my selection of quotes above, I find your negativity on
Smith//Approval (very similar to Max Covered Approval) a bit
inconsistent.<br>
<br>
A couple of somewhat relevant questions: <br>
<br>
(1)How often is a sincere Condorcet winner who is supported by the
smallest of three factions of voters the Approval winner?<br>
<br>
(2) How often is the Approval winner not in the Smith set?<br>
<br>
And so what is wrong with Condorcet//Approval?<br>
<br>
<blockquote type="cite">
<p dir="ltr">Jameson:-In Condorcet systems, the CW wins under
honesty by definition. But under SHOS, any CD-compliant method
gets the wrong answer.</p>
<p dir="ltr">Mike: No. In wv, a CWs isn't vulnerable to
truncation. S/he still wins. ...the right answer in such a
method.</p>
</blockquote>
<br>
But Winning Votes isn't a "CD-compliant method" .<br>
<br>
Jameson wrote:<br>
<br>
<blockquote type="cite">
<div>Support Accept Reject Abstain voting works as follows:</div>
<div><br>
</div>
<div>
<ul>
<li>Voters can support, accept, reject, or abstain on each
candidate. Default is abstain.<br>
</li>
<li>Call a candidate "acceptable" if they are rejected by
50% or less and supported or accepted by over 25%. If any
candidates are acceptable, eliminate all who aren't.<br>
</li>
<li>Give remaining candidates 2 points for each "support", 1
point for each "accept", and half a point for each
"abstain". Highest points wins.<br>
</li>
</ul>
</div>
<div><br>
</div>
</blockquote>
I still hate default being anything other than bottom/"reject",
and the "25%" figure looks arbitrary.<br>
<br>
With the default rule as it is, it looks like the method fails
Mono-add-Plump.<br>
<br>
Say the winner X has a lower point score than some other candidate
Y that is barely rejected by over 50%. Then adding some ballots
that do nothing <br>
but "support" X could raise the 50% threshold enough so that now Y
is no longer eliminated and wins.<br>
<br>
Chris Benham<br>
<br>
<br>
</div>
<blockquote type="cite">
<p dir="ltr"><br>
On Oct 23, 2016 8:21 AM, "Jameson Quinn" <<a href="mailto:jameson.quinn@gmail.com" target="_blank">jameson.quinn@gmail.com</a>>
wrote:<br>
><br>
> Center squeeze occurs in 3-candidate election when the CW
is the plurality loser.</p>
<p dir="ltr">So it refers to a special case of the problem of the
defensive strategy needed to protect the CWs's win.</p>
<p dir="ltr">Certainly, in IRV, Benham, & Woodall, the main
problem is when a middle Cws has the smallest faction.</p>
<p dir="ltr">And, in other pairwise-count methods, when I test for
truncation or burial vulnerability, I use such an example,
because it seems more favorable to finding vulnerability.</p>
<p dir="ltr">But a CWs can lose without being smallest, and I
don't make a distinction about that except that it's part of the
problem-examples in IRV, Benham, and Woodall.</p>
<p dir="ltr">You wrote:</p>
<p dir="ltr">There are different levels of the problem,
characterized by the level of strategy necessary for the CW to
win:</p>
<p dir="ltr">(endquote)</p>
<p dir="ltr">Sure. I was saying that with wv strategy, truncation
from one side can't take the win from the CWs. ...& that the
CWs's voters can deter burial by mere plumping.</p>
<p dir="ltr">No need for the non-offensive wing to vote any less
than sincerely in methods with wv strategy.</p>
<p dir="ltr">As you know, that isn't so with other Condorcet
versions or general pairwise-count methods.</p>
<p dir="ltr">(You wrote):</p>
<p dir="ltr">><br>
> -In systems like IRV or plurality, in order for the CW to
win even under honesty, the weaker of the two wings must betray
their sincere favorite.</p>
<p dir="ltr">(endquote)</p>
<p dir="ltr">Well, it isn't so much the size of the wing factions.
It's more a matter of which wing candidate is preferred by the
CWs's voters.</p>
<p dir="ltr">That's why I've been saying that IRV is fine for you
if you're majority-favored.</p>
<p dir="ltr">If the CWs's voters transfer the other way, then you
aren't in a mutual-majority, and then, for you, IRV is then no
better than Plurality.</p>
<p dir="ltr">Many of us have been explaining that to Rob Richie
for the past 30 years or so.</p>
<p dir="ltr">> -In systems like approval and score, the CW may
or may not win under "honesty" (however defined). Arguably, if
they do not, they should not.</p>
<p dir="ltr">(endquote)</p>
<p dir="ltr">Correct. When sincerely-voted Approval chooses
differently from Condorcet, it's choosing socially better.</p>
<p dir="ltr">Sure, not choosing the CWs got IRV repealed in
Burlington.</p>
<p dir="ltr">Not electing the CWs results in a majority who'd
prefer a different result.</p>
<p dir="ltr">But I think IRV was repealed for more than that:</p>
<p dir="ltr">Approval let's people protect the CWs, without
favorite-burial, if that were what they want to do. ...and I
suggest that it isn't, because electing from your top-set is
usually more important than electing the best particular
individual candidate you can.</p>
<p dir="ltr">CWs protection is more for rank methods, which are
about choosing _among_ your top-set, to elect the best
particular candidate you can.</p>
<p dir="ltr">(But see my earlier post yesterday, about that.)</p>
<p dir="ltr">If you have a top-set, then, by definition, electing
from it is the important thing.</p>
<p dir="ltr">Approve (only) your top-set.</p>
<p dir="ltr">(More about that in my post yesterday)</p>
<p dir="ltr">But, if it turned out to be really important to avoid
having a majority who'd prefer a different result, then that
could be a reason for voters in Approval to slightly modify
their voting to avoid approving past the expected CWs (CWse).
...though that would lower your Pt.</p>
<p dir="ltr">When approving your top-set, you'd just stop short of
approving past the CWse.</p>
<p dir="ltr">Yesterday, too, I spoke of the possibility of your
wing-faction having a social agreement to that effect.</p>
<p dir="ltr">What you're saying doesn't contract what I've been
saying.</p>
<p dir="ltr">(You wrote):</p>
<p dir="ltr">But even if they do win under honesty, they will
probably lose under "semi-honest offensive strategy" (SHOS) in
which the stronger wing truncates the CW to equal-bottom.</p>
<p dir="ltr">(endquote)</p>
<p dir="ltr">In rank methods, we've been calling that offensive
truncation.</p>
<p dir="ltr">In Approval, I don't regard it as an offensive
strategy at all. In Approval, the middle CWs doesn't need
support from both sides, as s/he does in general pairwise-count
methods.</p>
<p dir="ltr">The larger wing isn't the one that needs the CWs, if
you're after the best particular candidate you can get. But
you're talking about a strategy problem that shouldn't concern
voters in Approval.</p>
<p dir="ltr">(You wrote):</p>
<p dir="ltr">The defensive strategies that work are for the weaker
wing to give the CW near-top score, and/or the CW faction to
give the stronger wing near-bottom score.</p>
<p dir="ltr">(endquote)</p>
<p dir="ltr">Both, if people are trying for the best candidate
they can get. Then obviously the smaller wing should support the
CWs, and the CWs's voters should plump.</p>
<p dir="ltr">But I don't suggest that goal for Approval, for the
reasons stated above, & in earlier posts.</p>
<p dir="ltr">> -In Condorcet systems, the CW wins under honesty
by definition. But under SHOS, any CD-compliant method gets the
wrong answer.</p>
<p dir="ltr">No. In wv, a CWs isn't vulnerable to truncation. S/he
still wins. ...the right answer in such a method.</p>
<p dir="ltr">With burial, a potentially successful buial can
succeed or fail, depending on whether the CWs's voters plump.
Either way, the CWs doesn't win.</p>
<p dir="ltr">(You wrote):</p>
<p dir="ltr">; the strategy is effective if the CW faction plumps,
and backfires if the CW faction cooperates with the weaker wing.
Note that even a strategy backfire here is not in my opinion a
"good" result; because the strategy has some chance of winning,
it will be sometimes attempted. Strategic backfire is a good
thing if it discourages the strategy, but a bad thing if it
actually occurs.</p>
<p dir="ltr">Yes, that's what makes Condorcet at least a bit
questionable. ...especially with the possibility of the
perpetual burial fiasco.</p>
<p dir="ltr">But it can probably be argued that, with rank
methods' goal of getting the best individual candidate you can
get, wv strategy improves on Bucklin, because, even if people
misjudge who the CWs is, and so hir voters don't plump, the mere
threat of plumping could be enough to deter burial, because the
would-be buriers don't have better information than the
defenders have.<br>
</p>
<p dir="ltr">> -In most basic Bucklin systems, the CW faction
must defensively plump to counteract SHOS.</p>
<p dir="ltr">Yes, in Bucklin, if you aren't majority-favored, and
if you rank sincerely, and if the CWs's voters don't plump, then
that can result in the election of someone in your bottom-set.</p>
<p dir="ltr">(You wrote):</p>
<p dir="ltr">> -In a system like SARA, in most cases, even if
the CW does not defensively plump, the weaker wing can give
enough support to the CW to protect them from SHOS, without
having to rate them equal-top. (If the CW is only barely a CW,
the weak wing may have to rate equal-top for a successful
defense in this case. However, I think that very
tightly-balanced situations like this are not a large concern.)</p>
<p dir="ltr">(endquote)</p>
<p dir="ltr">That makes me sit up & take notice, because such
an improvement on Bucklin strategy, while keeping FBC, would be
major, & could outweigh the lack of CD enough to compete
with the best methods.</p>
<p dir="ltr">Michael Ossipoff</p>
<br>
</blockquote>
<br>
</div>
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<br></blockquote></div>