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<div class="moz-cite-prefix">On 10/20/2016 6:35 AM, Michael Ossipoff
wrote:<br>
<blockquote type="cite">An example is needed.</blockquote>
<br>
C: Not really. Logically it's impossible to have both any
Push-over incentive and FBC.<br>
<br>
Whenever you're determining the winner by who is pairwise
preferred out of the winner of method A and the winner of method
B,<br>
there will always be situations where you do better by not
equal-top voting your sincere favourite F so as to keep F out of
the final<br>
where F would lose to your worst W.<br>
<br>
Chris Benham<br>
<br>
<br>
</div>
<blockquote
cite="mid:CAOKDY5AJ_V2hZXXsoZZ+o1HXZFfv0YbS_DMQwNkuxxUHVZEW9w@mail.gmail.com"
type="cite">
<p dir="ltr">An example is needed.</p>
<div class="gmail_quote">On Oct 18, 2016 9:37 PM, "C.Benham" <<a
moz-do-not-send="true" 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_3547428967173254496moz-cite-prefix">On
10/19/2016 8:10 AM, Michael Ossipoff wrote:<br>
<br>
<blockquote type="cite">It should be MMPO, rather than
Smith//MMPO, for one finalist-choosing method, and
Approval, Inferred-Approval, or Score for the other,
because MMPO, Approval, & Score meet FBC.</blockquote>
<br>
FBC won't survive any Push-over incentive (as I'm sure
Kevin Venzke would confirm).<br>
<br>
Chris Benham<br>
<br>
</div>
<blockquote type="cite">
<p dir="ltr">It should be MMPO, rather than Smith//MMPO,
for one finalist-choosing method, and Approval,
Inferred-Approval, or Score for the other, because MMPO,
Approval, & Score meet FBC.</p>
<p dir="ltr">If Plain MMPO were replaced by anything else,
Weak CD would be lost.</p>
<p dir="ltr">If, for the other finalist-choosing method,
Approval, Inferred-Approval or Score were replaced by
MAM or Beatpath, then both finalist-choosing methods
would share the same strategic vulnerabilities.</p>
<p dir="ltr">Michael Ossipoff</p>
<div class="gmail_quote">On Oct 18, 2016 1:42 PM, "Forest
Simmons" <<a moz-do-not-send="true"
href="mailto:fsimmons@pcc.edu" target="_blank">fsimmons@pcc.edu</a>>
wrote:<br type="attribution">
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">
<div dir="ltr">
<div>
<div>
<div>
<div>
<div>
<div>
<div>
<div>
<div>I appreciate all of the great
insights from Kristofer, Chris
Benham, and Michael Ossipoff.<br>
<br>
</div>
Especially thanks to Kristofer for
being a good sport about my
forwarding an email with his private
earlier input included. It was too
late when I realized I hadn't
deleted that part.<br>
<br>
</div>
<div>Intuitively, I think Chris is
right that Pushover is the biggest
potential problem. But I don't see
an obvious example.<br>
</div>
<div><br>
</div>
Michael is right that we need to
consider other possibilities for the
two base methods for picking the
finalists.<br>
<br>
</div>
I like MMPO or Smith//MMPO as one of
them since MMPO is one method that
doesn't just reduce to Approval when all
candidates are ranked or rated at the
extremes. I think that the other method
should be one that does reduce to
Approval at the extremes, like River,
MAM/RankedPairs, or
Beatpath/Tideman/Schulz. It could be a
Bucklin variant like MJ, Andy Jennings's
Chiastic Approval, or Jameson's MAS. <br>
<br>
Like Michael I think that Range itself
gives too much incentive to vote at the
extremes on the strategic ballots.
Better to use Approval or an approval
variant so that the strategic ratings
are not unduly compressed for the other
base method. <br>
<br>
</div>
I like Kristofer's insights about the
subtle differences between the proposed
"manual" version in contradistinction to a
DSV version that automates strategy for
the two methods based on the first set of
(perhaps somewhat pre-strategized)
ratings.<br>
<br>
</div>
In particular he pointed out how certain
procedural rules can externalize the
paradoxes of voting. To a certain extent
Approval avoids bad properties by
externalizing them. The cost is the
"burden" of the voter deciding whom to
approve. As Ron LeGrand has so amply
demonstrated, any time you try to automate
approval strategy in a semi-optimal way, you
end up with a non-monotone method. By the
same token IRV can be thought of as a
rudimentary DSV approach to plurality
voting, so it should be no surprise that
IRV/STV is non-monotone.<br>
<br>
</div>
A better example, closer to the Kristofer's,
idea is Asset Voting. It externalizes
everything, which makes it impossible to
contradict any nice ballot based property.
Because of this there is an extreme resulting
strategic burden, but in this case that burden
is placed squarely onto the shoulders of the
candidates, not the voters. Presumably the
candidates are up to that kind of burden since
they are, after all, politicians (in our
contemplated public applications).<br>
<br>
</div>
But this brings up another intriguing idea. Let
one of the two base methods be Asset Voting, so
that the sincere ballots decide between (say)
the MMPO winner and the Asset Voting winner.<br>
<br>
</div>
Thanks Again,<br>
<br>
</div>
Forest<br>
<div class="gmail_extra"><br>
<div class="gmail_quote">On Tue, Oct 18, 2016 at
12:32 PM, Michael Ossipoff <span dir="ltr"><<a
moz-do-not-send="true"
href="mailto:email9648742@gmail.com"
target="_blank">email9648742@gmail.com</a>></span>
wrote:<br>
<blockquote class="gmail_quote" style="margin:0
0 0 .8ex;border-left:1px #ccc
solid;padding-left:1ex">
<p dir="ltr">If course the balloting for
choosing between the 2 finalists need only
be rankings, to show preferences between the
2 finalists, whoever they turn out to be.</p>
<p dir="ltr">Some variations occurred to me.
I'm not saying that any of them would be
better. I just wanted to mention them,
without any implication that they haven't
already occurred to everyone.</p>
<p dir="ltr">Both of the following
possibilities have disadvantages, in
comparison to the initial proposal:</p>
<p dir="ltr">1. What if, for the initial 2
counts, it were a Score-count, in addition
to the MMPO count.</p>
<p dir="ltr">One argument against that
variation is that a voter's inferred
approvals are likely to be more optimal for
hir than the Score ratings on which they're
based.</p>
<p dir="ltr">2. For the 2 initial counts, what
if the MMPO count used a separate ranking,
& the Approval count used a separate set
of Approval-marks?</p>
<p dir="ltr">Would that make it easier for
Chris's pushover strategist?</p>
<p dir="ltr">What other positive &
negative results?</p>
<p dir="ltr">One possible disadvantage that
occurs to me is that overcompromising voters
might approve lower than than necessary, if
the approval were explicitly voted. ...in
comparison to their ratings-which tend to
soften voting errors.</p>
<p dir="ltr">So far, it appears that the
initial proposal is probably the best one.</p>
<span
class="m_3547428967173254496m_2236720442496602401HOEnZb"><font
color="#888888">
<p dir="ltr">Michael Ossipoff</p>
</font></span>
<div
class="m_3547428967173254496m_2236720442496602401HOEnZb">
<div
class="m_3547428967173254496m_2236720442496602401h5">
<div class="gmail_quote">On Oct 17, 2016
1:49 PM, "Forest Simmons" <<a
moz-do-not-send="true"
href="mailto:fsimmons@pcc.edu"
target="_blank">fsimmons@pcc.edu</a>>
wrote:<br type="attribution">
<blockquote class="gmail_quote"
style="margin:0 0 0
.8ex;border-left:1px #ccc
solid;padding-left:1ex">
<div dir="ltr">
<div>
<div>
<div>
<div>Kristofer,<br>
<br>
Perhaps the way out is to
invite two ballots from each
voter. The first set of
ballots is used to narrow
down to two alternatives.
It is expected that these
ballots will be voted with
all possible manipulative
strategy ... chicken
defection, pushover, burial,
etc.<br>
<br>
</div>
The second set is used only to
decide between the two
alternatives served up by the
first set.<br>
<br>
</div>
A voter who doesn't like
strategic burden need not
contribute to the first set, or
could submit the same ballot to
both sets.<br>
<br>
</div>
<div>If both ballots were Olympic
Score style, with scores ranging
from blank (=0) to 10, there
would be enough resolution for
all practical purposes.
Approval voters could simply
specify their approvals with 10
and leave the other candidates'
scores blank.<br>
<br>
</div>
<div>There should be no
consistency requirement between
the two ballots. They should be
put in separate boxes and
counted separately. Only that
policy can guarantee the
sincerity of the ballots in the
second set.<br>
<br>
</div>
<div>In this regard it is
important to realize that
optimal perfect information
approval strategy may require
you to approve out of order,
i.e. approve X and not Y even if
you sincerely rate Y higher than
X. [We're talking about optimal
in the sense of maximizing your
expectation, meaning the
expectation of your sincere
ratings ballot, (your
contribution to the second
set).] <br>
<br>
</div>
<div>Nobody expects sincerity on
the first set of ballots. If
some of them are sincere, no
harm done, as long as the
methods for choosing the two
finalists are reasonable.<br>
<br>
</div>
<div>On the other hand, no
rational voter would vote
insincerely on hir contribution
to the second set. The social
scientist has a near perfect
window into the sincere
preferences of the voters.<br>
<br>
</div>
<div>Suppose the respective
finalists are chosen by IRV and
Implicit Approval, respectively,
applied to the first set of
ballots. People's eyes would be
opened when they saw how often
the Approval Winner was
sincerely preferred over the IRV
winner.<br>
<br>
</div>
<div>Currently my first choice of
methods for choosing the
respective finalists would be
MMPO for one of them and
Approval for the other, with the
approval cutoff at midrange (so
scores of six through ten
represent approval).<br>
<br>
</div>
<div>Consider the strategical
ballot set profile conforming to<br>
<br>
</div>
<div>40 C<br>
</div>
<div>32 A>B<br>
</div>
<div>28 B<br>
<br>
</div>
<div>The MMPO finalist would be A,
and the likely Approval finalist
would be B, unless too many B
ratings were below midrange.<br>
<br>
</div>
<div>If the sincere ballots were<br>
<br>
</div>
<div>40 C<br>
</div>
<div>32 A>B<br>
</div>
<div>28 B>A<br>
<br>
</div>
<div>then the runoff winner
determined by the second set of
ballots would be A, the CWs.
The chicken defection was to no
avail. Note that even though
this violates Plurality on the
first set of ballots, it does
not on the sincere set.<br>
<br>
</div>
<div>On the other hand, if the
sincere set conformed to<br>
<br>
</div>
<div>40 C>B<br>
</div>
<div>32 A>B<br>
</div>
<div>28 B>C<br>
<br>
</div>
<div>then the runoff winner would
be B, the CWs, and the C faction
attempt to win by truncation of
B would have no effect. A
burial of B by the C faction
would be no more rewarding than
their truncation of B.<br>
<br>
</div>
<div>So this idea seems to take
care of the tension between
methods that are immune to
burial and methods that are
immune to chicken defection.<br>
<br>
</div>
<div>Furthermore, the plurality
problem of MMPO evaporates.
Even if all of the voters vote
approval style in either or both
sets of ballots, the Plurality
problem will automatically
evaporate; on approval style
ballots the Approval winner
pairwise beats all other
candidates, including the MMPO
candidate (if different from the
approval winner).<br>
<br>
</div>
<div>What do you think?<br>
<br>
</div>
<div>Forest<br>
</div>
<div><br>
<br>
</div>
<div><br>
</div>
<br>
</div>
<div class="gmail_extra"><br>
<div class="gmail_quote">On Sun,
Oct 16, 2016 at 1:30 AM,
Kristofer Munsterhjelm <span
dir="ltr"><<a
moz-do-not-send="true"
href="mailto:km_elmet@t-online.de"
target="_blank">km_elmet@t-online.de</a>></span>
wrote:<br>
<blockquote class="gmail_quote"
style="margin:0 0 0
.8ex;border-left:1px #ccc
solid;padding-left:1ex"><span>On
10/15/2016 11:56 PM, Forest
Simmons wrote:<br>
> Thanks, Kristofer; it
seems to be a folk theorem
waiting for formalization.<br>
><br>
> That reminds me that
someone once pointed out
that almost all of the<br>
> methods favored by EM
list enthusiasts reduce to
Approval when only top<br>
> and bottom votes are
used, in particular when
Condorcet methods allow<br>
> equal top and multiple
truncation votes they fall
into this category<br>
> because the Approval
Winner is the pairwise
winner for approval style<br>
> ballots.<br>
><br>
> Everything else
(besides approval strategy)
that we do seems to be an<br>
> effort to lift the
strategical burden from the
voter. We would like to<br>
> remove that burden in
all cases, but at least in
the zero info case.<br>
> Yet that simple goal is
somewhat elusive as well.<br>
<br>
</span>Suppose we have a proof
for such a theorem. Then you
could have a<br>
gradient argument going like
this:<br>
<br>
- If you're never harmed by
ranking Approval style, then
you should do so.<br>
- But figuring out the correct
threshold to use is tough
(strategic burden)<br>
- So you may err, which leads
to a problem. And even if you
don't, if<br>
the voters feel they have to
burden their minds, that's a
bad thing.<br>
<br>
Here, traditional game theory
would probably pick some kind
of mixed<br>
strategy, where you
"exaggerate" (Approval-ize)
only to the extent that<br>
you benefit even when taking
your errors into account. But
such an<br>
equilibrium is unrealistic
(we'd have to find out why,
but probably<br>
because it would in the worst
case require everybody to know
about<br>
everybody else's level of
bounded rationality).<br>
<br>
And if the erring causes
sufficiently bad results,
we're left with two<br>
possibilities:<br>
<br>
- Either suppose that the
method is sufficiently robust
that most voters<br>
won't use Approval strategy
(e.g. the pro-MJ argument that
Approval<br>
strategy only is a benefit if
enough people use it, so most
people<br>
won't, so we'll have a
correlated equilibrium of
sorts)<br>
<br>
- That any admissible method
must have a "bump in the road"
on the way<br>
from a honest vote to an
Approval vote, where moving
closer to<br>
Approval-style harms the
voter. Then a game-theoretical
voter only votes<br>
Approval style if he can
coordinate with enough other
voters to pass the<br>
bump, which again is
unrealistic.<br>
<br>
But solution #2 will probably
destroy quite a few nice
properties (like<br>
monotonicity + FBC; if the
proof is by contradiction,
then we'd know<br>
some property combinations
we'd have to violate). So we
can't have it all.<br>
</blockquote>
</div>
<br>
</div>
</div>
</blockquote>
</div>
</div>
</div>
</blockquote>
</div>
<br>
</div>
</div>
</blockquote>
</div>
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