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<div class="moz-cite-prefix">This "each voter has two ballots" idea
certainly (strategically) allows the voter to be completely
sincere on one of them,<br>
but the cost is that the overall method becomes a festival of
fairly easy and obvious Push-over strategising.<br>
<br>
Of course one way to monitor this would be to look at the
(strategically and so presumably) sincere ballots and discover<br>
who would have won according to various methods on those ballots.<br>
<br>
(But if that was done openly it might introduce some incentives
based on fear of embarrassment and/or fear that the<br>
method will be abolished.)<br>
<br>
Chris Benham<br>
<br>
<br>
On 10/18/2016 11:13 AM, Michael Ossipoff wrote:<br>
</div>
<blockquote
cite="mid:CAOKDY5AsXcpPUoyZiQQE2FYpvm3OFr3URr-6f4ca5KMWnRpj_w@mail.gmail.com"
type="cite">
<p dir="ltr">I think it sounds super. The best yet, with the best
properties of the best methods, avoiding eachother's faults
& vulnerabilities.</p>
<p dir="ltr">More later.</p>
<p dir="ltr">Michael Ossipoff</p>
<div class="gmail_quote">On Oct 17, 2016 1:49 PM, "Forest Simmons"
<<a moz-do-not-send="true" href="mailto:fsimmons@pcc.edu">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>
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</div>
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