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<div class="moz-cite-prefix">Forest,<br>
<br>
I consider the problem of the smallest faction winning by
truncating (and perhaps "defecting" from a sincere solid
coalition) to be much much<br>
more serious than the problem of the largest faction winning by
truncation (perhaps insincerely). <br>
<br>
But in this post you seem to want to put them on the same level.
Also you seem to assume that all sincere pairwise preferences are
equally<br>
strong. Probably they aren't and if they aren't then we know the
voters' strongest pairwise preferences are between (on the one
side) candidates <br>
they vote below no other and (on the other) candidates they vote
above no other. But since we are giving the sincere scenarios, we
can include<br>
preference-strength information (">" vs ">>" in giving
voters' rankings).<br>
<br>
<blockquote type="cite">"A method satisfies the Economical Defense
Criterion (EDC) if and only if every potential unilateral
offensive move away from sincere ballots can be deterred by a
smaller unilateral defensive move."</blockquote>
<br>
I'd like the definition (in this context) of "deterred" spelt
out. It is much better if "offensive moves away from sincere
ballots" simply have no chance <br>
of being effective (in as many circumstances as possible) than if
the move is given some (less than 100%) chance of "backfiring"
by electing a candidate<br>
that the offensive strategizers like less than the one who would
have won if they'd voted sincerely.<br>
<br>
<blockquote type="cite">"How should we measure the size of a move?<br>
<br>
It should be by the total number of order changes over all
changed ballots. An order reversal of the type X>Y to Y>X
should count significantly more than a collapse of the type
X>Y to X=Y or the reverse process from X=Y to X>Y."</blockquote>
<br>
You don't fully answer your own (presumably rhetorical) question.
You don't specify how much more "significantly more" is.<br>
<br>
<blockquote type="cite">"Here's another criterion:<br>
<br>
A method satisfies the Semi-Sincere Criterion if and only if
each sincere ballot set can be modified without any order
reversals into a strategic equilibrium ballot set that preserves
the sincere winner."</blockquote>
<br>
Assuming that "strategic equilibrium ballot sets" aren't too
difficult to recognise, this looks interesting and possibly
useful.<br>
<br>
Chris Benham<br>
<br>
<br>
<br>
On 5/15/2014 9:41 AM, Forest Simmons wrote:<br>
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cite="mid:CAP29oncd4g_bfSeu2wHgNGYazvW39k0E+Sb81ChYZuntNG5wUw@mail.gmail.com"
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<div>Every
reasonable
method that
takes ranked
ballots has the
following
problem: not
every sincere
ballot set
represents a
strategic
equilibrium.<br>
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In other words, no
matter the method
there is some
scenario where a
loser can change
to winner through
unilateral
insincere voting.<br>
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For example,
consider the
following two
sincere scenarios:<br>
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34 A>B<br>
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31 B>A<br>
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35 C<br>
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and <br>
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34 X>Y<br>
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31 Y<br>
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35 Z>Y<br>
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All of the methods that we currently
consider reasonable (except perhaps
IRV) , make A win in the ABC
scenario, and make Y win in the XYZ,
scenario.<br>
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Now suppose that the B supporters
unilaterally truncate A in the first
scenario, and the Z supporters
unilaterally truncate Y in the second
scenario. The resulting insincere
ballot sets are<br>
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34 A>B<br>
31 B<br>
35 C<br>
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and<br>
<br>
34 X>Y<br>
31 Y<br>
35 Z .<br>
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By neutrality, if our method must pick
corresponding winners in the two
scenarios, i.e. either A and X, or B and
Y, or C and Z.<br>
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But plurality rules out A and X, while the
chicken dilemma criterion rules out B and
Y. Therefore our method must pick C and Z.<br>
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That's fine for the first scenario; it means
that sincere votes in that scenario could well
be a strategic equilibrium. But making z the
winner in the second scenario means that
sincere ballots were not a strategic
equilibrium position. The unilateral
defection of the Z faction was rewarded by the
election of Z.<br>
<br>
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The purpose of this example is to illustrate why
sincere votes cannot always be a strategic
equilibrium position.<br>
<br>
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Sometimes a faction can take advantage of this
problem by making a move (away from sincere
ballots) that (if not countered) would improve the
outcome from their point of view. Let's call such
a move an offensive move. Any move by another
faction that would make an offensive move
unrewarding can be called a defensive move.<br>
<br>
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Now here's the criterion:<br>
<br>
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A method satisfies the Economical Defense Criterion
(EDC) if and only if every potential unilateral
offensive move away from sincere ballots can be
deterred by a smaller unilateral defensive move.<br>
<br>
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How should we measure the size of a move?<br>
<br>
</div>
It should be by the total number of order changes over all
changed ballots. An order reversal of the type X>Y to
Y>X should count significantly more than a collapse of
the type X>Y to X=Y or the reverse process from X=Y to
X>Y.<br>
<br>
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Here's another criterion:<br>
<br>
</div>
A method satisfies the Semi-Sincere Criterion if and only if
each sincere ballot set can be modified without any order
reversals into a strategic equilibrium ballot set that
preserves the sincere winner.<br>
<br>
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This SSC criterion is similar to the FBC, but easier to
satisfy. I think it is just as good as the FBC for practical
purposes, since rational voters will always aim at strategic
equilibria.<br>
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<div>Gotta Go!<br>
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<div>Forest<br>
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