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<blockquote type="cite">"The 2nd one, as you said, seems
closely-related to FBC. Having just now read of it, I don't now
know how it differs.You say it's somewhat weaker. Then it could
be useful for comparing methods that don't meet the more
demanding FBC."</blockquote>
<br>
Mike,<br>
<br>
I don't see how they are similar.<br>
<br>
49 C<br>
27 A>B<br>
24 B<br>
<br>
<br>
<blockquote type="cite">"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>
</blockquote>
<br>
If Forest's criterion's "sincere ballot sets" allow truncation,
then it seems to me that it isn't compatible with both of
Plurality and Chicken Dilemma. A method meeting Plurality and CD<br>
must elect C in the above "sincere ballot set", but (assuming the
method meets Majority Favourite) it doesn't seem to be in
"strategic equilibrium" (because there is no "deterrent" to the <br>
A>B voters electing B by voting B>A or B).<br>
<br>
Or I could be wrong.<br>
<br>
49 C<br>
27 A>B<br>
24 B=C<br>
<br>
Is this a "strategic equilibrium ballot set" for a method that
meets all of Condorcet, Plurality and CD? It seems odd to see
some virtue in a faction being able to rescue the sincere<br>
method winner... at the expense of its favourite!<br>
<br>
<br>
Chris<br>
<br>
<br>
On 5/16/2014 12:42 AM, Michael Ossipoff wrote:<br>
</div>
<blockquote
cite="mid:CAOKDY5DehsRynwQJ7TfD1GahBb6zt=9KMj1UABbvoEV5=XZitQ@mail.gmail.com"
type="cite">
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<div class="gmail_extra">Interesting two criteria. For the first
one, would the magnitude of a change be measured by the total
number of half-reversals of candidate-order (the matter of
which is voted over which), where a half-reversal is a move
from voting X over Y, to voting nether over the other?</div>
<div class="gmail_extra"> </div>
<div class="gmail_extra">The 2nd one, as you said, seems
closely-related to FBC. Having just now read of it, I don't
now know how it differs.You say it's somewhat weaker. Then it
could be useful for comparing methods that don't meet the more
demanding FBC. </div>
<div class="gmail_extra"> </div>
<div class="gmail_extra">Do you know how MAM, Benham, Woodall,
MMLV(erw)M and your sequence based on covering and approval
do, by those two new criteria?</div>
<div class="gmail_extra"> </div>
<div class="gmail_extra">Michael Ossipoff<br>
<br>
</div>
<div class="gmail_quote">On Wed, May 14, 2014 at 8:11 PM, Forest
Simmons <span dir="ltr"><<a moz-do-not-send="true"
href="mailto:fsimmons@pcc.edu" target="_blank">fsimmons@pcc.edu</a>></span>
wrote:<br>
<blockquote style="margin:0px 0px 0px
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class="gmail_quote">
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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>
<br>
</div>
In other
words, no
matter the
method there
is some
scenario where
a loser can
change to
winner through
unilateral
insincere
voting.<br>
<br>
</div>
For example,
consider the
following two
sincere
scenarios:<br>
<br>
</div>
34 A>B<br>
</div>
31 B>A<br>
</div>
35 C<br>
<br>
</div>
and <br>
<br>
</div>
34 X>Y<br>
</div>
31 Y<br>
</div>
35 Z>Y<br>
<br>
</div>
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>
<br>
</div>
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>
<br>
34 A>B<br>
31 B<br>
35 C<br>
<br>
</div>
and<br>
<br>
34 X>Y<br>
31 Y<br>
35 Z .<br>
<br>
</div>
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>
<br>
</div>
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>
<br>
</div>
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>
</div>
The purpose of this example is to
illustrate why sincere votes cannot always
be a strategic equilibrium position.<br>
<br>
</div>
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>
</div>
Now here's the criterion:<br>
<br>
</div>
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>
</div>
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>
</div>
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>
</div>
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!<span
class="HOEnZb"><font
color="#888888"><br>
<br>
</font></span></div>
<span class="HOEnZb"><font
color="#888888">
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Forest<br>
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<br>
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<br>
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<div class="gmail_extra"><br>
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