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<div class="moz-cite-prefix">On 11/19/2016 10:26 AM, Forest Simmons
wrote:<br>
<br>
<blockquote type="cite">An interesting fact is that MDDA(pt/2) is
just another formulation of my version of ICA.</blockquote>
<br>
Yes, that had dawned on me. It's also like symmetrically
completing ballots only at the bottom, saying<br>
that above-bottom equal-rankings contribute nothing to the
pairwise scores of the candidates with the<br>
same above-bottom ranking versus each other, and then saying that
unless all candidates have a majority-<br>
strength defeat any that do are disqualified.<br>
<br>
But isn't that a little bit different from the normal version of
the "Tied-at-the-Top Rule", because that treats<br>
equal-top equal ranking differently from all below-top
equal-ranking?<br>
<br>
I am a bit concerned about this (sincere) scenario:<br>
<br>
40: A>B<br>
10: A=B<br>
35: B<br>
15: C<br>
<br>
With all the voters' approval cutoffs left in the default position
B wins but A is the CW. Of course if the 40 A>B<br>
preferrers vote A>>B there is no problem, but might there
be a case for the default placement being just below<br>
the top-voted candidate/s?<br>
<br>
For a method with this cute game-theoretic defence of the
'sincere CW who is the smallest faction's favourite' and also<br>
a way of addressing the Chicken Dilemma scenario , this looks very
good.<br>
<br>
It meets FBC, Mono-add-Plump and Irrelevant Ballots Independence,
Plurality and Mono-raise.<br>
<br>
Chris Benham<br>
<br>
<br>
<br>
On 11/19/2016 10:26 AM, Forest Simmons wrote:<br>
</div>
<blockquote
cite="mid:CAP29onchTsY83oNSRRkr3rxM+h8L84smEYt7OkGvfqLzXfJGdQ@mail.gmail.com"
type="cite">
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<div>Does
optional
approval
cutoff wreck
burial
protection?<br>
<br>
</div>
Suppose we
have a sincere
scenario<br>
<br>
</div>
40 C>B<br>
</div>
35 A>B<br>
</div>
25 B>C<br>
<br>
</div>
and the C
faction
decides to
bury the CWs
B. The B
faction
anticipates
this and
responds by
truncating C.
It is in the
interest of
the A faction
to leave the
default
implicit
approval
cutoff in
place. The C
faction
doesn't want
to give A too
much support
so they use
the explicit
cutoff option:<br>
<br>
</div>
40 C>>A<br>
</div>
35 A>B<br>
</div>
25 B<br>
<br>
</div>
The approval
winner is B
the CWs.<br>
<br>
</div>
<div>If they
left the
implicit
cutoff in
place it would
be worse for
them; their
last choice
would be
elected.<br>
</div>
<div><br>
</div>
So I think
MDDA with
optional
explicit
cutoff is fine
with respect
to truncation
and burial.<br>
<br>
</div>
How about the
CD?<br>
<br>
</div>
In this case
the sincere
profile is<br>
<br>
</div>
40 C<br>
</div>
35 A>B<br>
</div>
25 B>A<br>
<br>
</div>
The B>A faction
threatens to
defect from the AB
coalition.<br>
</div>
The A faction
responds by using
the explicit cutoff:<br>
<br>
</div>
40 C<br>
</div>
35 A>>B<br>
</div>
25 B<br>
<br>
</div>
The approval winner is C, so
the threatened defection
back-fires.<br>
<br>
</div>
It seems to me like that is
plenty of chicken defection
insurance.<br>
<br>
</div>
The obvious equilibrium position
(for the chicken scenario) is<br>
<br>
40 C<br>
35 A>>B<br>
25 B>>A<br>
<br>
</div>
Under MDDA(pt/2) the only
uneliminated candidate is A.<br>
<br>
</div>
But if the B faction defects, all
candidates are eliminated, and the
approval winner C is elected.<br>
<br>
</div>
This is why I like MDDA(pt/2).<br>
<br>
</div>
An interesting fact is that MDDA(pt/2)
is just another formulation of my
version of ICA. They are precisely
equivalent. Here's why:<br>
<br>
</div>
In my version of ICA, X beats Y iff <br>
<br>
</div>
[X>Y] > [Y>X] + [X=Y=T] +
[X=Y=between] , in other words,<br>
<br>
</div>
[X>Y] > [Y:>=X] - [X=Y=Bottom],<br>
<br>
</div>
which in turn equals<br>
<br>
</div>
100% - [X>Y] - [X=Y=Bottom], since 100%=
[X>Y] + [Y>=X].<br>
<br>
</div>
So X beats Y iff<br>
<br>
</div>
[X>Y] > 100% - [X>Y] - [X=Y=Bottom].<br>
<br>
</div>
If you add [X.Y] to both sides and divide by 2, you get<br>
<br>
</div>
[X>Y] +[X=Y=Bottom]/2 > 50%, <br>
<br>
</div>
precisely the "majority-with- half-power-truncation" rule.<br>
<br>
</div>
So (my version of) ICA is precisely equivalent to MDDA(pt/2).<br>
<br>
</div>
I believe it to be completely adequate for defending against
burial, truncation, and Chicken Defection.<br>
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<div class="gmail_extra"><br>
<div class="gmail_quote">Now suppose that p<q<r, and
p+q+r=100%, and we have three factions of respective sizes
p, q, and r:, with r + q > 50%.<br>
<br>
</div>
<div class="gmail_quote">p: C<br>
</div>
<div class="gmail_quote">q: A>>B<br>
</div>
<div class="gmail_quote">r: B>>A<br>
</div>
<br>
</div>
<div class="gmail_extra">Then under the pt/2 rule both C and B
are eliminated, but not A, so A is elected.<br>
<br>
</div>
<div class="gmail_extra">Suppose that the B factions defects.<br>
<br>
</div>
<div class="gmail_extra">Then A is also eliminated, and the
approval winner C is elected.<br>
<br>
</div>
<div class="gmail_extra">Etc.<br>
<br>
</div>
<div class="gmail_extra">So which of the two equivalent
formulations is easier to sell? ICA or MDDA(pt/2) ?<br>
<br>
</div>
<div class="gmail_extra">Forest<br>
</div>
</div>
<p class="" avgcert""="" color="#000000" align="left"><br>
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</blockquote>
<p><br>
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