[EM] Approval seeded by MinGS (etrw)
Forest Simmons
fsimmons at pcc.edu
Tue Jun 2 15:40:38 PDT 2015
Now I remember the interesting example that shows that IA-MPO can fail
Plurality when equal ranking at top is allowed:
33 A
16 C=A
02 C
16 C=B
33 B
The IA-MPO score for both A and B is 49-49=0, while the score for C is
34-33=1, so C wins.
This is a failure of Plurality because A (for example) is top ranked on 49
ballots, while C is ranked on only34 ballots.
However, any configuration in issue space that could give rise to this
ballot set would be more faithfully reflected in a ballot like
33 A
16 C>A
02 C
16 C>B
33 B
Why would C voters raise A and B to top if they didn't really like them as
well as the Condorcet Winner C?
It could be that (through typical disinformation) voters thought that C
didn't have a chance compared to the two main party candidates A and B.
They raised their lesser evil compromise candidates to hedge their bets.
It turns out that IA-MPO does satisfy a modified version of Plurality: If
A is ranked top above C on more ballots than C is ranked, then C cannot be
the IA-MPO winner.
In any case where this Plurality' would allow C to win while an ordinary
Plurality requirement would preclude C's right to win, the C voters would
(under perfect information conditions) rightly have an incentive to change
each instance of C=A to C>A .
Proof that IA-MPO satisfies this modified Plurality':
First note that the IA winner cannot have a negative IA-MPO score, because
it is ranked on as many (or more) ballots than any other candidate,
including the one that gives it max opposition.
Next note that if A is ranked top above C on more ballots than C is ranked,
then A's pairwise opposition against C is greater than C's IA score,
therefore C's IA-MPO score is negative, and therefore smaller than the
IA-MPO score of the IA, winner, and therefore not maximal.
In a way IA-MPO automatically compensates for voters' hypercautious raising
of compromises to equal top status. This should attract voters that don't
like Approval because they know that (under Approval) approving their
compromise can take the win away from a Condorcet Winner.
For this reason, I suggest that even on two slot approval style ballots, we
use the Approval-MPO score to determine the winner instead of Approval
alone.
Forest
On Mon, Jun 1, 2015 at 7:10 PM, Forest Simmons <fsimmons at pcc.edu> wrote:
> Chris,
>
> it is interesting to me that IA-MMPO (implicit approval minus max pairwise
> opposition) gives the same results as Approval Seeded by MinGS (etrw) in
> the four examples that you offered:
>
>
>> 46 A
>> 44 B>C
>> 10 C
>>
> The respective IA-MPO scores for A, B, and C are 46-54, 44-46, and
> 54-46, the only positive one.
>
>
>
>> 46 A
>> 44 B>C (sincere might be B or B>A)
>> 05 C>A
>> 05 C>B
>
> The respective IA-MPO scores are 51-54, 49-51, and 54-46, again the only
> positive one.
>
> 46 A>C
>> 10 B>A
>> 10 B>C
>> 34 B=C
>>
> The respective IA-MPO scores are 56-54, 54-46, and 90-56. C wins again.
>
>
>
>> 40 A>C
>> 15 B>A
>> 20 B
>> 15 C>A
>> 10 C
>>
> The respective scores are 70-35, 35-65, and 65-55. This time A wins with
> an IA-MPO score of 35 compared to C's 10.
>
> This IA-MPO method does satisfy the FBC, but is not chicken proof.
> However, small defensive moves can thwart chicken threats.
>
> It seems like I might have suggested IA-MPO before, but we were trying for
> something fancier at the time.
>
> Forest
>
>
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