[EM] Approval seeded by MinGS (etrw)
C.Benham
cbenham at adam.com.au
Wed Jun 3 19:43:06 PDT 2015
I was inspired to compare IA-MPO with my 3-slot Strong Minimal Defense,
Top Ratings method. That has a been shown
(by Kevin Venzke) to fail the Plurality criterion. This is his example:
21 A>C
08 B>A
23 B
11 C
B>A 31-21, A>C 29-11, C>B 32-31.
My method took account of 3 types of information: Top Ratings, Approval,
Maximum Approval Opposition. Any candidate
with a MAO score higher their Approval score is disqualified, and the
undisqualified candidate with the highest TR score is
elected.
Top Ratings scores: B31 A21 C11
(Implicit) Approval: B31 A29 C32
MAO scores: B32 A23 C31
(MPO scores: B32 A31 C31)
SMD,TR elects A (after disqualifying B) and IA-MPO elects C (the
only candidate with a positive IA-MPO score).
> "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."
Forest, I'm not sure that this isn't the same as the normal Plurality
criterion. The reference to "first preference" in the Plurality
criterion definition I think refers to exclusive first preference.
(I gather that Woodall's criteria are only about strict rankings from
the top, which may or may not be truncated,) I suppose it could and
should be extended to applying to ballots
that are symmetrically "completed" only at the top. Doing that to your
example gives:
41 A
18 C
41 B
Electing C on these ballots is insane and I don't see how electing C on
the original ballots (where some of the votes are given half to one
candidate and half to another) is
really any more justified.
Yes, this convinces me that the Plurality criterion should definitely be
applied to to the ballots symmetrically completed at the top and that we
can without regret
kiss IA-MPO goodbye.
Another version of the criterion is "Pairwise Plurality" (suggested a
while ago by Kevin or me): If candidate X's lowest pairwise score is
higher than candidate Y's highest
pairwise score, then Y must not be elected".
I like this. Both IA-MPO and SMD,TR fail it, as in the two examples.
In yours the pairwise results are A=B 49-49, A>C 33-18, B>C 33-18.
Getting back to Approval seeded by MinGS(etrw), that is the least
appealing of 3 different method ideas (all attempting to meet the FBC)
I've had recently.
Given its FBC failure, I withdraw my support for it.
I'll post the other two soonish.
Chris Benham
On 6/3/2015 8:10 AM, Forest Simmons wrote:
> 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
> <mailto: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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