[EM] Approval seeded by MinGS (etrw)
C.Benham
cbenham at adam.com.au
Fri Jun 5 12:36:41 PDT 2015
Forest,
Sorry you're right, I somehow miscounted.
However the method certainly fails "Pairwise Plurality", and I can't see
what the justification (in terms of criterion compliances) is for
the bad failure of Condorcet Loser.
Chris Benham
On 6/6/2015 4:06 AM, Forest Simmons wrote:
> Chris,
>
> in the second example the symmetrically completed ballots are
>
> 27 A
> 11 A>C
> 11 C>A
> 02 C
> 11 C>B
> 11 B>C
> 27 B
>
> Candidate C, the IA-MPO winner, is ranked on 46 ballots. Neither A nor
> B is top ranked on more than 38 ballots. So it seems to me that
> Plurality is not violated.
>
> In summary, IA-MPO does not violate the strong version of Plurality on
> the symmetrically completed ballots, and does not violate the
> (original) weaker version of Plurality (what I called Plurality') when
> applied to the original ballots. I think it is too early to throw it out.
>
> Forest
>
> Forest
>
> On Fri, Jun 5, 2015 at 9:46 AM, C.Benham <cbenham at adam.com.au
> <mailto:cbenham at adam.com.au>> wrote:
>
> Forest,
>
>> "Symmetrical completion normally would replace 16 A=C with 8 A>C
>> and 8 C>A . I understand why you didn't do it that way: you
>> didn't want to go outside the category of two slot ballots. But
>> just because the voters have to vote two slot ballots doesn't
>> mean that we are prohibited from using a counting method that
>> creates auxiliary data structures like matrices or three slot
>> rankings."
>
> Your presumption about my motive is wrong. I did it that way
> because (perhaps because of lack of sleep) that was the only way
> that occurred to me.
> I don't like 2-slot ballots and if they are used I can't take
> seriously the idea that anything other than Approval should be
> used to determine the winner.
>
> Also I wasn't suggesting or contemplating using the symmetric
> completion at the top to modify IA-MPO, rather I was just
> suggesting using it to test
> whether or not the result is in compliance with the Plurality
> criterion.
>
> Unfortunately your second example shows that even the newly
> modified version of IA-MPO (that works on the ballots
> symmetrically completed at
> the top) miserably fails Plurality.
>
> Chris Benham
>
>
>
> On 6/5/2015 8:15 AM, Forest Simmons wrote:
>>
>>
>> On Wed, Jun 3, 2015 at 7:43 PM, C.Benham <cbenham at adam.com.au
>> <mailto:cbenham at adam.com.au>> wrote:
>>
>> ...
>>
>> 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.
>>
>>
>> Symmetrical completion normally would replace 16 A=C with 8 A>C
>> and 8 C>A . I understand why you didn't do it that way: you
>> didn't want to go outside the category of two slot ballots. But
>> just because the voters have to vote two slot ballots doesn't
>> mean that we are prohibited from using a counting method that
>> creates auxiliary data structures like matrices or three slot
>> rankings.
>>
>> If we did this (I think more appropriate) kind of symmetric
>> completion, the working ballots would become
>>
>> 33 A
>> 08 A>C
>> 08 C>A
>> 02 C
>> 08 C>B
>> 08 B>C
>> 33 B
>> The resulting respective IA-MPO scores for A, B, and C would
>> become 49-49, 49-49, and 34-41, so this version of IA-MPO with a
>> front end of symmetric completion at the top would give a tie to
>> A and B, the only candidates with a non-negative score.
>>
>> Let's try it on
>>
>> 27 A
>> 22 A=C
>> 02 C
>> 22 B=C
>> 27 B
>>
>> Candidates A and B are tied for Approval Winner with 49 approvals
>> each against 46 for C, making C the ballot Condorcet Loser.
>>
>> Let's do the natural symmetric completion to see the likely
>> sincere ballots that would be voted if equal ranking at top were
>> not allowed (nor practically required,as in Approval):
>>
>> 27 A
>> 11 A>C
>> 11 C>A
>> 02 C
>> 11 C>B
>> 11 B>C
>> 27 B
>>
>> The respective IA-MPO scores for A, B, and C are 49-49, 49-49,
>> and 46-38, the only positive difference. So C wins. Note that C
>> is still the ballot Condorcet Loser.
>>
>> Whether or not we like this result probably reflects how much we
>> prefer a centrist over an extremist, all else being equal.
>>
>>
>> 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.
>>
>>
>> Nice idea!
>>
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