[EM] Approval seeded by MinGS (etrw)

[Forest Simmons]

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> 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> 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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>
>
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