[EM] Approval seeded by MinGS (etrw)

[Forest Simmons]

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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