[EM] Approval seeded by MinGS (etrw)

[C.Benham]

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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