[EM] Approval seeded by MinGS (etrw)

[C.Benham]

Kevin,

On reflection I'm sure you're right about FBC, but I think it would be much
harder to make an example of the method failing mono-raise.

Given the criterion (such as Plurality) compliances of the MiinGS(etrw) 
method
that selects the seed, I would think it  very rare for a candidate that 
can't win being
the seed to be able to win otherwise.

In the classic  49 A, 24 B, 27 C>B  example, A wins if  C is the seed 
but loses if A is
the seed. But of course MinGS(etrw) could never select as the seed such 
a weak
candidate as C .

If I'm wrong I'd be interested in seeing an example.

Chris Benham


On 5/28/2015 9:47 AM, Kevin Venzke wrote:
> Hi Chris,
>
> I like this kind of method where you pick a pivotal candidate and 
> check if the other
> candidates can defeat him, but typically these methods don't satisfy 
> FBC or mono-raise.
>
> Off the top of my head, what if some voters rank 
> Favorite=Compromise>...>Worst,
> resulting in Favorite being the seeded candidate and the winner being 
> Worst. Isn't it
> possible that if the voters lower Favorite in their rankings that 
> Favorite will no longer
> be the seed, and instead someone else will be the seed? If so, I don't 
> think there's
> a way to promise that Compromise would not go on to win the election.
>
> Regarding mono-raise, while it's obvious that getting raised can't 
> stop you from being
> the seed if you were the seed, what if you weren't the seed but you 
> won via approval in
> the second phase? Getting raised/lowered could change who the seed is, 
> and it may
> be that you can only win in phase 2 when certain candidates are the 
> seed. In fact,
> becoming the seed when you hadn't been the seed could even make you lose.
>
> Kevin
>
>
> ------------------------------------------------------------------------
> *De :* C.Benham <cbenham at adam.com.au>
> *À :* "election-methods at lists.electorama.com" 
> <election-methods at lists.electorama.com>
> *Envoyé le :* Mardi 26 mai 2015 1h57
> *Objet :* Approval seeded by MinGS (etrw)
>
> I've been trying to come up with a better method with Bucklin-like
> virtues including Later-no-Help, even though
> there seems to be no call for any such thing and it results in a method
> with a stronger truncation incentive than
> I like.
>
> The closest I came fills the bill with 3 candidates, but can probably
> fail Majority for Solid Coalitions (aka Mutual Majority)
> with more.
>
>   Approval seeded by Minimum Gross Score (equal-top rating whole):
>
> *Voters fill out a multi-slot ratings ballot (I suggest as many slots as
> there are candidates, up to say 4).
> Default rating (truncation) is bottom.
>
> Construct a pairwise matrix in which any ballot that rates/ranks
> candidate X and Y equal-top gives a whole vote to both
> in the X v Y pairwise comparison. Those that rate at least one of them
> in a lower position give a whole vote to one if they
> rate that one above the other, otherwise give no vote to either.
>
> We are only concerned with pairwise scores, not defeats or victories or
> ties. Select the candidate S whose lowest pairwise
> score is higher than any other candidate's lowest pairwise score.
>
> Then interpret all the ballots  that rate S above bottom as approving S
> and all other candidates they rate no lower than S,
> and all the other ballots as approving all the candidates they rate
> above bottom.
>
> Based on that interpretation, elect the most approved candidate.*
>
> I claim that this meets the Favorite Betrayal Criterion, Plurality,
> Irrelevant Ballots,  Later-no-Help  (maybe barring some fantastic
> scenario with many candidates), Condorcet(Gross), Minimal Defense,
> mono-raise, mono-add-top, mono-switch-plump, mono-add-plump,
> mono-append, and  3-candidate Majority for Solid Coalitions.
>
> Because I'm sure that it doesn't properly meet Majority for Solid
> Coalitions, I don't count this as a complete success.
>
> Without the approval stage and the rule about equal-top rating/ranking,
> it is Douglas Woodall's  "MinGS" method  (one of many
> he devised for test purposes).
>
> 46 A
> 44 B>C
> 10 C
>
> C> A 54-46,  A>B 46-44, B>C 44-10.    The method "seeds" A and then
> elects C.
>
> Electing A would be a failure of Minimal Defense and electing B would
> show a failure of  Later-no-Help.  Unfortunately the election of C
> is a failure of Chicken Dilemma (not compatible with the method's
> compliance with Plurality and Minimal Defense).
>
> 46 A
> 44 B>C  (sincere might be B or B>A)
> 05 C>A
> 05 C>B
>
> C> A 54-46,  A>B 51-49, B>C 44-10.    The method "seeds" A and elects C.
>
> Here it resists Burial strategy better than the MinMax (Margins) and
> (Losing Votes) Condorcet methods, which both elect B.
>
> 46 A>C
> 10 B>A
> 10 B>C
> 34 B=C
>
> C>B 80-54,  B>A 54-46.  A>C 56-44.  The method seeds B and elects C.
>
> Not electing the only candidate that is top-rated on more than half the
> ballots may be an odd look by comparison with Bucklin, but I'm not 
> bothered.
> All the candidates are pairwise beaten and the winner is rated above
> bottom on 90% of the ballots.
>
>
> 40 A>C
> 15 B>A
> 20 B
> 15 C>A
> 10 C
>
> A>B 55-35,  A>C 55-25,  C>B 65-35.  The method seeds A and elects A.
>
> There are 100 ballots and A is the Condorcet(Gross) winner (meaning that
> in each and all of A's pairwise contests A is
> strictly preferred to the other candidate by more than half the voters).
> Bucklin elects C.
>
> Chris Benham
>
>
>
>
>
>
>
> ----
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