# [EM] Approval seeded by MinGS (etrw)

Forest Simmons fsimmons at pcc.edu
Thu May 28 15:26:09 PDT 2015

```Chris,

to me this is impressive.  I think the Chicken Dilemma criterion needs to
be weakened somewhat: the only thing that matters to me with regard to
chicken is that a method should always have a way of thwarting a chicken
challenger by a small defensive move.

I am partial to methods like this one that are based on systematic ways of
assigning reasonable approval cutoffs.  Ideally the resulting approval
cutoffs should form a Nash equilibrium in some sense as much as possible.

Forest

On Mon, May 25, 2015 at 11:57 PM, C.Benham <cbenham at adam.com.au> wrote:

> 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-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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