[EM] Approval seeded by MinGS (etrw)
C.Benham
cbenham at adam.com.au
Mon May 25 23:57:52 PDT 2015
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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