[EM] Best Deterministic Ranked Preference Method?
fsimmons at pcc.edu
Wed Dec 23 19:08:19 PST 2020
This Stenholts fix needs a name.... until Kevin gives it a label in his
methods space diagram, I'll just refer to it as "Hog Belly Honey" in honor
of the late immortal R. A. Lafferty ... one of his characters gave that
name to his fateful invention "on account of it's so sweet!"
This method makes use of approval cutoffs, whether explicit, implicit, or
default. I would like to add another choice to the default category ... a
version of Joe Weinstein's approval strategy:
On each ranked ballot B approve alternative X iff the total random ballot
probability of the alternatives ranked strictly above X on ballot B is less
than 50 percent.
So together HBH & Weinstein say ...
... for each ballot B work down the ranks to the lowest level L such that
the random ballot probabilities of higher ranked alternatives sum to no
more than fifty percent.
Each alternative that is not pairwise beaten by any alternative ranked
above level L on ballot B gets a point from B.
Declare as winner the alternative with the greatest accumulation of points
from the various ballots.
It is important to note that this Weinstein approval add-on is monotone
when used as a stand alone DSV approval method for elections based on
rankings of the alternatives. Consequently, unless I am grossly mistaken,
the combined method HBH\\Weinstein must satisfy mono-raise, a true miracle
anong DSV-like methods!
On Wednesday, December 23, 2020, Kevin Venzke <stepjak at yahoo.fr> wrote:
> Forest wanted the below posted to EM.
> But Forest, the original is not BPW. BPW only cares about the first
> preference winner and is only for three candidates. I called your method
> "BTT" in my post.
> I'll take a look at your new idea.
> Le mercredi 23 décembre 2020 à 10:02:27 UTC−6, Forest Simmons <
> fsimmons at pcc.edu> a écrit :
> >Season's Greetings!
> Kristofer & Kevin pointed out the non-monotonicity and identified the
> original version as Stensholts BPW,
> and Kevin compared it wth some related methods with various relative
> advantages ... great work!
> I generalized in a different direction than Kevin, and got lucky ... the
> mono-raise problem fixed!
> Elect the alternative that (for the greatest number of ballots B) is not
> pairwise beaten by any of the
> alternatives that are approved on ballot B.
> This version is closest to BPW when "approved" means "ranked equal top."
> It works equally well wth implicit or explicit approval.
> This method always elects from Landau, i.e. the winner is always uncovered.
> This property can be traded in for the FBC by simply swapping out the
> phrase "not pairwise beaten" for
> the phrase "not majority defeated." (a trick I learned from Kevin many
> years ago)
> If the voters are not allowed explicit approval cutoffs, then they should
> be allowed equal top, or truncation
> at the very least, in order to accommodate a default cutoff. For the FBC
> compliant version equal top must
> be allowed.
> As we have seen from past experience, the explicit approval cutoff
> facilitates different responses to burial
> and chicken offensives.
> We can review that in another message.
> Best Wishes to All!
> P.S. Kristofer, please forward this to the EM list; when I do it, I always
> get some spam back for some
> mysterious reason.
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