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.

Kevin

Le mercredi 23 décembre 2020 à 10:02:27 UTC−6, Forest Simmons fsimmons@pcc.edu a écrit :

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!

Forest

P.S. Kristofer, please forward this to the EM list; when I do it, I always get some spam back for some 
mysterious reason.

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@yahoo.fr wrote:

Hi Forest,

Here are some thoughts. Recall your original non-monotone method is being called BTT.

Your approval method, I call BTA. I think this method is monotone only if you use an explicit approval cutoff. With implicit approval, raising a candidate (from the bottom) can change two candidates' approval and create a problem.

BTA is quite similar to MinMax(WV) and MinMax(AWP).

I thought it was odd that if one votes A>B (approving both) and B pairwise defeats A, then A can't get credit for this vote. So I took the liberty of devising another method called BTP (P=preferred). In BTP, instead of checking for losses to all the approved candidates, you check for losses to the candidates strictly preferred to the candidate you're scoring. This revised method turns out to be incredibly similar to MinMax(WV). It's not so obvious to me yet why it should be, but for now I'm amazed.

(Comparing BTP to other WV methods, Schulze/River/RP/MinMax are closer to each other than to BTP. Since BTP seems to satisfy Schwartz and mono-raise I wonder if it must have a clone problem or other weird flaw. By some metrics BTP seems to be less good.)

Your idea to make BTA satisfy FBC unfortunately doesn't seem to quite work. I call that version BTAM (M=majority). It's an indecisive method: Consider a scenario with no majorities at all, with perfect scores awarded to everyone. If you break ties with approval, it is very similar to MDDA. A problem for FBC is that your top-ranked candidates may stand in each other's way of getting credit for the vote. Example:

0.384: B>A>C
0.299: C>B>A
0.176: C=A>B  -----> change to C>A=B
0.138: A>C>B
0.002: B>C>A

There's an A>C>B>A majority cycle. Initially B wins. Then A is lowered on some ballots. This has no effect but to allow C to claim those ballots to their score. Now C wins.

That's it for now.

Kevin