That makes a lot of sense!

El lun., 18 de abr. de 2022 6:36 p. m., Kevin Venzke stepjak@yahoo.fr
escribió:

Hi Kristofer/Forest/all,

Kristofer wrote:

Not so advanced: I have MinMax(WV) performing about the same as Schulze(WV) and
better than both River and RP(WV). If anything Smith compliance could probably
be guessed to be a liability since no known FBC method does any path-tracing.

I've been thinking about this lately. Experimentally ICA gives results less
resembling MinMax(WV) etc. than MAMPO does, which is odd since ICA is at least
trying to satisfy Condorcet.

It seems that every FBC method is composed of one or more "layers" of logic,
with results of the combined whole determined basically DSC-style.

The layers have some properties:

1. Each one is calculated independently with no awareness of another layer.
2. Each one returns an ordering of the candidates, not necessarily strict. (As
   to use multiple layers there should be some indecision at the top.)
3. Each satisfies FBC, according to a definition that makes sense with
   orderings as opposed to candidate win odds.
4. A layer is used only to break ties on any layers already applied.

So layer examples would include the Bucklin(ERW) mechanism, FBC-compatible ways
of Borda scoring, implicit approval, a majority approval filter, the MMPO score,
Majority Defeat Disqualification, whatever MajBTP is doing, top rankings, and
Improved Condorcet, including the IC-modified MinMax(WV) score (which I call
tMMWV).

(IC usually uses a "tied at the top" rule; I've considered whether "tied and
approved" would better match voters' desires, but this would clearly make IC
less like Condorcet, so I won't consider that anymore.)

These layers seemingly can be applied in any order, and we can make them less
decisive if we want (such as the difference between approval and majority
approval).

So ICA is IC then approval. MDDA is MDD then approval. MAMPO is actually
majority approval, then MMPO, then approval (as a tiebreaker). MAMPOA really.

Since two of the most Condorcet-like rules are probably IC and MMPO, can we just
mix those for an "ICMPO" method? Probably not, because it fails Plurality.
That's an issue with a number of these rules, and a reason why MAMPO uses a
majority approval filter before MMPO.

ICMAMPO (or ICMAMPOA), though, does seem to be an improvement on MAMPO, at least
from the standpoint of resembling MinMax and maximizing Condorcet efficiency.
(And it satisfies Plurality.)

FBC-compatible layers that ensure Plurality seem to be possible.

Consider FPF ("FBC-compatible Plurality filter"): A candidate X is disqualified
(meaning: returned in the bottom rank of the layer's output ranking) if for some
other candidate Y, Y's top rankings minus the X-Y tied-at-the-top count exceeds
X's implicit approval.

That apparently isn't monotone. But this appears to be:

AC ("Approval check"): A candidate X is disqualified if their implicit approval
score is below the max PO against them.

Methods like AC-MPO-A and AC-tMMWV-MPO-A (using hyphens for readability) seem to
be very slightly better than MAMPO, but definitely not as good as ICMAMPO. If
one doesn't want to mess with tied-at-the-top or a majority approval threshold,
though, maybe this "ACMPO" or "ACMPOA" method could be attractive.

An adjacent issue that occurs to me is whether we can use any similar pattern to
make a new Later-no-harm method. There is a definite similarity between weak FBC
and LNHarm as they both can be conceived of as carving out a new ranking for one
of multiple candidates at either the top or bottom ranking.

A big problem is that there aren't as many known options for LNHarm "layers,"
and the ones that do exist are very hard for me to wrap my head around in order
to learn some general patterns. The MMPO and FPTP principles are pretty clear.
Chain Runoff could be seen as a hybrid of those two. The IRV and DSC principles
seem to not offer many variations.

Another problem is how to enforce Plurality. We can't use implicit approval in a
LNHarm method. Only MMPO really runs any risk of violating Plurality, but MMPO
seems like one of the more promising tools here.

And another issue is that for even three candidates it's clear that Plurality,
LNHarm, and minimal defense are incompatible. MD is usually a lower-hanging
fruit, but here it's impossible. Instead we have to ask for something "more like
Condorcet," a "weak Condorcet," but I don't know what that might look like.
"Elect a candidate with full majorities over everyone," i.e. Woodall's
Condorcet(gross), is not doable either.

Kevin

BTP has a symmetric version that might reduce the ties of MajBTP:

The (non majority) symmetric version is ...

On each ballot B give a merit point to each candidate that is not pairwise
beaten by any candidate that outranks it provided that it pairwise beats at
least one candidate that it outranks. [In particular this proviso keeps
candidates truncated by B from getting a point from B]

Also each candidate that is pairwise beaten by every candidate that it
outranks on B gets a demerit from B provided that it is also beaten by at
least one candidate ranked above it on B. [In particular this proviso makes
sure that no candidate top ranked on B gets a demerit from B]

These rules make sure that Condorcet candidates get points from all of the
ballots on which they are ranked above bottom, and that Condorcet losers
get demerits from all ballots on which they are outranked by at least one
candidate.

To convert this merit/demerit system to a three level approval DSV method,
we make the ballot approval coalitions solid by approving every candidate
on B with a merit point from the first rule above, as well as any candidate
ranked strictly above such a candidate.

Similarly, the Disapproval coalitions are made solid by disapproving
candidates with demerits on B as well as candidates strictly out ranked by
such candidates.

The candidates that end up neither approved nor disapproved get both zero
approval and zero disapproval.

One use is Score Sorted Margins.

Another potential use is to mimic DSC for both top anchored and bottom
anchored solid coalitions.

A top anchored coalition would be a solid subset of the approved candidates
that includes a top ranked candidate. Solid means that if Y is ranked
strictly between two members of the coalition, then Y is also a member of
the coalition.

A bottom anchored coalition would be a solid subset of the disapproved
candidates that included at least one candidate that was not ranked above
any candidate.

Exactly how to mimic DSC/DAC is a wide open topic. Any ideas?

-Forest

El mié., 20 de abr. de 2022 12:21 a. m., Kevin Venzke stepjak@yahoo.fr
escribió:

El mié., 20 de abr. de 2022 9:49 p. m., Forest Simmons <
forest.simmons21@gmail.com> escribió:

This conversion is potentially inconsistent because of the possibility of
some pair of candidates X and Y with X outranking Y on B, while X gets a
demerit and Y gets a merit point.

So X gets approved on B if X gets a merit point fro B and no candidate
ranked above X gets a demerit from B. Additionally any candidate that
outranks such an X on B also gets approved on B.

Similarly, Z gets a disapproval on ballot B if Z gets a demerit from B and
no candidate that Z outranks gets a merit point from B. Additionally any
candidate that is outranked by such a Z is also disapproved on B.

This use of merits and demerits to decide approvals and disapprovals on
ballot B makes the respective Approved and Disapproved sets on ballot B
into solid coalitions top and bottom anchored, respectively, as defined
below.

by approving every candidate on B with a merit point from the first rule

Suppose a method has a runoff between the MMPO winner X and the and DMC
winner Y.

If the runoff is by a separate trip to the polls, then the runoff votes
will all be sincere.

Now suppose instead, that the runoff is instant, but by a separate set of
ballots submitted simultaneously with the other ballots (the ones that
determined X and Y) ... and that this second (or third) set was expressly
limited for use in the runoff (for the case of distinct X and Y).

If the rational voters both understood and trusted this process, wouldn't
the runoff set be sincere?

Wouldn't the method as a whole be considered to satisfy the Plurality
Criterion ... even if the MMPO winner X beat Y on the runoff ballots, and Y
had more first place votes than X had above bottom votes on the original
ballots ... the strategic ballots that got X and Y into the finals?

Would the method as a whole be considered to satisfy the FBC?

Would the method as a whole satisfy the Condorcet Criterion even though it
is possible that neither X nor Y was the sincere CW even when there was one?

Would the method as a whole be considered UD compliant?

An if not, should that disqualify the method from adoption?

Is this instant runoff method (unlike IRV) efficiently precinct summable?
(Yes!)

-Forest

El mié., 20 de abr. de 2022 12:21 a. m., Kevin Venzke stepjak@yahoo.fr
escribió:

Hi Forest,

Le samedi 23 avril 2022, 12:37:18 UTC−5, Forest Simmons forest.simmons21@gmail.com a écrit :

Yes, a separate runoff ballot ought to be sincere.

(Moving this question up.) To the extent that the answer is no, we may have trouble answering
the other questions.

But there is at least a UD-compliant method that these rules can resolve: Just say everything is
done using a single ballot.

No, for me UD doesn't have anything to do with the actual merits of the method. It's more to do
with whether we will have a good, consistent way of assessing the merits.

If there were only one ballot then no, clearly not. You could have MMPO winner X pairwise beats
DMC winner Y while a third candidate Z disqualifies X. That could happen if X and Y are from the
same major party. Z voters might be almost half the electorate and are not able to side with
anyone in the runoff because there's only one ballot.

If there are multiple ballots, I'd still say no, because the problem is only "solved" if the Z
voters are required to pick between X/Y on the runoff ballot. I don't think that's a legitimate
way to satisfy Plurality.

Surely not. For one thing you're using DMC, which (as a method itself) fails it, and then you
end in a plain runoff, which I don't think any FBC method can do. Both the MMPO and DMC sides
will be corrupted by the incentive to set up a desirable final pairing.

Well, when we talk about UD criteria we don't have a concept of "sincere CW," only voted CW.

If there's only one ballot then yes, it satisfies Condorcet, because a Condorcet winner will
always be returned from the DMC side and it will always either beat or be the MMPO winner.

If we say that different ballots could show a different CW, or no CW, then I don't think the
question is answerable.

Kevin

Now suppose the method was a sincere instant runoff (SIRO) between X and Y,
where X was the highest score Smith candidate that defeated the lowest
score Smith candidate Y on the original ballots?

Wouldn't it assuage the consciences of the compromising strategic voters to
know that their sincere preferences were used on the final vote?

Could IRV claim as much?

Note that this SIRO method is precinct summable and Condorcet efficient.

To eliminate the possibility of tied scores except in the case of two or
more candidates that get top listing on exactly half of the ballots and
bottom (or no) listing on the other half of the ballots, I suggest using
the following ranked ballot scoring system:

For each candidate k, the score is given by the piece wise definition  ...

If Top(k)>50% , then s(k)=Top(k),

ElseIf Bot(k)>50%, then s(k)=-Bot(k),

Else s(k) equals one half of ...

(Top(k)-Bot(k))/(100%-Top(k)-Bot(k)),

where Top(k) and Bot(k) are the respective fractions of the ballots that
explicitly or implicitly consign k to top or bottom status, respectively.

Truncation is implicit relegation to bottom status.  In general, a
candidate has bottom status on any ballot B that does not explicity rank it
above another candidate.

According to the above piecewise definition s(k) is a number between
negative one and one, inclusive, except for the case where both Bot(k) and
Top(k) equal 50 percent; the formula reflects the inherent indeterminacy by
making the divisor equal to zero. Note that 100%-x-y can be zero  only if
x+y = 100%, and in this context that can only happen in the piecewise case
where neither x nor y is greater than 50 percent, which means both must be
50%.

In the rare case where s(k)=s(j), the tie can be broken by preference to
smaller Bot or larger Top depending on whether the common score is greater
or less than zero.

If s=0 for two or more candidates, then for every tied candidate k,
Bot(k)=Top(k). So I suggest adding a ballot that truncates all of the
candidates. This will get the tied candidates into the s<0 zone, where the
tie breaker is to elect the one with the greater Top count.

Thanks,

-Forest

El sáb., 23 de abr. de 2022 10:36 a. m., Forest Simmons <
forest.simmons21@gmail.com> escribió: