[EM] Favorite Betrayal and Condorcet, and LNHarm

[Forest Simmons]

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 at yahoo.fr>
escribió:

> Hi Kristofer/Forest/all,
>
> Kristofer wrote:
> > Kevin's simulations of
> >
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-June/114476.html
> > seem to indicate that Condorcet methods (at least "advanced" ones like
> > Schulze) have a low rate of FBC failure.
>
> 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.
>
> > The "Improved Condorcet"
> > methods would presumably be the flipside of this coin, passing FBC
> > absolutely but having some (low?) rate of Condorcet failure.
>
> 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
>
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