[EM] Favorite Betrayal and Condorcet, and LNHarm

[Forest Simmons]

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 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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