[EM] Favorite Betrayal and Condorcet, and LNHarm

[Forest Simmons]

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

> 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 ...
>

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
> 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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