[EM] Favorite Betrayal and Condorcet, and LNHarm

Forest Simmons forest.simmons21 at gmail.com
Sat Apr 23 12:51:56 PDT 2022

```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 at gmail.com> escribió:

> 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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