[EM] Automatic LIIA Independent of Locking Order

[Gustav Thorzen]

On Mon, 4 May 2026 23:27:34 +0000 (UTC)
Kevin Venzke <stepjak at yahoo.fr> wrote:

> Hi Gustav,
> 
> Le lundi 4 mai 2026 à 15:45:29 UTC−5, Gustav Thorzen via Election-Methods <election-methods at lists.electorama.com> a écrit :
> > > It would be interesting to have any additional method at all that satisfies weak FBC
> > > slash AFB and Later-no-harm. I think MMPO is the only known one. Or maybe one of the
> > > Borda interpretations does this too.
> > 
> > There is one, although I don't know if it is on electowiki.
> > Approval satisfied cardinal versions of AFB+Mono+Mutual Majority+LN-Help,
> > but if disapproval ballots are used rather then approval ballots,
> > we can create the following system:
> > Every voter markes any candidates of the choice as disapproved,
> > the sum of disapprovals for each candidate is calcualted,
> > every candidate is assigned a score equal to their sum of disapprovals
> > multiplied by negative one.
> > The candidate with the highest score wins.
> > This satisfies AFB+Mono+Mutual Majority+LN-Harm
> > and although it is functionally identical to approval.
> 
> That seems problematic. If I understand you correctly, you derived one method from
> another, but both yield exactly the same results. But you say they don't have the
> same properties. I'd be inclined to conclude from this that Approval must already
> satisfy the "cardinal" LNHarm (though I don't know the definition of that).

This is because the cardinal generalization (well, all I have seen)
treats lower score as the "later" part,
meaning giving one more candidate a disapproval, a minus 1,
counts as giving a "later" candidate a minus 1,
which can't hurt an "earlier" candidate, but it can help them.
Things like this only happens because LN-Help/Harm is
dependent on how the ballots are counted and inferense rules used,
so the math behind the criteria can change.

For example if a (in my opinion silly) inference rule for counting
ballots was the all unmentioned candidates are to be considered
equally top ranked above all mentioned candidates,
then this would affect LN-Help/Harm compliance,
as extending once listed preferences for one more candidate
in top down order would under a rule like this move them from top to bottom.
The disapproval voting is essentially this,
it changes how the ballots are counted in a way that changes LN-Help/Harm compliance.

Personally I think the criteria should be defined (clarified?)
as rankorder ballots exclusive for a specific inference rule.
The cardinal generalizations are fine,
but I would call for a pair of explicitly rankorder exclusive one
and an explicitly separate cardinal pair of criteria.

As for "they both yield the same result" is not strictly the case.
The strategy for your optimal disapproval vote can be calculated
by a bijective function of your strategically optimal vote in Approval,
but if voters provide the same ballots in Approval and Disapproval,
(I doubt this will happen, but that is what it takes to compre outside strategy,)
then the outcome can be expected to be different.

> Personally, I won't attribute rank ballot criteria to a method unless there's some
> rank ballot equivalent of it. If you apply them to an approval ballot, so that you
> allow the premise that voters only ever have two levels of preference, probably many
> strange things become compatible. (It would be hard to name any incompatibility
> proofs that would still work.)

Yes,like always electing Majority-Beat Condorcet winners of the ballots when one exist.
Conditioning on resticted voter preferences seem to be a problem in general,
but many implicit assumptions are often made.
Probably the most common one is that voters prefer electing any candidate over
a no winner scenario, no matter how terrible they think that candidates are.

> > It appears to me so far that basicly every system satisfying
> > Mono+LN-Help/Harm have a Mono+LN-Harm/Help equivalent,
> 
> That seems unlikely to me because more LNHelp methods than LNHarm methods have been
> discovered. It's more intuitive that a method would "want" to violate LNHarm than
> LNHelp.
> 
> Take Bucklin for example, could there be a LNHarm counterpart to that?

Looking at the definition of bucklin on https://electowiki.org/wiki/Bucklin_voting
the page could be more clear about whether the system described on page
actually satisfies AFB (It claims graded Bucklin usually comply better with it,
and a separate link for graded Bucklin is also privided).
I don't see how we can have LN-Help since you can't even extend your
later preferences without conditioning on preferences and/or breaking
candidate symmetry by resticting the number of participating candidates.
If AFB+Mono+LN-Help+Mutual Majority are held by some version
allowing for unlimited rankorder are allowed,
then I say I do think an LN-Harm counterpart can be found,
though I can't say it won't be like what Disapproval is to Approval
without knowing the definition of the system in question,
since "Bucklin" clearly is not one system,
but a category of (rankorder? cardinal?) ones.

I would be eager to look for a LN-Harm version since it looks like
a decent starting point for the AFB+Mono+Mutual Majority+LN-Help/Harm
I would like to have for baseline comparison,
since I recently found a counterexample to my last idea for
a MMPO ordering of Ranked Pairs variant (AFB+Mono failure as you predicted).

> > so just like MaxMin(Support LogicalOr Equality) turned out to
> > be a LN-Help version of MMPO,
> > there should be a LN-Harm version of MinGS similar to MMPO.
> 
> Considering the definitions of MinGS and MMPO, I would say they are LNHelp/LNHarm
> counterparts already. The issue is just that MinGS needed a tweak to satisfy AFB.

Did I missunderstand the previous thread?
I got the impression MinGS was a AFB+Mono+LN-Help from when you
said it was like MaxMin(Support LogicalOr Equality) but only using a
tied at the top rule to get AFB, but I never found a proper reference for it.
Can you please provide a link for me to read up on MinGS if there is one,
or whichever one uses the tied and the top rule to get AFB?
I suppose I ought to try and create a freestanding proof
of AFB+Mono+LN-Help for MaxMin(Support LogicalOr Equality)
at this point (also taking sugestions for a better name).

Anyways I consider MaxMin(Support LogicalOr Equality) to be the
LN-Help vesion of MMPO (assuming the criteria compliance is correct).

Hopefully clearing things up
Gustav