[EM] Automatic LIIA Independent of Locking Order

[Kevin Venzke]

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).

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.)

> 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?

> 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.

Kevin
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