[EM] Automatic LIIA Independent of Locking Order

[Kevin Venzke]

Hi Gustav,

Le mardi 5 mai 2026 à 03:22:38 UTC−5, Gustav Thorzen via Election-Methods <election-methods at lists.electorama.com> a écrit :
> > > 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.

I may or may not be following you. It kind of sounds like you're saying that you're
flipping the direction of the ballot's ratings, in order to get the opposite of
LNHarm/LNHelp. But if you do this, surely the flipped method fails most of the other
criteria you were trying to keep. It won't be monotone if your top slot is where you
put disapproved candidates.

> > 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.

Strange if this is common.

> > > 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 you want AFB then you have to be careful how to count equal ranking. You use what
we used to call "ER-Bucklin (whole)". If a ballot looks like this:
A=B>C>D>E...
Then the "C" preference should be added in only from the third round, not the
second. This is also needed for monotonicity.

Bucklin clearly satisfies LNHelp. I don't understand what you're saying about your
reservations about this, can you clarify? Are you thinking about ratings ballots?

In Bucklin we gradually add in more approvals for each candidate until someone
reaches majority. The additions of the approval are not conditional on anything
besides what round we are on.

I won't comment on graded Bucklin (though I understand why AFB would become clearer
in that context), just the rank version above. Though for LNHelp it doesn't matter
how equal ranking is treated or if it's even allowed. You just need to be able to
truncate lower preferences.

> 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.

At one point on this list there was an attempt to unify rank and cardinal Bucklin
under a single (different!) name. However, Bucklin is usually thought of as a *rank*
ballot method. The rating methods should be called "median rating" or something
else, in my opinion.

> 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).

MinGS is just a Woodall idea from a draft paper. The definition is:
Elect the candidate who maximizes the fewest votes *for* them in a pairwise contest.
MMPO is:
Elect the candidate who minimizes the most votes *against* them in a pairwise contest.

All I'm saying is they superficially look like counterparts.

My copy/paste on improving MinGS was this (slightly abridged):

"MaxMin(Pairwise Support): Woodall defines "MinGS" as the method under which one
elects the candidate X whose fewest votes (pairwise) against some other candidate Y
is the greatest. This satisfies Plurality, Later-no-help, Mono-raise, and
Mono-add-top, but not mutual majority, even in very basic situations. ... Forest
Simmons proposes to allow some candidate X to get a vote against some candidate Y
even when they are both ranked equal, but above bottom. Such a variation is called
"MMPS" and satisfies the weak Favorite Betrayal criterion (assuming equal ranking is
allowed). For that reason I am using this rule and this name for both the basic
method ... . The results of these methods are somewhat unusual."

When I started writing this post I thought that the rule to not grant votes to
candidates ranked equal-bottom was merely intuitive (i.e. the voter wouldn't want to
give the votes to their last-ranked candidates) but actually it seems like it is
needed for LNHelp.

Suppose we grant a vote to each side even when ranked bottom. Consider:
0.447: B=C=D>A
0.347: A>C>B>D
0.131: B>D>A=C -> B>D>A>C
0.073: D>C>A=B

Initially C wins (worst votes-for is .651 against A). But when the third faction
raises A, C loses votes against A, and B wins instead (worst votes-for being .578
against C).

(Forest's MMPS method picks B in both cases.)

So, it is probably necessary that adding a new lower preference not reduce the best
scores of the candidates who remain at the bottom.

Kevin
votingmethods.net