On 8/5/23 19:21, Forest Simmons wrote:

The "just barely" nature of implicit approval makes methods that use it
a little unsatisfactory to me. I'd like methods to degrade gracefully in
the sense that if everybody provides a full preference order, then they
don't result in a perfect tie; and they don't give undue power to a
single voter who doesn't provide a full preference order.

I guess that more generally, I consider honest equal-rank to be a voter
saying "My opinions about A and B are so close it's not worth it to me
to find out which it is"; and truncation to be "I know the rest are
worse than those I listed, but I don't know much more about them".

Consider a voter whose honest full preference is A>B>C>D. The resistance
of implicit approval methods, I would imagine (I haven't checked them),
comes from that either the voter can say

A>B

which means "I want to direct some of my voting power to further
separating {A, B} as acceptable candidates, from C and D, as less
acceptable ones"; or that voter can say

A>B>C>D

meaning "I want to direct some of my voting power to be able to say
that, even though I dislike both C and D, I still prefer C to D". The
voter has to economize between the two and can't do both at once, which
limits burial.

But this kind of underlying rationing of voting power introduces the
problem of Approval - not just that there are multiple honest ballots,
but that sincere voters have to deliberate which they should choose,
because choosing the wrong one comes with consequences.

(Strictly speaking, any method with equal-rank and/or truncation has
multiple honest ballots. But, at least to my mind, the stakes are lower
when the method doesn't read a distribution of voting strength into
which honest ballot the voter chooses to use.)

I haven't checked if implicit approval methods are burial resistant
because I've been similarly focused on full preference domains for now,
mainly IC. (I should write a spatial model, but haven't got around to do
it.)

That sounds odd; I would imagine them to have the same "irrelevant
candidate reordering problem" that IRV does. Perhaps I should code them
up and see.

That problem is, e.g. suppose raising A on some ballot changes the
ordering from ... > A > B > C > ... into ... > A > C > B > ..., then
even though A wasn't harmed, this can affect A's opposition and possibly
lead A to lose.

I think we'll need a more fundamental redesign, yes.

Perhaps X can be used for something else? I remember that Smith//IRV
fails mono-add-plump; perhaps method X passes it? Or its "more monotone"
nature can still be usable.

-km

The reason I'm willing to consider Implicit Approval at all is because so
far it's the only simple UD method we know of for generating a monotone,
clone free agenda for agenda based methods.

[The Ranked Pair finish order might work, but surely there's a simpler
solution than that!]

I do not think IA has any special burial resistance ... the burial
resistance is mostly if not entirely from the fact that in the three
candidate Smith case (the most common case by far when there is no ballot
CW) the lowest approval Smith candidate is the one most likely to have been
buried.

because nothing would substantially change strategically if truncations
were not allowed at all, because IA should be defined as total number of
ballots minus the equal bottom count, and (in such a way that) equal bottom
candidates can be either ranked equal bottom or all truncated together
without affecting ting the IA scores.

Candidate X's bottom count is the number of ballots on which X out ranks no
candidate, and her top count is the number of ballots on which she is not
outranked.

X's implicit approval score is best defined as the total number of ballots
minus its bottom count plus epsilon times its top count.

The epsilon term is the built in tie breaker that makes the method highly
decisive in public elections even when complete rankings are required as in
Australia.

Keep in mind that the only purpose of the method, as far as we are
concerned is to get an agenda order that is both monotone and clone free
without going outside of UD.

If grade ballots or other judgment ballots are preferred, that would suit
me fine ... but it would be exterior to UD.

My dream would be to have RCV ballots with optional strong approval and
strong disapproval annotations.

To me it is much easier to make those heart felt decisions than to put in
one all purpose cutoff that is supposed to separate the generally approved
from the unapproved.

The history of mathematics bears out this psychological observation (about
cutoff decisions): what we now call "calculus" was originally "The Calculus
of Infinitesimals" which involved distinguishing from ordinary numbers
those very close to zero and those very far from zero.

That calculus was the basis of all of the progress in mathematics from the
time of Newton, Leibniz,Euler; the Bernoullis, Laplace, Gauss, etc ...
until the time of Cauchy, Weirstrauss and eventually Cantor, when the
logical foundations of "infinities" of various kinds came under close
scrutiny ... resulting in a reformulation of analysis in terms of limits
and other set theoretic constructs. Infinitesimals were put on hold until
set theoreticians and other mathematical logicians (especially Abraham
Robinson in the 1960's) finally advanced enough to put infinitesimal
calculus on a rigorous footing ... a system as consistent as modern set
theory itself ... which Euler and company had long ago navigated flawlessly
with their unerring intuition.

This ability to have the top approval and bottom disapproval while still
distinguishing the rankswould be a great improvement over current implicit
approval that requires collapsing to equal top or equal bottom for the
ability express respective approval or disapproval .... the agonizing
decision of whether sacrificing ordinal information for approval/
disapproval information is worth it.

It seems to me that the decision of where to put these cutoffs would be no
harder than the current corresponding decisions about equal rankings and
truncations.

Am I the only one that feels that way?

fws

On Sat, Aug 5, 2023, 1:38 PM Kristofer Munsterhjelm km_elmet@t-online.de
wrote:

Kevin,

Copeland is the simplest monotone Landau method.

Do we have a clone free version of Copeland that is for sure monotone?

Here's another one that (unlike Copeland) is definitely clone free as well
as monotonic (if my proof holds warer):

Initialize a candidate variable X as the highest approval candidate. Then
while X is covered, update X to be the most approved candidate that covers
the recent value of X that we are updating.

If I am not mistaken Agenda Based Chain Climbing is monotonic in the sense
that if the winner moves "up" the agenda without disturbing the relative
agenda order of the other candidates ... then the winner will still win.

If the agenda is based on approval scores, it seems to me that this
requirement should be met.

Am I wrong?

fws

On Sat, Aug 5, 2023, 11:11 AM Kevin Venzke stepjak@yahoo.fr wrote:

On 8/6/23 03:11, Forest Simmons wrote:

Sorry about that, I must've misunderstood. My impression of IA was that
you'd basically count candidates that were explicitly ranked, so e.g. for

12: A>B>C
11: B>C>A
10: C>A>B

every candidate would have an IA count of 33, but if you did

12: A
11: B>C>A
10: C>A>B

then A would have an IA of 33, and the other two would have 21.

That's good: these methods should be testable without having to model
where voters would put their approval cutoffs. That should give more
evidence to whether methods using these orders are cloneproof, monotone,
and burial resistant.[1]

However, there's a slight complication. As I first noticed back when JGA
was doing his simulations, impartial culture is overly nice to
Antiplurality-type methods; IC simulations will say they're extremely
good at resisting strategy. I never found out why - I think it's an
artifact of the distribution, but I don't know what. But what it means
is that I should probably create a spatial model before I start testing
methods that use bottom counts :-)

Hopefully I'll get to it, eventually, but I'm also probably going to
think about whether there are ways to salvage method X, first.

I think it depends on the person. Myself, I find ranking easier than
rating, because I'm always trying (and failing) to find some natural
calibrated scale when rating, but ranking is easy: just "do I prefer a
world with X to one with Y?". And then if it's below my JND, equal-rank.

I seem to recall that you said you get a feeling for a natural scale
after rating for long enough, in reference to grading papers. Perhaps
that is true; perhaps most people find a natural rating scale and I'm
the odd one out.

Some cases are clear cut: if I were faced with an election with a bunch
of contemporary candidates, and then Stalin and Hitler, I know where I
would put my cutoff. But generalizing it in a more nuanced multiparty
environment is hard. For instance, the Norwegian parties currently
represented in Parliament are, from left to right:

Red Party
Socialist Left
Green Party
Labor
Patient Focus
Center Party
Christian Democrats
Liberal Party
Conservative Party
Progress Party

These are all democratic parties in the sense that they support the
continuation of parliamentary democracy. There are no Orban-style
autocrats, and thus nobody to really "intensely disapprove of" as such.
Sure, there are some whose policies I'd rather not have be enacted, but
not on that level.

Perhaps I would disapprove of the other end of the scale from where my
preferences lie, but if you were to add a (hypothetical) Stalinist party
and a Norwegian NSDAP (to mirror the Stalin and Hitler example above),
then my disapproval thresholds would probably change so that I would
disapprove of those two and approve of all the democratic parties.

And what that suggests to me is that when multiparty rule happens and
there's more of a gradual scale, then it gets harder to place dividing
lines, and that it's difficult to create an approval expression that
doesn't inherently violate the spirit of IIA due to calibration issues.

But it might just be me!

-km

[1] I'm not sure how it could be cloneproof though? Neither top nor
bottom preferences are cloneproof.

Given that you would not have a problem with graded ballots, but the problem is that it would be outside Universal/Unrestricted Domain, this raises the question of what about UD makes it so important to you in the first place?
I think I've said before on here that I think score/graded ballots should work very well with a Condorcet method, as long as you have enough grades so that voters can make a distinction between enough candidates that they are realistically likely to want to. I think it would be easier for the voter, since they can grade the candidates in any order they want without having to do so in order (and possibly miss one out), and it allows for ties in the middle of the ranking rather than just by truncating at the end. Voters wouldn't have to worry about the "meaning" of grades because they would only be used to generate a preference order, with ties allowed. It should also mitigate against the problem of burial. If the grade for a candidate is left blank, it would be taken to mean the bottom grade, and voters are likely to bottom grade or leave blank all candidates they don't really like, rather than having to individually rank them. A ranked ballot would likely encourage voters to bury their disliked frontrunner below other candidates they dislike or don't care about. With grades a voter could still bury this candidate if they wanted, but they wouldn't be "nudged" into it by the ballot type, which I think they would be more so with a ranked ballot.
Toby
On Sunday, 6 August 2023 at 02:12:26 BST, Forest Simmons forest.simmons21@gmail.com wrote:

Hi Forest,

Le samedi 5 août 2023 à 20:32:28 UTC−5, Forest Simmons forest.simmons21@gmail.com a écrit :

This I don't know, but such a simple method as Copeland satisfying Landau is quite
interesting, and I suppose we have to somehow proceed from Copeland in searching for
additional methods.

In a UD context relying on implicit approval, this doesn't work wrt monotonicity, because
a raised winner can obtain approval at the expense of another candidate.

For example say A is the approval winner and B covers A and wins. Then some ballots are
changed from ...A>B to ...B>A (these are the bottom of the ranking) so that A is losing
approval to B, and now some C is the approval winner, and B does not cover C.

With implicit approval I guess the issue appears.

Kevin
votingmethods.net

A note concerning monotonicity testing - even when there is no possible
pushover strategy for a voter/group of voters, it doesn't necessarily mean
that a given method is monotone.
In these examples, changing ABC to BAC makes C the winner, so the change
doesn't make sense from the voter's point of view and will go under the
radar of any strategy detector, I guess.

Another thing is that there are some election scenarios which an
impartial/spatial simulator might never notice. For the purposes of
strategy/critetia testing it might be good to include, for example, a
ballot generator that will produce random-size groups of voters, rather
that drawing voters one-by-one like a standard impartial generator does.

sob., 5 sie 2023, 13:52 użytkownik Kristofer Munsterhjelm <
km_elmet@t-online.de> napisał:

On 8/7/23 12:13, Filip Ejlak wrote:

You're right; I was using the Other strategy count as a proxy for what I
really wanted, because I hadn't implemented an actual monotonicity check
yet. It seemed to work for IRV (clearly nonmonotone), Adjusted Condorect
Plurality, and the other nonmonotone methods I tested it with.

I was actually thinking about this earlier today, by analogy to the
independence of clones criterion. If we have a B>A ballot, change it to
A>B, and the winner goes from B to A, that's pushover (analogous to the
types of cloning that can be exploited by running more or fewer
candidates). But if the winner changes from A to C, then it's like
crowding: still a failure but harder to strategically exploit.

James Green-Armytage did more general nomination incentive simulations
to determine the incentive to entry and exit. The reasoning above
suggests that there's a third way that nomination can affect the
outcome: unpredictably but not obviously to anyone's advantage. If his
"incentive to exit" is a more robust vote-splitting metric, and his
"incentive to entry" is a more robust teaming metric, then there may be
an "instability due to nomination" metric that corresponds to crowding.

If a method passes scale invariance, impartial culture should have a
chance of happening upon correlated electorate failures. That is to say,
if you have defined voting groups, something like

97: A>B>C>D
103: B>A>C>D

then that's not too far off
1: A>B>C>D
1: B>A>C>D

if the voting method only cares about the relative proportion of voters.
But more generally, it's a good point; models that just draw voters from
some distribution will only generate correlated behavior by chance, so
it might be a good idea to create models that generate deliberately
correlated voting.

-km

On Sun, Aug 6, 2023, 4:57 AM Kristofer Munsterhjelm km_elmet@t-online.de
wrote:

Your impression is the traditional flawed meaning of IA that Kevin, Chris,
and I have been fighting against for quite a while ... without making too
big a deal about it. DMC was the first context where we started making the
distinction, since DMC is based on eliminating candidates from the bottom
of the IA order until a pairwise unbeaten candidate emerges ... Benham
based on IA elimination.

of IA was that

I wonder if my old idea about max A>B restricted to A=Head and B=Tail would
work.  In ther words elect the head of the strongest minimal covering
chain. The strength of a chain is the strength of the Head>Tail defeat. The
covering requirement is that no candidate defeats every member of the
chain. A minimal covering is one that ceases to cover when any of its
members is removed.

That requirement takes the place of the 1/n quota requirement.

The method is NP hard in general, but in practice (public elections) no
minimal covering chain has more than two members.

To me "Below my JND" is the same as "infinitely close." And "I strongly
approve X" means I consider X to be infinitely close to my favorite.  "I
strongly disapprove Z" means I consider Z to be infinitely close to my
anti-favorite.

Try to rank all of the student solutions to problem one, then to problem
two, then to problem three, etc and then use those rankings to get a finish
order among the students ... and you still have to decide where in the
finish order to put the cutoffs for the different grades.

My other source of intuition for "infinitely close" to ballot favorite or
ballot anti-favorite ... that is strongly approved or disapproved ... is
the Internal Set Theory formulation of "infinitely close" in any standard
topological space whether metrizeable or not:

If P is a standard point of a standard topological space S, then point X is
infinitely close to P
if and only if
X is in every standard neighborhood of P.

Perhaps

You seem to be forgetting that strong approval and strong disapproval are
optional designations. If you do not feel strongly about approving or
disapproving a candidate, then you cannot honestly use those designations.

In infinitesimal calculus, you are not required to classify every number
you use as infinitely large, infinitesimal, or neither ...  but it is nice
to have those options.

and that it's difficult to create an approval expression that

I strongly approve of this message!

For me the UD challenge is like Climbing Everest barefoot ... can it be
done?

Did Tenzing do it?

On Sun, Aug 6, 2023, 6:01 AM Toby Pereira tdp201b@yahoo.co.uk wrote: