[EM] Method X, bummer

[Forest Simmons]

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.

>From my point of view your comments about truncation are a little off base
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 at t-online.de>
wrote:

> On 8/5/23 19:21, Forest Simmons wrote:
>
> > Do you consider Implicit Approval Chain Climbing to be burial resistant?
>
> 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.)
>
> > In general, Agenda Based Chain Climbing is monotone when the agenda
> > formation is monotone ... so Borda and Kemeny Chain Climbing are also
> > Banks efficient monotone methods that are probably burial resistant, but
> > neither one is clone proof.
>
> 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.
>
> > In general, elimination with "take down" is Banks efficient ... but not
> > monotone unless based on a fixed (no renormalization between
> > eliminations) monotone agenda.
> >
> > Implicit Approval is monotone and clone proof and UD, but just barely
> > UD. It is maddenly frustrating trying to find another UD monotone, clone
> > proof agenda forming method.
>
> 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
>
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