In addition to that, I still have some interest in the ranked rankings style votes (A>>B>C) where one preference step is considered more important than another step (forming a tree of preferences or something like that). I have not done my homework on this (been lazy for the last decade). Do you know if that approach would likely suffer from some (strategic voting or vote counting complexity related) problems that would make it unusable?

Juho

On 9/14/22 09:36, Juho Laatu wrote:

I think there would be a problem defining just what it means in the
honest case. Consider ranked ballots from a utility perspective: A>B
means that my utility for A is greater than my utility for B. Then
consider something like A>>B>C. Presumably this means that I like A a
lot more than B, and then I only like B a bit better than C. But how much?

From one perspective, you could use normalized ratings and say A>>B if
the difference between A's rating and B's rating is k or more. But then
you could just use ratings directly. To me it seems that hierarchical
preferences would just make for a very hard ballot to fill out.

One benefit of ordinary preferences is that they're unaffected by affine
scaling: if I think B is the next Stalin and I'm OK with A, my
preference is A>B, and if you think B is OK and A is great, your
preference is also A. The problem of (non-normalized) ratings is that I
don't know what one point difference is: is it the difference between
excellent and good, or between good and awful? Hierarchical rankings
lose that benefit because you have to know just how much of a change
merits an additional >.

As an inbetween between rankings and full (necessarily normalized)
ratings, I would probably suggest MJ's grade scale instead. If there is
a common agreement on what an additional > means, then I think it's more
intuitive for the voter to grade A Excellent, B Poor, and C as Reject,
than it is to vote A>>B>C.

On a side note, it would be interesting to devise a normalized ratings
method that maximizes VSE on a spatial model. The normalization
criterion could be something like "if the scale is unbounded and we
apply a monotone affine transformation to a ballot, then the outcome
shouldn't change".

-km

The approval eliminatiion method would have the same complexity as IRV,
since the current approval cutoff on a ballot can change at any step, just
like the current first choice can change at any step in IRV.

In fact IRV is precisely ranked-rankings elimination where all of the
ballots are (by fiat) of the form ...

A>>>>B>>>C>>D>E

So why not give the voters a little credit or (as Steve Brams calls it)
"voter sovereignty", by letting them prioritize their own rankings.

-Forest

On Wed, Sep 14, 2022, 12:36 AM Juho Laatu juho.laatu@gmail.com wrote:

On Wed, Sep 14, 2022, 12:49 PM Forest Simmons forest.simmons21@gmail.com
wrote:

Similarly, Coombs' method can be formulated as Ranked-Rankings Elimination
by specifying all ballots to be of the type

A>B>>C>>>D>>>>E ...

Here's the Benham version:

Proceed with Ranked-Rank Approval Elimination until there is a candidate
(to elect) that defeats pairwise each of the other remaining candidates.

Whether the voters vote sincerely or with sophisticated strategy, the
resulting VSE should be at least as good as ordinary Benham's VSE, in my
opinion.

Sincere voting means sincere order with rank symbols beefed up to reflect
subjectively felt stronger preferences where there are any.

For me personally this voting method would be easier and more satisfying
than either ordinary Benham or Score Based Benham.

Retrofitting with a Covering Embarrassment Protection Afterburner, would be
the frosting on the cake.

-Forest

On Wed, Sep 14, 2022, 12:49 PM Forest Simmons forest.simmons21@gmail.com
wrote:

On Wed, Sep 14, 2022, 2:19 AM Kristofer Munsterhjelm km_elmet@t-online.de
wrote:

I strongly doubt that quantitative considerations of utility help the
average voter decide between A>B,  A= B, and B>A.

It might be relevant in a Borda election with sophisticated voters, but not
in a Benham election with English "ploughboys voting" as Dodgson put it.

Then

It looks to me like you are stuck in the Borda mode with sophisticated
voters.

In an ordinary  Benham election, if the voter feels ever so slightly that
her A>B preference is stronger than her B>C preference, it would be
completely appropriate to express that as A>>B>C.  Unlike in the Borda
context, the double chevron does not imply that >> is approximately twice
as strong as a single chevron preference.

It's precisely analogous to a voter deciding to vote X>Y instead of X=Y
even though the preference is very weak. The voter is not dishonest in
expressing a strict preference even though the utility difference between X
and Y might be a tenth order infinitesimal.

But how much?

The whole point of ranked rankings is the preference strength is
qualitative rather than quantitative, just as ordinary rankings are
qualitative rather tha quantitative.

Otherwise, instead of ranked-rankings, we would be talking rated-rankings,
really a more appropriate name for the Borda analog I regrettably
introduced under the wrong name.

I did warn everybody that it was only one interpretation of the multiple
chevron notation ... but I should have known nobody would pay attention
that caveat.

My original use of the notation was with "dyadic approval" twenty years
ago. In that context there were two main applications .... the primary one
was for approval elimination. The secondary one was a shorthand for binary
ratings ... a form of decloned Borda, really.

On 9/15/22 05:11, Forest Simmons wrote:

I might have overcomplicated things. I was simply trying to formalize
that whether a honest voter votes A>B, A=B, or B>A depends only on his
preferences (which are unambiguous) and neither on the method or the
strength of that preference, apart possibly from A=B, where concerns of
precision come into account.

My point is that I'm not sure how you could make a similar
method-agnostic unambiguous definition of what it means for an honest
voter to vote A>>B instead of A>B.

I guess I'd very much like honest voters to just be able to vote their
preferences without having to concern themselves with what method is
doing the counting or which honest vote is the right one.

That suggests to me that, in a utilitarian model, you'd vote A>>B if you
voted C>D and (utility of A - utility of B) > (utility of C - utility of
D). And similarly that you'd vote E>>>F if there's an A>>B so that
(utility of E - utilify of F) > (utility of A - utility of B).

Which at least gives an idea of how such notation could be independently
defined :-)

It feels to me, though, like it would be easier to just ask for ratings,
making clear that strengths of preference aren't directly taken into
account (because it's not really a cardinal election), and then have the
method calculate which gaps are the largest.[1]

That is, in terms of user experience, it feels like asking for something
like (A: 22, B: 11, C: 8, D: 20, E: 31, F: 0) is much easier than asking for

E>>>>A>D>>>>B>>C>>>F

where

At least it was for me :-)

-km

[1] This poses no problems to von Neumann-Morgenstern because rankings
of differences are unchanged over arbitrary positive affine
transformations. Which is another way to say, like you did, that they're
qualitative.

Kristofer,

A sophisticated voter that preferred voting ratings but was forced to use
ranked-rankings style ballots, should first express his ratings in binary
point expansions normalized between zero and one. Then conversion to dyadic
approval ballots is straightforward.

Dyadic approval ballots are just ranked-rankings where two ranking symbols
of the same strength must have a symbol of greater strength somewhere
between them. For example ...

A>B>>C>D>>>E>F>>G>H

The respective binary point expansions corresponding to A through H would
be ...

.111, .110, .101, .100, .011, .010, .001, and .000

An application of dyadic approval that appealed to Kevin was a kind of
reminiscent of Bucklin:

Imagine collapsing the dyadic ballots in stages where stronger and stronger
rank symbols are replaced by equal signs. When on each ballot all symbols
but one have been replaced by equal signs, construct the pairwise matrix
M1for these collapsed ballots.  Then uncollapse a level and construct the
pairwise matrix M2 for this stage. Then uncollapse another level to get M3,
etc.

Now list the alternatives in the pairwise order of M1, taking advantage of
the acyclic nature of M1 being based on a single rank symbol per ballot ...
i.e. equivalent to an approval ballot. Then use M2 to do sorted margins on
that list. Then use M3 to refine that sort, etc.

The final sorted list is the finish order.

You can think of this as a coarse to fine sorting process.

The method is clone free, monotone, and Smith efficient.

It is very easy to program on the basis of binary point ratings.

-Forest

On Thu, Sep 15, 2022, 2:43 AM Kristofer Munsterhjelm km_elmet@t-online.de
wrote: