On Tue, Nov 2, 2021 at 3:12 PM Rob Lanphier roblan@gmail.com wrote:

I've camped out at https://whereby.com/robla on Tuesday afternoons
my time since the end of October.  I think my biggest problem is that
I've been too worried to promote the URL.  I'm going to see what
happens when I post it to this mailing list.

During yesterday's Whereby discussion, a couple of us were able to
teach a former work colleague of mine about Yee diagrams:
https://electowiki.org/wiki/Yee_diagram

That work colleague skimmed the webpage that Yee still hosts (here:
http://zesty.ca/voting/sim/) and instantly understood the
implications.  The discussion over on the electionscience.org's
Discord server (here: https://electionscience.org/discord) quickly
got lost in the weeds about how two dimensions are not enough to
perfectly model an electorate.  Of course, two dimensions are not
enough to perfectly model the planet Earth, but road maps (even
Mercator projections) are incredibly useful tools for traveling.  I
suspect that Yee diagrams are going to be useful for persuading people
that appreciate road maps.

Anyway, I hope to see more people next Tuesday (starting November 16
at 2pm PST).  For those of you in Europe, that's apparently 22:00 UTC:
https://www.timeanddate.com/worldclock/converter.html?iso=20211116T220000&p1=224&p2=1440&p3=136&p4=37&p5=179

I'm hoping to see some of you on https://whereby.com/robla this
coming Tuesday at 2pm PST.

Rob

Yee Diagrams of IRV in three and more dimensions retain all of the 2 dim
bizarre features ... fragmented win regions with holes, candidates exterior
to their own win regions, etc, because each 2 dim example can be
isometrically embedded in any symmetrical higher dimensional multivariate
normal distribution.

By contrast in every dimension the win regions for every Condorcet method
are the Dirichlet/Voronoi regions centered on the respective candidates
because for every centrally symmetric distribution the candidate closest to
the center of symmetry is the Condorcet Winner for that distribution.

Remember how we used to always say that in one dimension the Condorcet
candidate is always the first choice of the median voter?

In this context we can say the Condorcet candidate is always the first
choice of the voter at the center of symmetry.

If you take any horrible method and modify the front end to elect the CW if
there is one, suddenly it gets the same Yee diagrams as Ranked Pairs,
River, CSSD, Black, Copeland, etc. because every Yee diagram voter
distribution has a CW, namely the candidate nearest the center of symmetry
of that multivariate normal distribution.

If people interested in voting methods reform would take the time to digest
these basic facts about Yee diagrams ... and then believe their own eyes
.... they would never accept any "ranked choice voting" method unless it
satisfied the Condorcet Criterion ... even if it had to be grafted with
duct-tape and baling wire onto the front end of the proposed method ....
but how much better if incorporated seamlessly!

Pretty easy fix ... lots of bang for the nickel!

El mié., 10 de nov. de 2021 1:10 p. m., Rob Lanphier roblan@gmail.com
escribió:

On Wed, Nov 10, 2021 at 11:22 PM Forest Simmons forest.simmons21@gmail.com
wrote:

+1  :-D

I've been a fan of Condorcet for decades but I only discovered Yee diagrams
recently. I was shocked at how bad IRV is. It's shocking that a candidate
can be right at the center of the voter distribution and somehow lose.

Cheers,

Dr. Daniel Carrera
Postdoctoral Research Associate
Iowa State University

On Thu, Nov 11, 2021 at 9:49 AM Daniel Carrera dcarrera@gmail.com wrote:

I was like you when I learned about Yee diagrams.  Apparently, even
Yee was surprised at how badly Hare's method performed in the
simulations:
http://lists.electorama.com/pipermail/election-methods-electorama.com/2006-April/083434.html

I suspect that those of us who have convinced ourselves that we're
"good at math" AND had also mentally worked out many of the problems
with Hare/IRV have no problem understanding something as clearly and
concisely explained as Yee's work is. But I also think that Yee's work
is an example of people who are "good at math" talking to each other.
Someone who is from a disadvantaged population who is eager to see
proportional mult-winner methods enter the American mainstream might
feel threatened by such sharp (and jagged) criticism of Hare.  It
seems we need to figure out how to communicate Yee's work to a broad
and diverse audience who may be skeptical of the nerd talk.

I deeply appreciate Nicky Case's work:
https://ncase.me/ballot/

I suspect there are many people who discovered Yee's work via Case's
work.  It's incredibly impressive, and helps those with learning
styles that require interactivity.  But I don't think this is enough.
How do we get more people to have the "aha" moment that many of us
here on this mailing list have had?

Rob

On Thu, Nov 11, 2021 at 11:35 AM KenB kdbearman@gmail.com wrote:

I'm not sure.  What (in your mind) would be the competing hypothesis?
How would one invalidate the intuitions drawn from a two-dimensional
projection of voter preferences?

Rob

Mr Rob,

Supposition about the supporters of the Hare system is not science. I can easily substantiate the independent inventors of proportional representation, Thomas Hare and Carl Andrae. Their method the proportional count of the preference vote is based on the foundation of our civilisation, in the sciences and the arts, namely order and proportion.
To be more specific, it conforms to the work of S. S. Stevens, in Science, in the 1940s, on the scales of measurement, including the ordinal scale and the ratio scale, conspicuous by their absence in so many dud voting methods, not entirely absented from this mailing list.

Regards,
Richard Lung.

On 11 Nov 2021, at 9:19 pm, Rob Lanphier roblan@gmail.com wrote:

I'm not sure.  What (in your mind) would be the competing hypothesis?
How would one invalidate the intuitions drawn from a two-dimensional
projection of voter preferences?

Rob

Election-Methods mailing list - see https://electorama.com/em for list info

Good question, but it is a little bit like asking Galileo if there is peer
reviewed research validating what you see when you look through a telescope
pointed at the night sky.

Yee Diagrams are graphical tools in the same way that Cartesian graphs,
Directed graphs, Histograms, Scatter Plots, etc, are.

It's more a matter of learning how to use the tool ... to be able to
interpret what you see. A trained radiologist can interpret an X-ray with
authority, but that doesn't mean that an amateur cannot appreciate the
image of a compound fracture.

What is needed is not so much an  official validating document, but rather
a good users' manual.

The website Rob used is a good starting place, as is Warren Smith's Range
Voting website.

The definition of the Yee Diagram is non-controversial ... Yee himself, the
inventor has the right to define his invention. Everything else follows
from basic Euclidean Geometry as taught anciently ...and even today in
Russian and Chinese public schools.

About 380 B.C., Plato founded his Academy. At the entrance of this re-
search institute was the inscription (in Greek): LET NO ONE IGNORANT OF
GEOMETRY ENTER HERE!

Here's a Euclidean Proof of the central interpretive fact of Yee Diagrams
... namely, that if X is closer to the center of symmetry of a centrally
symmetric distribution of voters than Y is, then a majority of the voters
will prefer X over Y:

Proof:

Let line L be the perpendicular bisector of the line segment XY. This line
L divides the Euclidean plane into two half planes HX and HY, containing X
and Y, respectively.

Because every point of HX is closer to X than to Y, we only need to show
that HX contains more than half of the voters.

[The basic assumption of all geometric based voting spaces ... not only Yee
diagrams .. is that voters prefer nearby camdidates over more distant ones.]

To show that indeed HX has more than half of the voters, first note that
the center of symmetry C of the vote distribution is in HX because by
assumption C is closer to X than it is to Y.

Next construct a line L' parallel to line L through C, and let S be the set
of voters in the strip between L and L'. All of these voters are in the
half plane HX, as are all of the voters on the other side of L' (i.e. the
side not containing S) which by symmetry consists of fully half of the
voters.

In summary, the voters that prefer X over Y consist of the entire half of
the electorate on the opposite side of L' from the strip between L and L',
plus the set S of voters in that strip ... a full majority of the voters,
QED.

This argument generalizes to all dimensions ... the parallel lines L and L'
are replaced with parallel hyper-planes perpendicular to the line segment
XY, etc.

If you don't think I know what I'm talking about, run it by Substack ...
they can spot mistakes faster than any other peer review process, and they
are ruthless!

-FWS

El jue., 11 de nov. de 2021 11:00 a. m., KenB kdbearman@gmail.com
escribió: