[EM] Yee diagrams (was Re: robla's weekly hangout: 2pm-4pm PDT/PST on Tuesdays)
Forest Simmons
forest.simmons21 at gmail.com
Thu Nov 11 14:28:28 PST 2021
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 at gmail.com>
escribió:
> Is there any rigorous peer-reviewed research showing the validity of Yee
> diagrams and the conclusions about them?
> - Ken Bearman, Minneapolis MN
> ----
> Election-Methods mailing list - see https://electorama.com/em for list
> info
>
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