<div dir="auto">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.<div dir="auto"><br></div><div dir="auto">Yee Diagrams are graphical tools in the same way that Cartesian graphs, Directed graphs, Histograms, Scatter Plots, etc, are.<br></div><div dir="auto"><br></div><div dir="auto">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.</div><div dir="auto"><br></div><div dir="auto">What is needed is not so much an official validating document, but rather a good users' manual.</div><div dir="auto"><br></div><div dir="auto">The website Rob used is a good starting place, as is Warren Smith's Range Voting website. </div><div dir="auto"><br></div><div dir="auto">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.</div><div dir="auto"><br></div><div dir="auto"><span style="color:rgb(77,81,86);font-family:roboto,"helvetica neue",arial,sans-serif;font-size:18px;background-color:rgb(255,255,255)">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! </span><br></div><div dir="auto"><br></div><div dir="auto">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:</div><div dir="auto"><br></div><div dir="auto">Proof: </div><div dir="auto"><br></div><div dir="auto">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.</div><div dir="auto"><br></div><div dir="auto">Because every point of HX is closer to X than to Y, w<span style="font-family:sans-serif">e only need to show that HX contains more than half of the voters.</span><br></div><div dir="auto"><br></div><div dir="auto">[The basic assumption of all geometric based voting spaces ... not only Yee diagrams .. is that voters prefer nearby camdidates over more distant ones.]</div><div dir="auto"><br></div><div dir="auto">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.</div><div dir="auto"><br></div><div dir="auto">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.</div><div dir="auto"><br></div><div dir="auto">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.</div><div dir="auto"><br></div><div dir="auto">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.</div><div dir="auto"><br></div><div dir="auto">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!</div><div dir="auto"><br></div><div dir="auto">-FWS</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">El jue., 11 de nov. de 2021 11:00 a. m., KenB <<a href="mailto:kdbearman@gmail.com" target="_blank" rel="noreferrer">kdbearman@gmail.com</a>> escribió:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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<font face="Comic Sans MS">Is there any rigorous peer-reviewed
research showing the validity of Yee diagrams and the conclusions
about them?<br>
- Ken Bearman, Minneapolis MN<br>
</font>
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