Yee diagram: Difference between revisions
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[[File:Yee diagram IrvSq2.png|thumb|A
== Production ==
{{Image frame
<youtube width="300" height="230">-4FXLQoLDBA</youtube>▼
|content=<youtube width="300" height="230">7btAd1HYvjU</youtube>
|caption=Video describing how Yee diagrams are created, then showing animated versions that model different sets of candidates, for [[FPTP]], [[IRV]], [[Score]], and [[STAR]], then their divergence from the ideal single-voter case.<ref name=":0" /><ref>Note that in these simulations, voters are assumed to normalize their ballots under Score and STAR voting, which is why Score has the "center-expansion" effect</ref>▼
|caption=[[Ka-Ping Yee]] at a 2021 event hosted by [[The Center for Election Science]]. In this video, Yee explains several of the diagrams named after Yee, and discusses a broad range of electoral-reform topics.
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Each candidate is assigned a color and shown as a point, and every other point in the space is colored according to which candidate would win under a given voting method, if the center of public opinion were at that point. Typically, this forms large ''win regions'' of the same color. In other words, the candidates stay fixed, while the collective opinions of the voters move to every point in the space, testing who would win in each case.<ref name=":0">{{Cite web|url=https://www.youtube.com/watch?v=-4FXLQoLDBA|title=Animated Voting Methods|last=Frohnmayer|first=Mark|date=Jun 16, 2017|website=YouTube|publisher=Equal Vote Coalition|url-status=live|archive-url=|archive-date=|access-date=2020-04-06}}</ref>
The voters are usually modeled using a [[W:Normal distribution|Gaussian ("bell curve") distribution]], though their number, [[W:Statistical dispersion|dispersion]], and [[Tactical voting|strategy]] can vary from one diagram to the next
== The ideal case ==
[[File:Yee diagram VorSq2.png|thumb|
The ideal Yee diagram for a given set of candidates is given by the single-voter scenario: whichever candidate is ideologically most similar to the single voter wins. (This produces a [[W:Voronoi diagram|Voronoi diagram]] of the candidates, with each win region defined by the candidate that minimizes [[W:Euclidean distance|Euclidean distance]] to that point.)
Any discrepancy from this ideal diagram means that a voting method is unfairly biased
▲Any discrepancy from this ideal diagram means that a voting method is unfairly biased toward or against some candidates, purely as a consequence of where they are located relative to other candidates (how ideologically similar they are).
▲[[File:Yee diagram VorSq2.png|thumb|Yee diagram of ideal single-voter case with 4 candidates]]
For example, a voting method that suffers from [[Center squeeze effect|center squeeze]] might not show any win region at all for a candidate who has been "squeezed out" by the others. This candidate can ''never'' win under that method, even if their ideology is the best match for the average voter.
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== Variations ==
[[File:Nonmonotonicity-city-yee-2005.png|left|thumb|Screenshot of "Nonmonotonicity City" section of http://zesty.ca/voting/sim/]]
The diagrams can also be animated, quickly illustrating how the voting
While originally intended for displaying [[Single-winner method|single-winner methods]], they can be adapted to [[Multi-winner method|multi-winner methods]] by producing multiple diagrams for a given scenario.<ref>{{Cite web|url=http://bolson.org/voting/sim_one_seat/20090810/|title=Multiwinner Election Simulation in 2-space|last=Olson|first=Brian|date=2009-08-10|website=bolson.org|url-status=live|archive-url=|archive-date=|access-date=2020-04-06}}</ref>
== Software ==
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▲<youtube width="300" height="230">-4FXLQoLDBA</youtube>
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* Warren D. Smith's [https://rangevoting.org/IEVS/IEVS.c IEVS]
* Mark Frohnmayer's [https://github.com/nardo/Equal.Vote/tree/master/ElectionAnimation animated diagrams]
* Brian Olson's [http://voteutil.googlecode.com/svn/sim_one_seat sim_one_seat]
== References ==
<references />
[[Category:Voting method simulations]]
[[Category:Voting models]]
[[Category:Political spectrum]]
[[Category:Infographics]]
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