Yee diagram: Difference between revisions
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[[File:Yee diagram IrvSq2.png|thumb|A
== Production ==
{{Image frame
|width=300
|content=<youtube width="300" height="230">7btAd1HYvjU</youtube>
|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.
}}
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.<ref>{{Cite web|url=http://bolson.org/voting/sim_one_seat/20081203/|title=Many small voting space graphs, varying gaussian population sigma|last=Olson|first=Brian|date=2008-12-03|website=bolson.org|url-status=live|archive-url=|archive-date=|access-date=2020-04-06}}</ref> These properties do affect the output, but cannot be known from the image itself.
== The ideal case ==
[[File:Yee diagram VorSq2.png|thumb|The ideal single-voter case with the same four candidates as above. The candidate most similar to the voter always wins.]]
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 in favor of or against some candidates, purely as a consequence of where they are located relative to other candidates (how ideologically similar they are).
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.
This discrepancy from the ideal can be shown as a second [[W:Heat map|heat map]] diagram alongside the Yee diagram.<ref name=":0" />
== 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 method would perform under many different scenarios (if the candidates held different sets of positions).<ref name=":0" /><ref>{{Cite web|url=https://www.youtube.com/watch?v=IPMks6afuM8|title=Yee Animations 0.8|last=Frohnmayer|first=Mark|date=May 30, 2017|website=YouTube|publisher=Equal Vote Coalition|url-status=live|archive-url=|archive-date=|access-date=2020-04-06}}</ref>
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>
==
{{Image frame|width=300|content=
<youtube width="300" height="230">-4FXLQoLDBA</youtube>
|caption=A video featuring [[Mark Frohnmayer]] 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>
|max-width=}}
* 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] (Archive: https://archive.ph/8YwuP )<br/> (probably similar to https://github.com/brianolson/election_simulator/blob/master/spacegraph.cpp or https://bolson.org/voting/sim_one_seat/ )
== References ==
<references />
[[Category:Voting method simulations]]
[[Category:Voting models]]
[[Category:Political spectrum]]
[[Category:Infographics]]
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