Yee diagram: Difference between revisions
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A '''Yee diagram''', or '''Yee picture,''' (named after Ka-Ping Yee, who first created them) is used to illustrate the behavior of election methods, given a fixed set of candidates in a [[Spatial model of voting|two-dimensional |
A '''Yee diagram''', or '''Yee picture,''' (named after Ka-Ping Yee, who first created them) is used to illustrate the behavior of election methods, given a fixed set of candidates in a [[Spatial model of voting|two-dimensional preference space]].<ref>{{Cite web|url=http://zesty.ca/voting/sim/|title=Voting Simulation Visualizations|last=Yee|first=Ka-Ping|date=2006-12-08|website=zesty.ca|url-status=live|archive-url=|archive-date=|access-date=2020-04-06}}</ref> |
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== Production == |
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Each candidate is assigned a color and shown as a point, and |
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> |
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The voters are usually modeled using a [[W:Normal distribution|Gaussian ("bell curve") distribution]], though their number, [[W:Statistical dispersion|dispersion]], and strategy can vary from one diagram to the next. These properties do affect the output, but cannot be |
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. These properties do affect the output, but cannot be seen in the image itself.<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> |
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== The ideal case == |
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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 the win region defined by [[W:Euclidean distance|Euclidean distance]] to the candidates. 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). 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 can be shown as a second [[W:Heat map|heat map]] diagram alongside the Yee diagram.<ref name=":0" /> |
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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 candidate that minimizes [[W:Euclidean distance|Euclidean distance]] to that point.) |
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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). |
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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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This discrepancy from the ideal can be shown as a second [[W:Heat map|heat map]] diagram alongside the Yee diagram.<ref name=":0" /> |
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== Variations == |
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The diagrams can also be animated, quickly illustrating how the voting methods would perform if the candidates held different 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> |
The diagrams can also be animated, quickly illustrating how the voting methods would perform if the candidates held different 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> |
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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> |
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> |
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= References = |
== References == |
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<references /> |
<references /> |
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Revision as of 05:34, 6 April 2020
A Yee diagram, or Yee picture, (named after Ka-Ping Yee, who first created them) is used to illustrate the behavior of election methods, given a fixed set of candidates in a two-dimensional preference space.[1]
Production
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.[2]
The voters are usually modeled using a Gaussian ("bell curve") distribution, though their number, dispersion, and strategy can vary from one diagram to the next. These properties do affect the output, but cannot be seen in the image itself.[4]
The ideal case
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 Voronoi diagram of the candidates, with each win region defined by candidate that minimizes Euclidean distance to that point.)
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).
For example, a voting method that suffers from 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 heat map diagram alongside the Yee diagram.[2]
Variations
The diagrams can also be animated, quickly illustrating how the voting methods would perform if the candidates held different positions.[2][5]
While originally intended for displaying single-winner methods, they can be adapted to multi-winner methods by producing multiple diagrams for a given scenario.[6]
References
- ↑ Yee, Ka-Ping (2006-12-08). "Voting Simulation Visualizations". zesty.ca. Retrieved 2020-04-06.
- ↑ a b c d Frohnmayer, Mark (Jun 16, 2017). "Animated Voting Methods". YouTube. Equal Vote Coalition. Retrieved 2020-04-06.
- ↑ 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
- ↑ Olson, Brian (2008-12-03). "Many small voting space graphs, varying gaussian population sigma". bolson.org. Retrieved 2020-04-06.
- ↑ Frohnmayer, Mark (May 30, 2017). "Yee Animations 0.8". YouTube. Equal Vote Coalition. Retrieved 2020-04-06.
- ↑ Olson, Brian (2009-08-10). "Multiwinner Election Simulation in 2-space". bolson.org. Retrieved 2020-04-06.