Yee diagram

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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 two-dimensional ideology space.[1]

Each candidate is assigned a color and shown as a point, and the rest of the space is colored according to which candidate would win under a given voting method, if the center of public opinion were at a given 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 read from the image itself.[3]

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 the win region defined by 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 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 heat map diagram alongside the Yee diagram.[2]

While originally intended for displaying single-winner methods, they can be adapted to multi-winner methods by producing multiple diagrams for a given scenario.[4]


  1. Yee, Ka-Ping (2006-12-08). "Voting Simulation Visualizations". Retrieved 2020-04-06.
  2. a b Frohnmayer, Mark (Jun 16, 2017). "Animated Voting Methods". YouTube. Equal Vote Coalition. Retrieved 2020-04-06.
  3. Olson, Brian (2008-12-03). "Many small voting space graphs, varying gaussian population sigma". Retrieved 2020-04-06.
  4. Olson, Brian (2009-08-10). "Multiwinner Election Simulation in 2-space". Retrieved 2020-04-06.