Yee diagram: Difference between revisions

Line 1:

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>

[[File:Yee diagram IrvSq2.png|thumb|A Yee diagram of [[IRV]] with four candidates, showing that the Yellow candidate has been [[Center squeeze|squeezed out]] and cannot win.]]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>

== Production ==

Line 12:

== 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 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 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]]

[[File:Yee diagram IrvSq2.png|thumb|Same candidates as above, except using [[IRV]]. The Yellow candidate has been [[Center squeeze|squeezed out]] and cannot win.]]

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.