Political spectrum: Difference between revisions
expand on different compasses
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* a '''distance function''' d: V × V → ℜ that is positive definite and symmetric and satisfies the triangle inequality. Ballots are determined from the assumption that voters prefer candidates which are closer (according to this distance function) to them.
Ultimately, these are projections of [[Spatial model of voting|a multi-dimensional political space]] onto a space of fewer dimensions, to generalize and make discussion simpler.
==One-dimensional==
The simplest example of a political spectrum is the [[uniform linear political spectrum]], in which n=1, v(x)=1, and d(x,y)=|x-y|. The directions on this spectrum are normally referred to as left and right.
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There are many two-dimensional political spaces. The [[W:Nolan chart|Nolan chart]] and [[W:The Political Compass|Political Compass]] are two popular examples, which can be seen as rotated versions of each other. The [[W:Pournelle chart|Pournelle chart]] is another variation with a different set of axes.
[[File:Political Compass.jpg]]
== Higher dimensions ==
Political opinion can be divided into essentially any number of dimensions. Some other examples include the 3-dimensional [https://sapplyvalues.github.io Sapply Compass], the 4-dimensional [https://8values.github.io/ 8values] space, and the [https://9axes.github.io/ 9Axes] space.
One study of German voters found that at least four dimensions were required to adequately represent all political parties.<ref name=":2">{{Cite journal|last1=Alós-Ferrer|first1=Carlos|last2=Granić|first2=Đura-Georg|date=2015-09-01|title=Political space representations with approval data|url=http://repub.eur.nl/pub/111247|journal=Electoral Studies|volume=39|pages=56–71|doi=10.1016/j.electstud.2015.04.003|quote=The analysis reveals that the underlying political landscapes ... are inherently multidimensional and cannot be reduced to a single left-right dimension, or even to a two-dimensional space. ... From this representation, lower-dimensional projections can be considered which help with the visualization of the political space as resulting from an aggregation of voters' preferences. ... Even though the method aims to obtain a representation with as few dimensions as possible, we still obtain representations with four dimensions or more.|hdl=1765/111247}}</ref>
==Calculations==
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* [[Mean minimum political distance]]
== References ==
<references />
[[Category:Voting theory]]
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