Editing Political spectrum (section)

== Spatial model ==
{{see also|Issue voting|Issue voting#Models of issue voting|l2=Models of issue voting}}
The [[spatial model of voting]] plots voters and candidates in a multi-dimensional space where each dimension represents a single political issue<ref name=":1">{{Cite journal|last1=Davis|first1=Otto A.|last2=Hinich|first2=Melvin J.|last3=Ordeshook|first3=Peter C.|date=1 January 1970|title=An Expository Development of a Mathematical Model of the Electoral Process|journal=The American Political Science Review|volume=64|issue=2|pages=426–448|doi=10.2307/1953842|jstor=1953842|s2cid=1161006|quote=Since our model is multi-dimensional, we can incorporate all criteria which we normally associate with a citizen's voting decision process — issues, style, partisan identification, and the like.}}</ref><ref>{{Cite journal|last1=Stoetzer|first1=Lukas F.|last2=Zittlau|first2=Steffen|date=1 July 2015|title=Multidimensional Spatial Voting with Non-separable Preferences|journal=Political Analysis|volume=23|issue=3|pages=415–428|doi=10.1093/pan/mpv013|issn=1047-1987|quote=The spatial model of voting is ''the'' work horse for theories and empirical models in many fields of political science research, such as the equilibrium analysis in mass elections ... the estimation of legislators' ideal points ... and the study of voting behavior. ... Its generalization to the multidimensional policy space, the Weighted Euclidean Distance (WED) model ... forms the stable theoretical foundation upon which nearly all present variations, extensions, and applications of multidimensional spatial voting rest.}}</ref> sub-component of an issue,{{efn|If voter preferences have more than one peak along a dimension, it needs to be decomposed into multiple dimensions that each only have a single peak.  "We can satisfy our assumption about the form of the loss function if we increase the dimensionality of the analysis — by decomposing one dimension into two or more"}} or candidate attribute.<ref>{{Cite web|last1=Tideman|first1=T|last2=Plassmann|first2=Florenz|date=June 2008|title=The Source of Election Results: An Empirical Analysis of Statistical Models of Voter Behavior|url=https://www.researchgate.net/publication/228920943|quote=Assume that voters care about the "attributes" of candidates. These attributes form a multi-dimensional "attribute space."}}</ref>   Voters are then modeled as having an "ideal point" in this space and voting for the nearest candidates to that point. The dimensions of this model can also be assigned to non-political properties of the candidates, such as perceived corruption, health, etc.<ref name=":1" />

Most of the other spectra in this article can then be considered [[Projection (mathematics)|projections]] of this multi-dimensional space onto a smaller number of dimensions.<ref name=":2">{{Cite journal|last1=Alós-Ferrer|first1=Carlos|last2=Granić|first2=Đura-Georg|date=1 September 2015|title=Political space representations with approval data|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|url=http://repub.eur.nl/pub/111247|hdl-access=free}}</ref> For example, a study of German voters found that at least four dimensions were required to adequately represent all political parties.<ref name=":2" />