Spatial models of voting: Difference between revisions

The '''spatial model of voting''' puts voters and candidates in a multi-dimensional space, where each dimension represents a single political issue,<ref name=":1">{{Cite journal|last=Davis|first=Otto A.|last2=Hinich|first2=Melvin J.|last3=Ordeshook|first3=Peter C.|date=1970-01-01|title=An Expository Development of a Mathematical Model of the Electoral Process|url=https://semanticscholar.org/paper/66661f9678dbe956e525e87a50b5b4ee6bf280f1|journal=The American Political Science Review|volume=64|issue=2|pages=426–448|doi=10.2307/1953842|jstor=1953842|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|last=Stoetzer|first=Lukas F.|last2=Zittlau|first2=Steffen|date=2015-07-01|title=Multidimensional Spatial Voting with Non-separable Preferences|url=https://www.cambridge.org/core/journals/political-analysis/article/multidimensional-spatial-voting-with-nonseparable-preferences/112FA71B889588C52C011CE7CEBBDAF2|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.|via=}}</ref> sub-component of an issue,<ref>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"</ref> or candidate attribute,<ref>{{Cite journal|last=Tideman|first=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.”|via=}}</ref> even including non-political properties of the candidates, such as perceived corruption, health, etc.<ref name=":1" /> Voters are then modeled as having an ''ideal point'' in this space, with a preference distance between themselves and each candidate (usually [[W:Euclidean distance|Euclidean distance]]), i.e. a voter may be closer to a candidate on gun control, but disagree on abortion. Voters are then modeled as voting for the candidates whose attributes or policy proposals are nearest to their ideal point (or [[Tactical voting|strategically voting]] to try to minimize their distance to the actual winner).<ref>{{Cite web|url=https://www.pitt.edu/~woon/courses/ps2703_Lec4.pdf|title=Introduction to spatial modeling|last=Woon|first=Jonathan|date=|website=University of Pittsburgh|url-status=live|archive-url=|archive-date=|access-date=}}</ref> Other models that follow the idea of “closeness” are called proximity models.<ref name=":0">{{cite journal | last1 = Rabinowitz | first1 = George | last2 = Macdonald | first2 = Stuart Elaine | title = A directional theory of issue voting | journal = American Political Science Review | volume = 83 | issue = 1 | pages = 93–121 | doi = 10.2307/1956436 | jstor = 1956436 | date = March 1989 | ref = harv |url=|via=}}</ref>{{Rp|93, 96}}

 

The common one-dimensional [[political spectrum]], or various two-dimensional [[W:Political compass|political compasses]], can then be considered [[W:Projection (mathematics)|projections]] of this multi-dimensional space onto a smaller number of dimensions.<ref name=":2">{{Cite journal|last=Alós-Ferrer|first=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> For example, a study of German voters found that at least four dimensions were required to adequately represent all political parties.<ref name=":2" />

 

The number of candidates and the dimensionality of the space impose [[Dimensional limitations of the spatial model|fundamental limitations]] on the information content of ballots, as well as the commensurability of their information content.

 

== See also==