# Spatial model of voting

The **spatial model of voting** puts voters and candidates in a multi-dimensional space, where each dimension represents a single political issue,^{[1]}^{[2]} sub-component of an issue,^{[3]} or candidate attribute,^{[4]} even including non-political properties of the candidates, such as perceived corruption, health, etc.^{[1]} Voters are then modeled as having an *ideal point* in this space, with a preference distance between themselves and each candidate (usually 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 strategically voting to try to minimize their distance to the actual winner).^{[5]} Other models that follow the idea of “closeness” are called proximity models.^{[6]}^{:93, 96}

The common one-dimensional political spectrum, or various two-dimensional political compasses, can then be considered projections of this multi-dimensional space onto a smaller number of dimensions.^{[7]} For example, a study of German voters found that at least four dimensions were required to adequately represent all political parties.^{[7]}

The Spatial Model attempts to show the perceptions and decisions of voters when issue voting strategies are used in elections.^{[8]}^{:275} This model assumes that if someone’s issue preferences are placed on a hypothetical spatial field along with all possible candidates’ policy positions, the individual will vote for the candidate whose political stances are closest to their own.^{[6]}^{:94}^{[9]}

## See also[edit | edit source]

## References[edit | edit source]

- ↑
^{a}^{b}Davis, Otto A.; Hinich, Melvin J.; Ordeshook, Peter C. (1970-01-01). "An Expository Development of a Mathematical Model of the Electoral Process".*The American Political Science Review*.**64**(2): 426–448. doi:10.2307/1953842. JSTOR 1953842.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.

- ↑ Stoetzer, Lukas F.; Zittlau, Steffen (2015-07-01). "Multidimensional Spatial Voting with Non-separable Preferences".
*Political Analysis*.**23**(3): 415–428. doi:10.1093/pan/mpv013. ISSN 1047-1987.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. - ↑ 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"
- ↑ Tideman, T; Plassmann, Florenz (June 2008). "The Source of Election Results: An Empirical Analysis of Statistical Models of Voter Behavior".
Assume that voters care about the “attributes” of candidates. These attributes form a multi-dimensional “attribute space.”

Cite journal requires`|journal=`

(help) - ↑ Woon, Jonathan. "Introduction to spatial modeling" (PDF).
*University of Pittsburgh*. - ↑
^{a}^{b}Rabinowitz, George; Macdonald, Stuart Elaine (March 1989). "A directional theory of issue voting".*American Political Science Review*.**83**(1): 93–121. doi:10.2307/1956436. JSTOR 1956436. - ↑
^{a}^{b}Alós-Ferrer, Carlos; Granić, Đura-Georg (2015-09-01). "Political space representations with approval data".*Electoral Studies*.**39**: 56–71. doi:10.1016/j.electstud.2015.04.003. hdl:1765/111247.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.

- ↑ Cho, Sungdai; Endersby, James W. (March 2003). "Issues, the spatial theory of voting, and British general elections: a comparison of proximity and directional models".
*Public Choice*.**114**(3): 275–293. doi:10.1023/A:1022616323373. JSTOR 30025956. - ↑ McCullough, B. Claire (Summer 1978). "Effects of variables using panel data: a review of techniques".
*Public Opinion Quarterly*.**42**(2): 199–220. doi:10.1086/268443.