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Spatial model of voting

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In political science and social choice theory, the spatial (sometimes ideological or ideal-point) model of voting is a mathematical model of voting behavior. It describes voters and candidates as varying along one or more axes (or dimensions), where each axis represents an attribute of the candidate that voters care about.[1]: 14 Voters are modeled as having an ideal point in this space and voting for the candidates closest to them.

The most common example of a spatial model is a political spectrum or compass, such as the traditional left-right axis,[2] but issue spaces can be more complex. For example, a study of German voters found at least four dimensions were required to adequately represent all political parties.[2]

Besides ideology, a dimension can represent any attribute of the candidates, such as their views on one particular issue.[3][4][5] It can also represent to non-ideological properties of the candidates, such as their age, experience, or health.[3]


A study of three-candidate elections analyzed 12 different models of voter behavior, including several variations of the impartial culture model, and found the spatial model to be the most accurate to real-world ranked-ballot election data.[6]: 244 (Their real-world data was 883 three-candidate elections of 350 to 1,957 voters, extracted from 84 ranked-ballot elections of the Electoral Reform Society, and 913 elections derived from the 1970–2004 American National Election Studies thermometer scale surveys, with 759 to 2,521 "voters.") A previous study by the same authors had found similar results, comparing 6 different models to the ANES data.[1]: 37

A study of evaluative voting methods developed several models for generating rated ballots, and recommend the spatial model as the most realistic.[7] (Their empirical evaluation was based on two elections, the 2009 European Election Survey of 8 candidates by 972 voters,[8] and the Voter Autrement poll of the 2017 French presidential election, including 26,633 voters and 5 candidates.[9])


The earliest roots of the model are the one-dimensional Hotelling's law of 1929 and Black's median voter theorem of 1948.[10]

See also[edit]


  1. ^ a b Tideman, T; Plassmann, Florenz (June 2008). "The Source of Election Results: An Empirical Analysis of Statistical Models of Voter Behavior". {{cite journal}}: Cite journal requires |journal= (help)
  2. ^ 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 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.
  3. ^ 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. S2CID 1161006. 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.
  4. ^ 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.
  5. ^ 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.
  6. ^ Tideman, T. Nicolaus; Plassmann, Florenz (2012), Felsenthal, Dan S.; Machover, Moshé (eds.), "Modeling the Outcomes of Vote-Casting in Actual Elections", Electoral Systems: Paradoxes, Assumptions, and Procedures, Studies in Choice and Welfare, Berlin, Heidelberg: Springer, pp. 217–251, doi:10.1007/978-3-642-20441-8_9, ISBN 978-3-642-20441-8, retrieved 2021-11-13
  7. ^ Rolland, Antoine; Aubin, Jean-Baptiste; Gannaz, Irène; Leoni, Samuela (2021-04-15). "A Note on Data Simulations for Voting by Evaluation". arXiv:2104.07666 [cs.AI].
  8. ^ Egmond, Marcel Van; Brug, Wouter Van Der; Hobolt, Sara; Franklin, Mark; Sapir, Eliyahu V. (2013), European Parliament Election Study 2009, Voter Study (in German), GESIS Data Archive, doi:10.4232/1.11760, retrieved 2021-11-13
  9. ^ Bouveret, Sylvain; Blanch, Renaud; Baujard, Antoinette; Durand, François; Igersheim, Herrade; Lang, Jérôme; Laruelle, Annick; Laslier, Jean-François; Lebon, Isabelle (2018-07-25), Voter Autrement 2017 - Online Experiment, doi:10.5281/zenodo.1199545, retrieved 2021-11-13
  10. ^ Tanner, Thomas (1994). The spatial theory of elections: an analysis of voters' predictive dimensions and recovery of the underlying issue space (MS thesis). Iowa State University. doi:10.31274/rtd-180813-7862. hdl:20.500.12876/70995.