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Spatial voting

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In <a href="Political_science" title="Political science">political science</a> and <a href="Social_choice_theory" title="Social choice theory">social choice theory</a>, the spatial (sometimes ideological or ideal-point) model of voting, also known as the Hotelling–Downs model, is a <a href="Mathematical_model" title="Mathematical model">mathematical model</a> of voting behavior. It describes voters and candidates as varying along one or more <a href="Dimension" title="Dimension">axes</a> (or <a href="Dimension" title="Dimension">dimensions</a>), where each axis represents an attribute of the candidate that voters care about.<a href="#cite_note-:0-1">[1]</a>: <span title="Page / location: 14

Quotation: "Assume that voters care about the “attributes” of candidates. These attributes form a multi-dimensional “attribute space.”"" class="tooltip tooltip-dashed" style="border-bottom: 1px dashed;">14 Voters are modeled as having an <a href="Bliss_point_(economics)" title="Bliss point (economics)">ideal point</a> in this space and preferring candidates closer to this point over those who are further away; these kinds of preferences are called <a href="Single-peaked_preferences" class="mw-redirect" title="Single-peaked preferences">single-peaked</a>.

The most common example of a spatial model is a <a href="Political_spectrum" title="Political spectrum">political spectrum or compass</a>, such as the traditional left-right axis,<a href="#cite_note-:2-2">[2]</a> 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.<a href="#cite_note-:2-2">[2]</a>

Besides ideology, a dimension can represent any attribute of the candidates, such as their views on <a href="Single-issue_politics" title="Single-issue politics">one particular issue</a>.<a href="#cite_note-:1-3">[3]</a><a href="#cite_note-4">[4]</a><a href="#cite_note-5">[5]</a> It can also represent non-ideological properties of the candidates, such as their age, experience, or health.<a href="#cite_note-:1-3">[3]</a>

<div class="mw-heading mw-heading2"><h2 id="Accuracy">Accuracy</h2></div>

A study of three-candidate elections analyzed 12 different models of voter behavior, including several variations of the <a href="Impartial_culture" title="Impartial culture">impartial culture</a> model, and found the spatial model to be the most accurate to real-world <a href="Ranked_voting" title="Ranked voting">ranked-ballot</a> election data.<a href="#cite_note-6">[6]</a>: <span title="Page / location: 244

Quotation: "the spatial model is likely to yield accurate predictions about the occurrence of voting events in actual elections, while all other models are inadequate for this purpose."" class="tooltip tooltip-dashed" style="border-bottom: 1px dashed;">244 (Their real-world data was 883 three-candidate elections of 350 to 1,957 voters, extracted from 84 ranked-ballot elections of the <a href="Electoral_Reform_Society" title="Electoral Reform Society">Electoral Reform Society</a>, and 913 elections derived from the 1970–2004 <a href="American_National_Election_Studies" title="American National Election Studies">American National Election Studies</a> <a href="Thermometer_scale" class="mw-redirect" title="Thermometer scale">thermometer scale</a> 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.<a href="#cite_note-:0-1">[1]</a>: <span title="Page / location: 37

Quotation: "the spatial model of voting, augmented by errors in the probabilities assigned to rankings, is a more suitable description of voter behavior than several other models."" class="tooltip tooltip-dashed" style="border-bottom: 1px dashed;">37

A study of <a href="Cardinal_voting" class="mw-redirect" title="Cardinal voting">evaluative voting methods</a> developed several models for generating rated ballots and recommended the spatial model as the most realistic.<a href="#cite_note-7">[7]</a> (Their empirical evaluation was based on two elections, the 2009 European Election Survey of 8 candidates by 972 voters,<a href="#cite_note-8">[8]</a> and the Voter Autrement poll of the <a href="2017_French_presidential_election" title="2017 French presidential election">2017 French presidential election</a>, including 26,633 voters and 5 candidates.<a href="#cite_note-9">[9]</a>)

<div class="mw-heading mw-heading2"><h2 id="History">History</h2></div>

The earliest roots of the model are the one-dimensional <a href="Hotelling's_law" title="Hotelling's law">Hotelling's law</a> of 1929 and <a href="Duncan_Black" title="Duncan Black">Black</a>'s <a href="Median_voter_theorem" title="Median voter theorem">median voter theorem</a> of 1948.<a href="#cite_note-10">[10]</a> Anthony Downs, in his 1957 book <a href="An_Economic_Theory_of_Democracy" title="An Economic Theory of Democracy">An Economic Theory of Democracy</a>, further developed the model to explain the dynamics of party competition, which became the foundation for much follow-on research.<a href="#cite_note-11">[11]</a>

<ul><li><a href="Issue_voting#Models_of_issue_voting" title="Issue voting">Issue voting § Models of issue voting</a></li>

<li><a href="Location_model" class="mw-redirect" title="Location model">Location model</a> - a model that demonstrates consumer preference for particular brands of goods and their locations.</li>

<li><a href="Budget-proposal_aggregation" title="Budget-proposal aggregation">Budget-proposal aggregation</a> - another problem in which agents vote by reporting their ideal outcome.</li></ul>

<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>

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</style><cite id="CITEREFArrow1990" class="citation book cs1">Arrow, Kenneth (1990-06-29). Enelow, James M.; Hinich, Melvin J. (eds.). <a rel="nofollow" class="external text" href="https://www.cambridge.org/core/product/identifier/9780511896606/type/book">Advances in the Spatial Theory of Voting</a> (1 ed.). Cambridge University Press. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2Fcbo9780511896606">10.1017/cbo9780511896606</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-521-35284-0</bdi>.</cite> – <a rel="nofollow" class="external text" href="https://www.cambridge.org/core/books/advances-in-the-spatial-theory-of-voting/C3529FBBD985DBA4C9B1FA74D34BDCFC">via TWL</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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<li id="cite_note-:0-1">^ <a href="#cite_ref-:0_1-0">a</a> <a href="#cite_ref-:0_1-1">b</a> <cite id="CITEREFTidemanPlassmann2008" class="citation web cs1">Tideman, Thorwald Nicolaus; Plassmann, Florenz (June 2008). <a rel="nofollow" class="external text" href="https://www.researchgate.net/publication/228920943">"The Source of Election Results: An Empirical Analysis of Statistical Models of Voter Behavior"</a>.</cite>

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<li id="cite_note-:2-2">^ <a href="#cite_ref-:2_2-0">a</a> <a href="#cite_ref-:2_2-1">b</a> <cite id="CITEREFAlós-FerrerGranić2015" class="citation journal cs1">Alós-Ferrer, Carlos; Granić, Đura-Georg (2015-09-01). <a rel="nofollow" class="external text" href="https://repub.eur.nl/pub/111247">"Political space representations with approval data"</a>. Electoral Studies. 39: 56–71. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.electstud.2015.04.003">10.1016/j.electstud.2015.04.003</a>. <a href="Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<a rel="nofollow" class="external text" href="https://hdl.handle.net/1765%2F111247">1765/111247</a>. <q>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.</q></cite>

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<li id="cite_note-:1-3">^ <a href="#cite_ref-:1_3-0">a</a> <a href="#cite_ref-:1_3-1">b</a> <cite id="CITEREFDavisHinichOrdeshook1970" class="citation journal cs1">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. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F1953842">10.2307/1953842</a>. <a href="JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/1953842">1953842</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:1161006">1161006</a>. <q>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.</q></cite>

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<li id="cite_note-4"><a href="#cite_ref-4">^</a> <cite id="CITEREFStoetzerZittlau2015" class="citation journal cs1">Stoetzer, Lukas F.; Zittlau, Steffen (2015-07-01). "Multidimensional Spatial Voting with Non-separable Preferences". Political Analysis. 23 (3): 415–428. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fpan%2Fmpv013">10.1093/pan/mpv013</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1047-1987">1047-1987</a>. <q>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.</q></cite>

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<li id="cite_note-5"><a href="#cite_ref-5">^</a> 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.

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<li id="cite_note-6"><a href="#cite_ref-6">^</a> <cite id="CITEREFTidemanPlassmann2012" class="citation cs2">Tideman, T. Nicolaus; Plassmann, Florenz (2012), Felsenthal, Dan S.; Machover, Moshé (eds.), <a rel="nofollow" class="external text" href="https://doi.org/10.1007/978-3-642-20441-8_9">"Modeling the Outcomes of Vote-Casting in Actual Elections"</a>, Electoral Systems: Paradoxes, Assumptions, and Procedures, Studies in Choice and Welfare, Berlin, Heidelberg: Springer, pp. 217–251, <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-642-20441-8_9">10.1007/978-3-642-20441-8_9</a>, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-642-20441-8</bdi>, retrieved 2021-11-13</cite>

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<li id="cite_note-7"><a href="#cite_ref-7">^</a> <cite id="CITEREFRollandAubinGannazLeoni2021" class="citation arxiv cs1">Rolland, Antoine; Aubin, Jean-Baptiste; Gannaz, Irène; Leoni, Samuela (2021-04-15). "A Note on Data Simulations for Voting by Evaluation". <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/2104.07666">2104.07666</a> [<a rel="nofollow" class="external text" href="https://arxiv.org/archive/cs.AI">cs.AI</a>].</cite>

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<li id="cite_note-8"><a href="#cite_ref-8">^</a> <cite id="CITEREFEgmondBrugHoboltFranklin2013" class="citation cs2 cs1-prop-foreign-lang-source">Egmond, Marcel Van; Brug, Wouter Van Der; Hobolt, Sara; Franklin, Mark; Sapir, Eliyahu V. (2013), <a rel="nofollow" class="external text" href="https://search.gesis.org/research_data/ZA5055?doi=10.4232/1.11760">European Parliament Election Study 2009, Voter Study</a> (in German), GESIS Data Archive, <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.4232%2F1.11760">10.4232/1.11760</a>, retrieved 2021-11-13</cite>

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<li id="cite_note-9"><a href="#cite_ref-9">^</a> <cite id="CITEREFBouveretBlanchBaujardDurand2018" class="citation cs2">Bouveret, Sylvain; Blanch, Renaud; Baujard, Antoinette; Durand, François; Igersheim, Herrade; Lang, Jérôme; <a href="Annick_Laruelle" title="Annick Laruelle">Laruelle, Annick</a>; Laslier, Jean-François; Lebon, Isabelle (2018-07-25), <a rel="nofollow" class="external text" href="https://zenodo.org/record/1199545">Voter Autrement 2017 - Online Experiment</a>, <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.5281%2Fzenodo.1199545">10.5281/zenodo.1199545</a>, retrieved 2021-11-13</cite>

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<li id="cite_note-10"><a href="#cite_ref-10">^</a> <cite id="CITEREFTanner1994" class="citation thesis cs1">Tanner, Thomas (1994). <a rel="nofollow" class="external text" href="https://lib.dr.iastate.edu/rtd/17175">The spatial theory of elections: an analysis of voters' predictive dimensions and recovery of the underlying issue space</a> (MS thesis). Iowa State University. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.31274%2Frtd-180813-7862">10.31274/rtd-180813-7862</a>. <a href="Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<a rel="nofollow" class="external text" href="https://hdl.handle.net/20.500.12876%2F70995">20.500.12876/70995</a>.</cite>

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<li id="cite_note-11"><a href="#cite_ref-11">^</a> <cite id="CITEREFKurella2017" class="citation book cs1">Kurella, Anna-Sophie (2017). <a rel="nofollow" class="external text" href="https://link.springer.com/10.1007/978-3-319-53378-0_2">"The Evolution of Models of Party Competition"</a>. Issue Voting and Party Competition. Contributions to Political Science. Cham: Springer International Publishing. pp. 11–25. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-319-53378-0_2">10.1007/978-3-319-53378-0_2</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-319-53377-3</bdi>.</cite>

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