Spatial voting
{{Short description|Model simulating voters in an election}}
In political science and social choice theory, the spatial (sometimes ideological or ideal-point) model of voting, also known as the Hotelling–Downs model, 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.{{Cite web|url=https://www.researchgate.net/publication/228920943|last1=Tideman|first1=Thorwald Nicolaus|last2=Plassmann|first2=Florenz|date=June 2008|title=The Source of Election Results: An Empirical Analysis of Statistical Models of Voter Behavior}}{{Rp|14|quote=Assume that voters care about the “attributes” of candidates. These attributes form a multi-dimensional “attribute space.”}} Voters are modeled as having an ideal point in this space and preferring candidates closer to this point over those who are further away; these kinds of preferences are called single-peaked.
The most common example of a spatial model is a political spectrum or compass, such as the traditional left-right axis,{{Cite journal|last1=Alós-Ferrer|first1=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 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|hdl-access=free}} 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.
Besides ideology, a dimension can represent any attribute of the candidates, such as their views on one particular issue.{{Cite journal |last1=Davis |first1=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 |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.}}{{Cite journal |last1=Stoetzer |first1=Lukas F. |last2=Zittlau |first2=Steffen |date=2015-07-01 |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.}}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. It can also represent non-ideological properties of the candidates, such as their age, experience, or health.
Accuracy
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.{{Citation|last1=Tideman|first1=T. Nicolaus|title=Modeling the Outcomes of Vote-Casting in Actual Elections|date=2012|url=https://doi.org/10.1007/978-3-642-20441-8_9|work=Electoral Systems: Paradoxes, Assumptions, and Procedures|pages=217–251|editor-last=Felsenthal|editor-first=Dan S.|series=Studies in Choice and Welfare|place=Berlin, Heidelberg|publisher=Springer|language=en|doi=10.1007/978-3-642-20441-8_9|isbn=978-3-642-20441-8|access-date=2021-11-13|last2=Plassmann|first2=Florenz|editor2-last=Machover|editor2-first=Moshé}}{{Rp|244|quote=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.}} (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.{{Rp|37|quote=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.}}
A study of evaluative voting methods developed several models for generating rated ballots and recommended the spatial model as the most realistic.{{cite arXiv|last1=Rolland|first1=Antoine|last2=Aubin|first2=Jean-Baptiste|last3=Gannaz|first3=Irène|last4=Leoni|first4=Samuela|date=2021-04-15|title=A Note on Data Simulations for Voting by Evaluation|class=cs.AI|eprint=2104.07666}} (Their empirical evaluation was based on two elections, the 2009 European Election Survey of 8 candidates by 972 voters,{{Citation|last1=Egmond|first1=Marcel Van|title=European Parliament Election Study 2009, Voter Study|date=2013|url=https://search.gesis.org/research_data/ZA5055?doi=10.4232/1.11760|publisher=GESIS Data Archive|language=de|doi=10.4232/1.11760|access-date=2021-11-13|last2=Brug|first2=Wouter Van Der|last3=Hobolt|first3=Sara|last4=Franklin|first4=Mark|last5=Sapir|first5=Eliyahu V.}} and the Voter Autrement poll of the 2017 French presidential election, including 26,633 voters and 5 candidates.{{Citation|last1=Bouveret|first1=Sylvain|title=Voter Autrement 2017 - Online Experiment|date=2018-07-25|url=https://zenodo.org/record/1199545|doi=10.5281/zenodo.1199545|access-date=2021-11-13|last2=Blanch|first2=Renaud|last3=Baujard|first3=Antoinette|last4=Durand|first4=François|last5=Igersheim|first5=Herrade|last6=Lang|first6=Jérôme|last7=Laruelle|first7=Annick|author7-link=Annick Laruelle|last8=Laslier|first8=Jean-François|last9=Lebon|first9=Isabelle}})
History
The earliest roots of the model are the one-dimensional Hotelling's law of 1929 and Black's median voter theorem of 1948.{{Cite thesis|last=Tanner|first=Thomas|date=1994|title=The spatial theory of elections: an analysis of voters' predictive dimensions and recovery of the underlying issue space|type=MS thesis|publisher=Iowa State University|url=https://lib.dr.iastate.edu/rtd/17175|doi=10.31274/rtd-180813-7862|hdl=20.500.12876/70995|doi-access=free}} Anthony Downs, in his 1957 book An Economic Theory of Democracy, further developed the model to explain the dynamics of party competition, which became the foundation for much follow-on research.{{Cite book |last=Kurella |first=Anna-Sophie |title=Issue Voting and Party Competition |chapter-url=http://link.springer.com/10.1007/978-3-319-53378-0_2 |chapter=The Evolution of Models of Party Competition |series=Contributions to Political Science |date=2017 |publisher=Springer International Publishing |isbn=978-3-319-53377-3 |location=Cham |pages=11–25 |doi=10.1007/978-3-319-53378-0_2}}
See also
- Issue voting § Models of issue voting
- Location model - a model that demonstrates consumer preference for particular brands of goods and their locations.
- Budget-proposal aggregation - another problem in which agents vote by reporting their ideal outcome.
Further reading
- {{Cite book |last=Arrow |first=Kenneth |url=https://www.cambridge.org/core/product/identifier/9780511896606/type/book |title=Advances in the Spatial Theory of Voting |date=1990-06-29 |publisher=Cambridge University Press |isbn=978-0-521-35284-0 |editor-last=Enelow |editor-first=James M. |edition=1 |doi=10.1017/cbo9780511896606 |editor-last2=Hinich |editor-first2=Melvin J.|url-access=subscription}} – [https://www.cambridge.org/core/books/advances-in-the-spatial-theory-of-voting/C3529FBBD985DBA4C9B1FA74D34BDCFC via TWL]