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The McKelvey–Schofield chaos theorem is a result in social choice theory. It states that if preferences are defined over a multidimensional policy space, then majority rule is in general unstable: there is no Condorcet winner. Furthermore, any point in the space can be reached from any other point by a sequence of majority votes.
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References
- 1 2 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) - 1 2 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.
- 1 2 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.
- ↑ 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.
- ↑ 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
- ↑ 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].
- ↑ 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
- ↑ 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
- ↑ 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.