Fuzzy one-dimensional models

Terry D. Clark, Jennifer M. Larson, John N. Mordeson, Joshua D. Potter, Mark J. Wierman

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The aim of formal modeling under the research agenda of The New Institutionalism is to predict political outcomes on the basis of the preferences of political actors and the design of institutions that aggregate those preferences into a single policy choice. Spatial models plot preferences and policies in n-dimensional issue space and use rules of geometry over that space to make predictions. In this chapter, we introduce the single dimensional model. To contrast crisp with fuzzy methods, as well as continuous fuzzy with discrete fuzzy methods, we rely on an example of presidential veto offered by Kiewiet and McCubbins' (1988). The first section introduces the example as Kiewiet and McCubbins do, in its original crisp form. By assuming that all actors have a single ideal point, prefer points closer to the ideal point to points farther away in either direction, and have strict preferences over any two distinct policies however similar, the model yields predictions about when a president would accept a proposal and when she would exercise a veto. We conclude the crisp section by explaining limitations implicit in such assumptions, limitations that a fuzzy reformulation can bypass. The remainder of the chapter reconsiders the veto example first using continuous fuzzy representations of preferences, then using discrete fuzzy representations. Both approaches jettison the single point and the Euclidean distance assumptions, and the discrete approach also relaxes the perfectly specified strict preference assumption. From here, we increase the dimensionality of the issue space and consider multi-dimensional models in the next chapter.

Original languageEnglish
Title of host publicationApplying Fuzzy Mathematics to Formal Models in Comparative Politics
Pages81-107
Number of pages27
Volume225
DOIs
StatePublished - 2008

Publication series

NameStudies in Fuzziness and Soft Computing
Volume225
ISSN (Print)14349922

Fingerprint

One-dimensional Model
Fuzzy Model
Farthest Point
Formal Modeling
Multidimensional Model
Prediction
Spatial Model
Euclidean Distance
Remainder
Reformulation
Exercise
Dimensionality
n-dimensional
Geometry
Distinct
Predict
Model
Policy

All Science Journal Classification (ASJC) codes

  • Computer Science (miscellaneous)
  • Computational Mathematics

Cite this

Clark, T. D., Larson, J. M., Mordeson, J. N., Potter, J. D., & Wierman, M. J. (2008). Fuzzy one-dimensional models. In Applying Fuzzy Mathematics to Formal Models in Comparative Politics (Vol. 225, pp. 81-107). (Studies in Fuzziness and Soft Computing; Vol. 225). https://doi.org/10.1007/978-3-540-77461-7_4

Fuzzy one-dimensional models. / Clark, Terry D.; Larson, Jennifer M.; Mordeson, John N.; Potter, Joshua D.; Wierman, Mark J.

Applying Fuzzy Mathematics to Formal Models in Comparative Politics. Vol. 225 2008. p. 81-107 (Studies in Fuzziness and Soft Computing; Vol. 225).

Research output: Chapter in Book/Report/Conference proceedingChapter

Clark, TD, Larson, JM, Mordeson, JN, Potter, JD & Wierman, MJ 2008, Fuzzy one-dimensional models. in Applying Fuzzy Mathematics to Formal Models in Comparative Politics. vol. 225, Studies in Fuzziness and Soft Computing, vol. 225, pp. 81-107. https://doi.org/10.1007/978-3-540-77461-7_4
Clark TD, Larson JM, Mordeson JN, Potter JD, Wierman MJ. Fuzzy one-dimensional models. In Applying Fuzzy Mathematics to Formal Models in Comparative Politics. Vol. 225. 2008. p. 81-107. (Studies in Fuzziness and Soft Computing). https://doi.org/10.1007/978-3-540-77461-7_4
Clark, Terry D. ; Larson, Jennifer M. ; Mordeson, John N. ; Potter, Joshua D. ; Wierman, Mark J. / Fuzzy one-dimensional models. Applying Fuzzy Mathematics to Formal Models in Comparative Politics. Vol. 225 2008. pp. 81-107 (Studies in Fuzziness and Soft Computing).
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