Fuzzy spatial 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

    Most political issues are more than one-dimensional in scope. For example, budget bills contain funding across a number of issue areas, and political parties engaged in cabinet formation must concern themselves with several issue dimensions in determining a government program capable of uniting a legislative majority. Hence, spatial models must incorporate n > 1 dimensions to be useful. Unfortunately, increasing the space to include multiple dimensions opens the possibility of cycling. The conditions under which cycling can occur have been the object of study for decades, and the conclusion is that the possibility of cycling is pervasive. Plott (1967), for instance, found that a maximal set exists in two-dimensional space only when ideal points are arrayed symmetrically to one another (the radial symmetry condition); and McKelvey (1976) found that in the absence of a maximal set, cycling is possible over the entire two-dimensional space. In order to reduce the likelihood of cycling, scholars have adopted increasingly restrictive assumptions in their models. While this has permitted the models to predict outcomes, increasingly restrictive assumptions remove the models further from reality, and empirical tests have often falsified the predictions. As a consequence, formal models have come under increasing criticism for the gap between their predictions and their empirical implications. The empirical implications in theoretical models (EITM) movement is one reflection of these criticisms (see Achen et al., 2002; De Marchi, 2005).

    Original languageEnglish (US)
    Title of host publicationApplying Fuzzy Mathematics to Formal Models in Comparative Politics
    Pages109-135
    Number of pages27
    Volume225
    DOIs
    StatePublished - 2008

    Publication series

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

    Fingerprint

    Spatial Model
    Cycling
    Fuzzy Model
    Radial Symmetry
    Prediction
    Formal Model
    Theoretical Model
    Likelihood
    Entire
    Model
    Predict

    ASJC Scopus subject areas

    • Computer Science (miscellaneous)
    • Computational Mathematics

    Cite this

    Clark, T. D., Larson, J. M., Mordeson, J. N., Potter, J. D., & Wierman, M. J. (2008). Fuzzy spatial models. In Applying Fuzzy Mathematics to Formal Models in Comparative Politics (Vol. 225, pp. 109-135). (Studies in Fuzziness and Soft Computing; Vol. 225). https://doi.org/10.1007/978-3-540-77461-7_5

    Fuzzy spatial 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. 109-135 (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 spatial models. in Applying Fuzzy Mathematics to Formal Models in Comparative Politics. vol. 225, Studies in Fuzziness and Soft Computing, vol. 225, pp. 109-135. https://doi.org/10.1007/978-3-540-77461-7_5
    Clark TD, Larson JM, Mordeson JN, Potter JD, Wierman MJ. Fuzzy spatial models. In Applying Fuzzy Mathematics to Formal Models in Comparative Politics. Vol. 225. 2008. p. 109-135. (Studies in Fuzziness and Soft Computing). https://doi.org/10.1007/978-3-540-77461-7_5
    Clark, Terry D. ; Larson, Jennifer M. ; Mordeson, John N. ; Potter, Joshua D. ; Wierman, Mark J. / Fuzzy spatial models. Applying Fuzzy Mathematics to Formal Models in Comparative Politics. Vol. 225 2008. pp. 109-135 (Studies in Fuzziness and Soft Computing).
    @inbook{94a5963241074f449e06f0b7538a9dc0,
    title = "Fuzzy spatial models",
    abstract = "Most political issues are more than one-dimensional in scope. For example, budget bills contain funding across a number of issue areas, and political parties engaged in cabinet formation must concern themselves with several issue dimensions in determining a government program capable of uniting a legislative majority. Hence, spatial models must incorporate n > 1 dimensions to be useful. Unfortunately, increasing the space to include multiple dimensions opens the possibility of cycling. The conditions under which cycling can occur have been the object of study for decades, and the conclusion is that the possibility of cycling is pervasive. Plott (1967), for instance, found that a maximal set exists in two-dimensional space only when ideal points are arrayed symmetrically to one another (the radial symmetry condition); and McKelvey (1976) found that in the absence of a maximal set, cycling is possible over the entire two-dimensional space. In order to reduce the likelihood of cycling, scholars have adopted increasingly restrictive assumptions in their models. While this has permitted the models to predict outcomes, increasingly restrictive assumptions remove the models further from reality, and empirical tests have often falsified the predictions. As a consequence, formal models have come under increasing criticism for the gap between their predictions and their empirical implications. The empirical implications in theoretical models (EITM) movement is one reflection of these criticisms (see Achen et al., 2002; De Marchi, 2005).",
    author = "Clark, {Terry D.} and Larson, {Jennifer M.} and Mordeson, {John N.} and Potter, {Joshua D.} and Wierman, {Mark J.}",
    year = "2008",
    doi = "10.1007/978-3-540-77461-7_5",
    language = "English (US)",
    isbn = "9783540774600",
    volume = "225",
    series = "Studies in Fuzziness and Soft Computing",
    pages = "109--135",
    booktitle = "Applying Fuzzy Mathematics to Formal Models in Comparative Politics",

    }

    TY - CHAP

    T1 - Fuzzy spatial models

    AU - Clark, Terry D.

    AU - Larson, Jennifer M.

    AU - Mordeson, John N.

    AU - Potter, Joshua D.

    AU - Wierman, Mark J.

    PY - 2008

    Y1 - 2008

    N2 - Most political issues are more than one-dimensional in scope. For example, budget bills contain funding across a number of issue areas, and political parties engaged in cabinet formation must concern themselves with several issue dimensions in determining a government program capable of uniting a legislative majority. Hence, spatial models must incorporate n > 1 dimensions to be useful. Unfortunately, increasing the space to include multiple dimensions opens the possibility of cycling. The conditions under which cycling can occur have been the object of study for decades, and the conclusion is that the possibility of cycling is pervasive. Plott (1967), for instance, found that a maximal set exists in two-dimensional space only when ideal points are arrayed symmetrically to one another (the radial symmetry condition); and McKelvey (1976) found that in the absence of a maximal set, cycling is possible over the entire two-dimensional space. In order to reduce the likelihood of cycling, scholars have adopted increasingly restrictive assumptions in their models. While this has permitted the models to predict outcomes, increasingly restrictive assumptions remove the models further from reality, and empirical tests have often falsified the predictions. As a consequence, formal models have come under increasing criticism for the gap between their predictions and their empirical implications. The empirical implications in theoretical models (EITM) movement is one reflection of these criticisms (see Achen et al., 2002; De Marchi, 2005).

    AB - Most political issues are more than one-dimensional in scope. For example, budget bills contain funding across a number of issue areas, and political parties engaged in cabinet formation must concern themselves with several issue dimensions in determining a government program capable of uniting a legislative majority. Hence, spatial models must incorporate n > 1 dimensions to be useful. Unfortunately, increasing the space to include multiple dimensions opens the possibility of cycling. The conditions under which cycling can occur have been the object of study for decades, and the conclusion is that the possibility of cycling is pervasive. Plott (1967), for instance, found that a maximal set exists in two-dimensional space only when ideal points are arrayed symmetrically to one another (the radial symmetry condition); and McKelvey (1976) found that in the absence of a maximal set, cycling is possible over the entire two-dimensional space. In order to reduce the likelihood of cycling, scholars have adopted increasingly restrictive assumptions in their models. While this has permitted the models to predict outcomes, increasingly restrictive assumptions remove the models further from reality, and empirical tests have often falsified the predictions. As a consequence, formal models have come under increasing criticism for the gap between their predictions and their empirical implications. The empirical implications in theoretical models (EITM) movement is one reflection of these criticisms (see Achen et al., 2002; De Marchi, 2005).

    UR - http://www.scopus.com/inward/record.url?scp=39049098715&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=39049098715&partnerID=8YFLogxK

    U2 - 10.1007/978-3-540-77461-7_5

    DO - 10.1007/978-3-540-77461-7_5

    M3 - Chapter

    SN - 9783540774600

    VL - 225

    T3 - Studies in Fuzziness and Soft Computing

    SP - 109

    EP - 135

    BT - Applying Fuzzy Mathematics to Formal Models in Comparative Politics

    ER -