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As we discussed in the opening chapter of this volume, cycling is a persistent and troubling problem for formal models in comparative politics. While the problem is not as acute in single-dimensional problems as it is in multi-dimensional models, chapter five demonstrated that a fuzzy set theory approach can reduce the problem substantially in spatial models. In this concluding chapter we give consideration to the degree to which fuzzy spatial models are plagued by cycling. We argue that while the use of fuzzy math reduces the extent of the problem in a number of circumstance, it does not do away entirely with cycling. We conclude by identifying future avenues for research on this important topic.
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References
Barrett, C.R., Pattanaik, P.K., Salles, M.: Rationality and aggregation of preferences in an ordinally fuzzy framework. Fuzzy Sets and Systems 49, 9–13 (1992)
George, M., Kuriakose, S., Thomaskutty, P.: A fuzzy preference based choice function. The Journal of Fuzzy Mathematics 15(1), 239–246 (2007)
Kacprzyk, J., Fedrizzi, M., Nurmi, H.: Group decision making and consensus under fuzzy preferences and fuzzy majority. Fuzzy Sets and Systems 49, 21–31 (1992)
Nurmi, H.: Approaches to collective decision making with fuzzy preference relations. Fuzzy Sets and Systems 6, 249–259 (1981a)
Nurmi, H.: A fuzzy solution to a majority voting game. Fuzzy Sets and Systems 5, 187–198 (1981)
Nurmi, H., Kacprzyk, J.: Fuzzy sets in political science: An overview. New Mathematics and Natural Computation 3(3), 1–19 (2007)
Plott, C.R.: A notion of equilibrium and its possibility under majority rule. American Economic Review 57, 787–806 (1967)
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Clark, T.D., Larson, J.M., Mordeson, J.N., Potter, J.D., Wierman, M.J. (2008). Cycling in Fuzzy Spatial Models. In: Applying Fuzzy Mathematics to Formal Models in Comparative Politics. Studies in Fuzziness and Soft Computing, vol 225. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77461-7_7
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DOI: https://doi.org/10.1007/978-3-540-77461-7_7
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