### 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 language | English |
---|---|

Title of host publication | Applying Fuzzy Mathematics to Formal Models in Comparative Politics |

Pages | 81-107 |

Number of pages | 27 |

Volume | 225 |

DOIs | |

State | Published - 2008 |

### Publication series

Name | Studies in Fuzziness and Soft Computing |
---|---|

Volume | 225 |

ISSN (Print) | 14349922 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Science (miscellaneous)
- Computational Mathematics

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*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

}

TY - CHAP

T1 - Fuzzy one-dimensional 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 - 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.

AB - 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.

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U2 - 10.1007/978-3-540-77461-7_4

DO - 10.1007/978-3-540-77461-7_4

M3 - Chapter

SN - 9783540774600

VL - 225

T3 - Studies in Fuzziness and Soft Computing

SP - 81

EP - 107

BT - Applying Fuzzy Mathematics to Formal Models in Comparative Politics

ER -