Creighton University

ABSTRACT: The discrepancy between instability in spatial models and political stability in empirical reality has led to the development of the uncovered set (see Miller 1980) and institutional models (e.g., Laver and Shepsle 1996). This article considers an alternative to these approaches using fuzzy mathematics.  We offer a formal proof that in all but a limited number of cases, fuzzy spatial models result in an empty maximal set under majority rule if and only if the Pareto set is a union of cycles.  Furthermore, we demonstrate that if the maximal set exists, at least one of its elements must be contained in the Pareto set.   We conclude by completing characterizing the exceptions in a three-player game.

ABSTRACT: The first Council of Representatives elected under the new Iraqi Constitution was unable to pass legislation required to achieve the political benchmarks set by the government.  We argue that the exercise of a qualified veto by the three-member Presidency Council essentially required near unanimity among the nine parties of the governing coalition.  Our analysis makes use of a fuzzy veto players model.  We derive fuzzy preference measures from party level text data using Wordfish.  The placement of the government parties along a single dimension based on these preferences reveals no common area of agreement among the parties.

ABSTRACT: The uncovered set was developed in order to predict outcomes when spatial models result in an empty core.   In contrast to conventional approaches, fuzzy spatial models induce a substantial degree of individual and collective indifference over alternatives.  Hence, existing definitions of the covering relationship return differing results.  We develop a definition for a fuzzy covering relation.  Our definition results in an uncovered set that is, in most cases, contained within the Pareto set.  We conclude by characterizing the exceptions.

ABSTRACT: Public choice models can be a powerful tool for the explanation and prediction of political phenomena in the discipline of political science. However, the predictions of such models can only be substantiated if the preferences of political actors can be measured and quantified into usable data. This problem currently faces the Colloquium for Fuzzy Preference Aggregation and Collective Choice Models at Creighton University. The Colloquium attempts to apply the principles of fuzzy set theory to geometric public choice models. Although a number of methods have been designed for the extraction of preference measures from empirical data, these measures represent players’ preferences as precise “crisp” points in an infinite Euclidean space. Fuzzy public choice models, however, represent players’ preferences as bounded areas existing in non-Euclidean space. A suitable method for extracting fuzzy preference measures from raw data must be designed if the fuzzy model is to be tested.

The goal of this paper is to design a method for deriving fuzzy preference measures from preference measures extracted from raw text data by the Comparative Manifesto Project. We select Comparative Manifesto Project (CMP) data because of its breadth and availability. We also chose CMP data because it has been applied broadly and has been demonstrated to perform better when estimating the preferences of political actors in democratic systems outside the United States. Finally, the CMP offers an interesting opportunity to extract fuzzy preferences, because it derives crisp preference measures from text data that is inherently fuzzy.