Fuzzy Set Theory and U.S. Arms Transfers: Modeling the Decision-Making Process

Abstract

This paper has three main objectives: (1) to develop a fuzzy set model of arms export decision making; (2) to describe how the optimal arms strategy of an exporter for a particular importer can be derived from the model; and (3) to test the model by predicting the transfer strategies of the United States for a random sample of prospective importers. The exporter's optimal strategy for a given importer is derived from a fuzzy set of countries in the import region that are important to the exporter and several fuzzy sets representing the exporter's utilities for its arms options. The tests conducted show the model to have considerable promise. Its predictive accuracy exceeds the success rates of two null models; it captures the policymaking for different transfer strategies; and it applies to importers in several regions. The model also outperforms a comparable expected-utility model, which is especially significant given the differences between the fuzzy and expected-utility approaches on the subject of decision-making imprecision. This paper is a preliminary examination of the applicability of fuzzy set theory to arms transfer decision making. It has three basic purposes: (1) to develop a fuzzy set model of the process through which an arms exporting country selects a transfer strategy for a prospective importer; (2) to present a method for deriving the exporter's optimal strategy in any arms trade setting; and (3) to test the model by comparing its ability to predict the policy choices of the United States for Third World importers with the predictive capabilities of two expected-utility models. The comparisons of the fuzzy and expected-utility models are particularly important because of the different ways in which the two modeling approaches contend with the issue of policymaking imprecision. Both kinds of models acknowledge that imprecision affects the strategy selection process; however, while the two expected-utility models ascribe imprecision to decisionmaker uncertainty, the fuzzy set model attributes it to the intrinsic fuzziness of key concepts in the decision problem. Comparing the performances of the expected-utility and fuzzy models should indicate whether uncertainty or fuzziness is more prominent in the arms trade process. There are a number of simplifying assumptions that facilitate the development of the fuzzy set model. Among these is the standard premise that the deliberative process is a rational, utility-maximizing enterprise conducted by a collective decision-making unit known as the state. The model also assumes that the utilities which the state seeks to maximize reflect the state's concern about its relations with all politically important countries of the arms import region. The