Book Review: Beyond Earth Day: Fulfilling the Promise. Gaylord Nelson with Susan Campbell and Paul Wozniak. Madison,WI: The University of Wisconsin Press, 2002: 160 pp.

Population and Environment -     

Increasing contraceptive use in Bangladesh: The role of demand and supply factors

This article analyzes the determinants of contraceptive use in Bangladesh, focusing on the roles of demand for additional children and of family planning service supply. Data from the Matlab Family Planning Health Services Project are used to examine the contributions of these factors to the difference in prevalence of modern contraceptive use between the project area and a control area served by the government family planning and health programs. Results of multivariate analysis deriving from the Easterlin synthesis framework show the importance of family planning supply factors in reducing psychic and resource costs of fertility regulation and in activating latent demand for contraception. Demand for birth limiting and for birth spacing emerge as important explanatory factors; demand for birth spacing is greater in the project area, and both demand measures exert a stronger effect on contraceptive behavior in that area.     

ON THE INDEPENDENCE OF THE SAMPLE MEAN AND TRANSLATION-INVARIANT STATISTICS FOR MATRIX NORMAL DISTRIBUTIONS

We present an explicit characterization of the joint dependency structure of an n×p matrix normal random matrix such that the p-dimensional sample mean vector is independent of all translation invariant statistics.     

Designing ChSP-4(c1, c2) plans

In this paper, the notion of average total inspection (ATI) is introduced to ChSP-4(c1,c2) sampling plans. Procedures have been developed for the construction and selection of ChSP-4(c1, c2 plans, minimizing ATI at a given process average, while protection to the consumer is given in terms of the (i) average outgoing quality limit and (ii) limiting quality level.A wide range of c1 and c2 values are considered for developing tables which cover almost all practical situations. The procedure described is similar to that of Dodge and Romig.     

On the existence and uniqueness of maximizers of two likelihood functions

While applying theclassical maximum likelihood method for a certain statistical inference problem, Smith and Weissman [5] have noted that there are conditions under which the likelihood function may be unbounded above or may not possess local maximizers. Ariyawansà and Templeton [1] have derived inference procedures for this problem using the theory of structural inference [2,3,4]. Based on numerical experience, and without proof, they state that the resulting likelihood functions possess unique, global maximizers, even in instances where the classical maximum likelihood method fails in the above sense. In this paper, we prove that under quite mild conditions, these likelihood functions that result from the application of the theory of structural inference are well-behaved, and possess unique, global maximizers. This research was supported in part by the Applied Mathematical Sciences subprogram of the U.S. Department of Energy under contract W-31-109-Eng-38 while the author was visiting the Mathematics and Computer Science Division of Argonne National Laboratory, Argonne, Illinois.     

Arrow's paradox and mathematical theory of democracy

Two measures, the weight of coalitions and the probability of situations in decision making, are used to characterize the representativeness, i.e. the capability of individuals to represent the social preference. It is proved that there always exists an individual who represents a majority on average, and an individual who represents a majority in most cases. This result is applied to Arrow's social choice model. It follows that there always exists a dictator who is a representative of the society rather than a dictator in a proper sense. After the concept of dictator has been refined to a dictator in a proper sense, Arrow's axioms become consistent. The idea of optimal representation is extended to limited groups of representatives which make decisions on behalf of the whole society. We consider the cabinet (named by analogy with the cabinet of ministers) which consists of a few representatives with delimited domains of competence, and the council which makes decisions by means of voting. It is shown that the representativeness of optimal cabinets and councils tends to 100% of maximally possible values as the number of their members increases, independently of the size of the society. We suggest a geometric interpretation of optimal representatives, cabinets, and councils, based on approximation formulas for the indicators of representativeness derived for the model with a large number of independent individuals. Finally, for cabinets and councils we establish the consistency of different concepts of optimality with respect to different indicators of representativeness. Our consideration is applicable to multicriteria decision making. An appointment of a cabinet or a council corresponds to selecting a few partial criteria. Therefore, the obtained results can be used for reducing the set of partial criteria to a certain sufficient minimum. The concepts of dictator, cabinet, and council can be understood as models of president, government, and parliament, respectively. Thus our results justify reducing social choice to individual choice or small group choice. Although it is in use in all democratic systems, its acceptability is not evident at all. In other words, we justify the demoncraticity of such forms of political power as the president, the parliament, and the government.