EVALUATING ALTERNATIVE LINEAR PROGRAMMING MODELS TO SOLVE THE TWO-GROUP DISCRIMINANT PROBLEM

The two-group discriminant problem has applications in many areas, for example, differentiating between good credit risks and poor ones, between promising new firms and those likely to fail, or between patients with strong prospects for recovery and those highly at risk. To expand our tools for dealing with such problems, we propose a class of nonpara-metric discriminant procedures based on linear programming (LP). Although these procedures have attracted considerable attention recently, only a limited number of computational studies have examined the relative merits of alternative formulations. In this paper we provide a detailed study of three contrasting formulations for the two-group problem. The experimental design provides a variety of test conditions involving both normal and nonnormal populations. Our results establish the LP model which seeks to minimize the sum of deviations beyond the two-group boundary as a promising alternative to more conventional linear discriminant techniques.     

Applications and Implementation

We propose an alternative solution to the discriminant problem, one that requires little more than a minimum familiarity with linear programming. The approach shows promise for eliminating the complexities of conventional statistical approaches without sacrificing the essential power of existing methods.     

Construal Processes in Preference Assessment

Interpreting people's preferences requires understanding how they have construed their tasks, interpreting the proposed alternatives in the context where the evaluation is being made. With stylized experimental or survey choices, researchers' challenge is typically identifying the features that people add in order to make their task real enough to answer (i.e., how they read between the lines). With rich “real world” choices, researchers' challenge is typically identifying the features that people neglect, as they reduce their task to manageable complexity (i.e., which lines they choose to read). In either case, if people misunderstand or mistrust the stated transaction, they may evaluate a different offer than the one that was proposed. Such misconstruals are a nuisance for investigators, insofar as dealing with them delays the measurements that motivated the research. However, they can also provide an opportunity, by focusing attention on how people give meaning to choice situations. This article describes procedures for studying construal processes, strategies for getting people to answer the questions that interest researchers, and options for interpreting responses when people construe questions differently than was intended.     

Beliefs and practices resulting in female deaths and fewer females than males in India

A preference for sons and the low status of females are implicated in the preponderance of males over females as reported in each census of India from the first one taken in the 19th century. A number of cultural practices, some of which are quite ancient, are involved in this sexual imbalance, namely, maternal mortality due to unhygienic lying-in and postpartum conditions and practices, female infanticide, female feticide, Sati, murder, dowry murder, and suicide. This discussion is based both on 19th and 20th century sources and on fieldwork conducted in the North Indian village of Shanti Nagar in 1958–59 and 1977–78. These practices are most prominent in Punjab, Uttar Pradesh, Maharashtra, Gujarat, and the Union Territory of Delhi. Initially the British tended to overlook some of them, but in the early 19th century and thereafter the British Raj passed laws to curb, especially, female infanticide and Sati. The modern Government of India has also sought to abolish dowry which would, presumably, put an end to dowry murder. Moreover, the Government has issued three circulars directing that action be taken under the penal code against anyone using a prenatal sex-determination test with the object of abortion—a directive aimed at stopping female feticide. Again with the intent of curbing female feticide, a bill providing for punishment and heavy fines for doctors violating the ban on sex-determination tests has recently been introduced in the state legislature of Maharashtra. Despite these efforts, most of the beliefs and practices here described have proved to be tenacious.     

REVIEWS

PROFESSIONAL BOOKS: Prata, G. (1990). A systmic harpoon into family games: Preventive interventions in therapy.     

Hijacking Planes to Cuba: An Up-Dated Version of the Birthday Problem

Modern desk calculators compute distribution functions for many of the standard tabled distributions. Two such machines and some of their capabilities are discussed. Generally more is available from the calculators than is found in voluminous tables. One of the biggest advantages of the machines over tables arises from their capacity to compute probabilities for the two parameter F distribution, a set of values that is cumbersome to tabulate.     

A mixed-integer programming approach to the clustering problem

A mixed-integer programing formulation for clustering is proposed, one that encompasses a wider range of objectives--and side conditions--than standard clustering approaches. The flexibility of the formulation is demonstrated in diagrams of sample problems and solutions. Preliminary computational tests in a practical setting confirm the usefulness of the formulation.     

COMPETITION AND COOPERATION IN A PUBLIC GOODS GAME: A FIELD EXPERIMENT

We explore the effects of competitive and cooperative motivations on contributions in a field experiment. A total of 10,000 potential political donors received solicitations referencing past contribution behavior of members of the competing party (competition treatment), the same party (cooperative treatment), or no past contribution information (control). We first theoretically analyze the effect of these treatments on the contribution behavior of agents with different social preferences in a modified intergroup public good (IPG) game. Then, we report the empirical results: Contribution rates in the competitive, cooperative, and control treatments were 1.45%, 1.08%, and 0.78%, respectively. With the exception of one large contribution, the distribution of contributions in the competitive treatment first order stochastically dominates that of the cooperative treatment. Qualitatively, it appears that the cooperative treatment induced more contributions around the common monetary reference point, while the competitive treatment led to more contributions at twice this amount. These results suggest that eliciting competitive rather than cooperative motivations can lead to higher contributions in IPG settings. (JEL D72, H41, C93)