On the number of separable partitions

Consider partitions of a given set A of n distinct points in general position in ℝ ^d into parts where each pair of parts can be separated by a hyperplane that contains a given set of points E. We consider the problem of counting and generating all such partitions (correcting a classic 1967 result of Harding about the number of such partitions into two parts). Applications of the result to partition problems are presented.     

Severity of illness: red herring or horse of different color? Part 2.

In this continuation of his article, the author defines severity and acuity of illness and discusses approaches to the measurement of the two factors. He provides some background on severity of illness measures that are in current use and prepares for a discussion of the uses of these measures.     

The geometry of implementation: a necessary and sufficient condition for straightforward games

 We characterize games which induce truthful revelation of the players’ preferences, either as dominant strategies (straightforward games) or in Nash equilibria. Strategies are statements of individual preferences on R ⁿ . Outcomes are social preferences. Preferences over outcomes are defined by a distance from a bliss point. We prove that g is straightforward if and only if g is locally constant or dictatorial (LCD), i.e., coordinate-wise either a constant or a projection map locally for almost all strategy profiles. We also establish that: (i) If a game is straightforward and respects unanimity, then the map g must be continuous, (ii) Straightforwardness is a nowhere dense property, (iii) There exist differentiable straightforward games which are non-dictatorial. (iv) If a social choice rule is Nash implementable, then it is straightforward and locally constant or dictatorial. Received: 30 December 1994/Accepted: 22 April 1996     

Career Counselors Confront a Critical Crossroad: A Vision of the Future

The current challenges confronting career counselors require increased discourse regarding career counseling models. Some authors have initiated this discourse, but more participants are needed. The need also exists to communicate more aggressively the special expertise that career counselors bring to their work. As career counselors construct contemporary intervention models, they will need to engage in action research to demonstrate accountability and to document that their services are effective. Career counselors can embrace these activities by building on past practices to construct a vision for the future.     

Sample Selection in Models of Academic Performance

This article shows how admission and enrollment processes affect the interpretation of simple validation studies of academic performance. In a competitive market for students, optimal behavior of admissions committees and applicants drives the simple correlation between test scores and performance toward zero, regardless of the relationship in the population of prospective students. Data from our university's MBA program support the prediction that applicants exhibit a higher correlation between test scores and undergraduate GPAs than do current students. This suggests that standard validation studies will understate the importance of GMAT scores in predicting performance of potential MBA students. (JEL C24 , I121 , C52 )