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 )     

Eye-Tracking Data: New Insights on Response Order Effects and Other Cognitive Shortcuts in Survey Responding

Survey researchers since Cannell have worried that respondents may take various shortcuts to reduce the effort needed to complete a survey. The evidence for such shortcuts is often indirect. For instance, preferences for earlier versus later response options have been interpreted as evidence that respondents do not read beyond the first few options. This is really only a hypothesis, however, that is not supported by direct evidence regarding the allocation of respondent attention. In the current study, we used a new method to more directly observe what respondents do and do not look at by recording their eye movements while they answered questions in a Web survey. The eye-tracking data indicate that respondents do in fact spend more time looking at the first few options in a list of response options than those at the end of the list; this helps explain their tendency to select the options presented first regardless of their content. In addition, the eye-tracking data reveal that respondents are reluctant to invest effort in reading definitions of survey concepts that are only a mouse click away or paying attention to initially hidden response options. It is clear from the eye-tracking data that some respondents are more prone to these and other cognitive shortcuts than others, providing relatively direct evidence for what had been suspected based on more conventional measures.     

The frisch-waugh theorem and generalized least squares

We discuss the standard linear regression model with nonspherical disturbances, where some regressors are annihilated by considering only the residuals from an auxiliary regression, and where, analogous to the Frisch-Waugh procedure, the original GLS procedure is applied to the transformed data. We call this procedure pseudo-GLS and give conditions for pseudo-GL5 to be equal to genuine GLS. We also show via examples that these conditions are often violated in empirical applications, and that the Frisch-Waugh Theorem still “works” with nonspherical disturbances if efficient estimation is applied to both the original and the transformed data.     

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BAYESIAN HIDDEN MARKOV MODELS FOR LONGITUDINAL COUNTS

This paper describes a Bayesian approach to modelling carcinogenity in animal studies where the data consist of counts of the number of tumours present over time. It compares two autoregressive hidden Markov models. One of them models the transitions between three latent states: an inactive transient state, a multiplying state for increasing counts and a reducing state for decreasing counts. The second model introduces a fourth tied state to describe non‐zero observations that are neither increasing nor decreasing. Both these models can model the length of stay upon entry of a state. A discrete constant hazards waiting time distribution is used to model the time to onset of tumour growth. Our models describe between‐animal‐variability by a single hierarchy of random effects and the within‐animal variation by first‐order serial dependence. They can be extended to higher‐order serial dependence and multi‐level hierarchies. Analysis of data from animal experiments comparing the influence of two genes leads to conclusions that differ from those of Dunson (2000). The observed data likelihood defines an information criterion to assess the predictive properties of the three‐ and four‐state models. The deviance information criterion is appropriately defined for discrete parameters.     

A Rank-Sum-Type Test for Paired Data with Multiple Endpoints

Clinical trials and other types of studies often examine the effects of a particular treatment or experimental condition on a number of different response variables. Although the usual approach for analysing such data is to examine each variable separately, this can increase the chance of false positive findings. Bonferroni's inequality or Hotelling's T² statistic can be employed to control the overall type I error rate, but these tests generally lack power for alternatives in which the treatment improves the outcome on most or all of the endpoints. For the comparison of independent groups, O'Brien (1984) developed a rank-sum type test that has greater power than the Bonferroni and T² procedures when one treatment is uniformly better (i.e. for all endpoints) than the other treatment(s). In this paper we adapt the rank-sum test to studies involving paired data and demonstrate that it, too, has power advantages for such alternatives. Simulation results are described, and an example from a study measuring the effects of sleep loss on glucose metabolism is presented to illustrate the methodology.