Clarifying Amateurism: A Logical Approach to Resolving the Exploitation of College Athletes Dilemma

In this paper we investigate the logical consequences of the common understanding of amateurism in the context of big-time US college athletics, and in so doing, illustrate a method based on linguistic analysis and logic. The initial thrust of the paper centres on the term ‘amateur’ as presupposed by the late Professor Brand in his attempt to justify the ‘business’ of NCAA-sponsored Division I sports by decoupling the ‘participants from the enterprise’. Next, we examine a more rigorous definition of the term ‘amateur’ in order to show more clearly the difficulties posed by the current situation in college athletics. Additionally, our use of linguistic analysis exposes a flaw in the NCAA's recent move to amend by-law 12.02 in an attempt to avoid the charge of exploitation. Lastly, we put forth a new proposal for better dealing with the central issues swirling around the NCAA as it strives to formulate sound policy at this ‘tectonic’ juncture of players, fans, college programmes and academic integrity.     

礼与食孰重:儒墨之辩新论

孔墨“俱道尧舜”但政治理想却截然不同,其主要原因在于两方面,首先是他们有着各不相同的历史传统和政治理想,其次是他们对于中国轴心时代的社会现实有着完全不同的认识和评价。两家显学的根本分歧在于“礼与食孰重”,儒家认为生活资料的匮乏是由于人的动物性欲望未能得到有效的遏制,因而特别强调了一整套礼仪制度对于文明的重要性。墨家则认为正是由于礼仪制度本身的维系严重消耗了社会的物质基础,才使得人们为了满足饥饿的食本能而不得不弱肉强食。这个思想史的问题至今仍未结束。     

Commodious Axiomatization of Quantifiers in Multiple-Valued Logic

We provide tools for a concise axiomatization of a broad class of quantifiers in many-valued logic, so-called distribution quantifiers. Although sound and complete axiomatizations for such quantifiers exist, their size renders them virtually useless for practical purposes. We show that for quantifiers based on finite distributive lattices compact axiomatizations can be obtained schematically. This is achieved by providing a link between skolemized signed formulas and filters/ideals in Boolean set lattices. Then lattice theoretic tools such as Birkhoff's representation theorem for finite distributive lattices are used to derive tableau-style axiomatizations of distribution quantifiers.     

Binary action based estimation of propensities

An observer is to make inference statements about a quantityp, called apropensity and bounded between 0 and 1, based on the observation thatp does or does not exceed a constantc. The propensityp may have an interpretation as a proportion, as a long-run relative frequency, or as a personal probability held by some subject. Applications in medicine, engineering, political science, and, most especially, human decision making are indicated. Bayes solutions for the observer are obtained based on prior distributions in the mixture of beta distribution family; these are then specialized to power-function prior distributions. Inference about logp and log odds is considered. Multiple-action problems are considered in which the focus of inference shifts to theprocess generating the propensitiesp, both in the case of a process parameter known to the subject and unknown. Empirical Bayes techniques are developed for observer inference aboutc when is known to the subject. A Bayes rule, a minimax rule and a beta-minimax rule are constructed for the subject when he is uncertain about.This research was partially supported by the Defense Advanced Research Projects Agency of the Department of Defense and was monitored by ONR under Contract No. N00014-77-C-0095. Any opinions, findings, conclusions or recommendations expressed herein are those of the author and do not necessarily reflect the views of the Defense Advanced Research Projects Agency, the Office of Naval Research, or Carnegie-Mellon University.     

Measuring nominal scale agreement between a judge and a known standard

Two designs for comparing a judge's ratings with a known standard are presented and compared. Design A pertains to the situation where the judge is asked to categorize each ofN subjects into one ofr (known) classes with no knowledge of the actual number in each class. Design B is employed when the judge is given the actual number in each class and is asked to categorize the individuals subject to these constraints. The probability distribution of the total number of correct choices is developed in each case. A power comparison of the two procedures is undertaken.     

Estimating the parameters of the latent population distribution

Under consideration is a test battery of binary items. The responses ofn individuals are assumed to follow a Rasch model. It is further assumed that the latent individual parameters are distributed within a given population in accordance with a normal distribution. Methods are then considered for estimating the mean and variance of this latent population distribution. Also considered are methods for checking whether a normal population distribution fits the data. The developed methods are applied to data from an achievement test and from an attitude test.     

A latent class approach to fitting the weighted Euclidean model,clascal

A weighted Euclidean distance model for analyzing three-way proximity data is proposed that incorporates a latent class approach. In this latent class weighted Euclidean model, the contribution to the distance function between two stimuli is per dimension weighted identically by all subjects in the same latent class. This model removes the rotational invariance of the classical multidimensional scaling model retaining psychologically meaningful dimensions, and drastically reduces the number of parameters in the traditional INDSCAL model. The probability density function for the data of a subject is posited to be a finite mixture of spherical multivariate normal densities. The maximum likelihood function is optimized by means of an EM algorithm; a modified Fisher scoring method is used to update the parameters in the M-step. A model selection strategy is proposed and illustrated on both real and artificial data.The second author is supported as Bevoegdverklaard Navorser of the Belgian Nationaal Fonds voor Wetenschappelijk Onderzoek.     

A latent class unfolding model for analyzing single stimulus preference ratings

A multidimensional unfolding model is developed that assumes that the subjects can be clustered into a small number of homogeneous groups or classes. The subjects that belong to the same group are represented by a single ideal point. Since it is not known in advance to which group of class a subject belongs, a mixture distribution model is formulated that can be considered as a latent class model for continuous single stimulus preference ratings. A GEM algorithm is described for estimating the parameters in the model. The M-step of the algorithm is based on a majorization procedure for updating the estimates of the spatial model parameters. A strategy for selecting the appropriate number of classes and the appropriate number of dimensions is proposed and fully illustrated on some artificial data. The latent class unfolding model is applied to political science data concerning party preferences from members of the Dutch Parliament. Finally, some possible extensions of the model are discussed.The first author is supported as Bevoegdverklaard Navorser of the Belgian Nationaal Fonds voor Wetenschappelijk Onderzoek. Part of this paper was presented at the Distancia meeting held in Rennes, France, June 1992.     

Intuitions about sample size: the empirical law of large numbers

According to Jacob Bernoulli, even the ‘stupidest man’ knows that the larger one's sample of observations, the more confidence one can have in being close to the truth about the phenomenon observed. Two-and-a-half centuries later, psychologists empirically tested people's intuitions about sample size. One group of such studies found participants attentive to sample size; another found participants ignoring it. We suggest an explanation for a substantial part of these inconsistent findings. We propose the hypothesis that human intuition conforms to the ‘empirical law of large numbers’ and distinguish between two kinds of tasks–one that can be solved by this intuition (frequency distributions) and one for which it is not sufficient (sampling distributions). A review of the literature reveals that this distinction can explain a substantial part of the apparently inconsistent results. © 1997 John Wiley & Sons, Ltd.     

The relationship between wives' estimates of time spent doing housework,support and wives' well-being

This study examines the relationship between the distribution of labour at home and employed women's psychological distress. The distribution of labour at home is measured by wives' estimates of their own and their husbands' time spent doing housework. It is hypothesized that what is more important to women's well-being is their estimates of their husbands' time spent doing housework rather than their own time. It is further hypothesized that one pathway in which wives' estimates of husbands' time spent doing housework influences their well-being is through perceptions of support. In a sample of 153 employed married women, using regression analyses, results are consistent with the predictions made. First, wives' estimates of their husbands' time spent doing housework is a better predictor of their well-being than their estimates of their own time spent. Second, support acts as a partial mediator in this relationship. These findings are discussed with respect to recent work in the area. © 1997 John Wiley & Sons, Ltd.