A fair division solution to the problem of redistricting

Redistricting is the political practice of dividing states into electoral districts of equal population in response to decennial census results to ensure equal representation in the legislative body. Where the boundaries are drawn can dramatically alter the number of districts a given political party can win. As a result, a political party which has control over the legislature, can (and does) manipulate the boundaries to win a larger number of districts, thus affecting the balance of power in the US House of Representatives. This work introduces a novel solution to the problem of fairly redistricting a state that is motivated by the ideas of fair division. Instead of trying to ensure fairness by restricting the shape of the possible maps or by assigning the power to draw the map to nonbiased entities, this solution ensures fairness by balancing competing interests against each other. Essentially, it is a simple interactive protocol that presents two parties with the opportunity to achieve their fair representation in a state (where the notion of fairness is rigorously defined) and as a result a balanced electoral map is created.     

On multiple comparisons among K samples subject to unequal patterns of censorship

Two multiple comparisons procedures for determining which of K arbitrarily censored populations differ from each other are proposed. The procedures are based on multiple comparisons using the generalized Wilcoxon and log-rank statistics. The procedures incorporate a pairwise ranking scheme, rather than the joint ranking scheme proposed by Breslow (1970) and Crowley and Thomas (1975). A conservative testing method suggested by an inequality due to ?idák (1967) is given; a numerical example is presented.     

Scale estimators for symmetric stable distributions

This paper reports on a simulation comparison of scale estimators for symmetric stable distributions in terms of their ability to identify the population with the greater scale. The modified geometric mean is found to be superior to the sample standard deviation and the Fama-Roll estimator for the larger values of the characteristic exponent, while the Fama-Roll estimator is judged superior for the smaller values. Further, this study sheds some light on the question of the appropriate sample size for discriminating risk measurement in investment analysis when the samples are taken from symmetric stable distributions.     

Third order asymptotics: connections among test quantities

Saddlepoint methods, extended to distribution functions, can provide highly accurate tail probabilities for testing real parameters in exponential models. For extensions, asymptotic connections among various test quantities are needed. For five quantities, the maximum likelihood departure standardized by observed and expected information, the score function standardized by observed and expected information, and the signed square root of the likelihood ratio statistic, the needed connections to third order are recorded. Their use is illustrated by a simple integration proof of the Lugannani and Rice formula.     

Methods of Self-Confrontation in Family Therapy

The research, clinical applications, and effects of audiotape and videotape self-confrontation techniques to family therapy are reviewed. A variety of new applications, such as cross-confrontation and interpersonal process recall, are integrated into the practice of family therapy. Thirteen specific audiovisual self-confrontation methods are reviewed along with reported positive and negative effects of their use. As most novel additions to a therapists "bag of tricks", self-confrontation methods are being abused, applied randomly and unsystematically. There is an urgent need for well-designed and relevant research in the area.     

On the stability of maximum-likelihood estimators of orthogonal parameters

If two parameters ψ and λ, are orthogonal, λψ, the maximum-likelihood estimate of λ for given ψ, varies only slowly with ψ in the neighbourhood of the overall maximum-likelihood point. The same is true if ψλ is replaced by a nonlinear function h(ψλ). The detailed form of the variation of ψλ with ψ is studied, and a basis suggested for choosing a particular function h(ψλ) that shows the dependence in the least informative fashion.