Seat biases of apportionment methods for proportional representation

In proportional representation systems, an important issue is whether a given apportionment method favors larger parties at the expense of smaller parties. For an arbitrary number of parties, ordered from largest to smallest by their vote counts, we calculate (apparently for the first time) the expected differences between the seat allocation and the ideal share of seats, separately for each party, as a function of district magnitude, with a particular emphasis on three traditional apportionment methods. These are (i) the quota method with residual fit by greatest remainders, associated with the names of Hamilton and Hare, (ii) the divisor method with standard rounding (Webster, Sainte-Laguë), and (iii) the divisor method with rounding down (Jefferson, Hondt). For the first two methods the seat bias of each party turns out to be practically zero, whence on average no party is advantaged or disadvantaged. On the contrary, the third method exhibits noticeable seat biases in favor of larger parties. The theoretical findings are confirmed via empirical data from the German State of Bavaria, the Swiss Canton Solothurn, and the US House of Representatives.     

A radiographic assessment of pediatric fracture healing and time since injury

Past studies and pediatric bone physiology indicate that younger individuals may heal at a faster rate. Additionally, in adults upper limb fractures heal faster than lower limb fractures; this trend is expected for pediatric fractures. This study aims to evaluate and compare rates of fracture repair in children based on age and skeletal element. Six stages are used to describe the bone repair process in 294 radiographs of tibial and radial fractures from 107 infants and young children. Healing rates are examined using ANOVA and Welch's t-test with a 95% confidence interval. Results indicate that younger individuals spend less time at stage 1, suggesting a delay in the start of healing. Furthermore, forearm fractures heal faster than leg fractures at stages 2 and 3, suggesting a role in the osseous reaction of bone healing. The healing schedule presented may allow the timing of injuries to be estimated from radiographs.     

Avoiding overstating the strength of forensic evidence: Shrunk likelihood ratios/Bayes factors

When strength of forensic evidence is quantified using sample data and statistical models, a concern may be raised as to whether the output of a model overestimates the strength of evidence. This is particularly the case when the amount of sample data is small, and hence sampling variability is high. This concern is related to concern about precision. This paper describes, explores, and tests three procedures which shrink the value of the likelihood ratio or Bayes factor toward the neutral value of one. The procedures are: (1) a Bayesian procedure with uninformative priors, (2) use of empirical lower and upper bounds (ELUB), and (3) a novel form of regularized logistic regression. As a benchmark, they are compared with linear discriminant analysis, and in some instances with non-regularized logistic regression. The behaviours of the procedures are explored using Monte Carlo simulated data, and tested on real data from comparisons of voice recordings, face images, and glass fragments.     

The effect of education on police attitudes

This paper examines the effect of education on police attitudes. Although the literature seems to suggest that college-educated policemen will be more tolerant than their non-college counterparts, studies to date are highly ambiguous. The present study examines the attitudes of the members of one police department. Findings from the correlation analysis indicate that the educational level of the police does not significantly affect their attitudes. It is suggested that this is due, in part, to the vocational orientation of many police college students and to be pervasive effect of the police role     

Self-image of adolescents with cystic fibrosis

Cystic fibrosis (CF) is a lethal genetic disease, yet improved care has extended the mean age of survival into the young adult years. Many of the surviving adolescents have respiratory and digestive problems which delay growth and sexual development. It has been suggested that the specter of fatal disease interferes with adjustment to adolescence. We administered the Offer Self-Image Questionnaire to three groups with mean height less than the fifth percentile: CF males aged 12–19 (n=16); CF females aged 12–19 (n=8); and otherwise healthy males with short stature and/or delayed puberty aged 13–19 (n=34). The values obtained were compared to published normative data for a large number of normal adolescents and a smaller number of adolescents actively undergoing treatment for emotional disorders. CF males showed an abnormal pattern of adjustment that could be considered comparable to disturbed males and to growth-delayed and sexually delayed males. The CF female group was concordant with the normal population, rather than with the emotionally disturbed population. Thus CF and pubertally delayed males have a self-perception of maladjustment to the psychologic problems of adolescence. This suggests that adjustment problems of the CF male may be related to growth retardation and pubertal delay, the social stigma of which may be more easily disguised in the female. This is important in health care, since recent evidence suggests that exemplary attention to medical compliance and nutrition may ameliorate some of the growth lag both in pubertal delay and CF.Postdoctoral medical research fellow in allergy, immunology, and respiratory disease at Children's Hospital at Stanford. Received his M.D. from the University of Southern California and pediatric training at Stanford University Hospital. Main research interests are clinical nutrition and behavioral intervention in adolescents with chronic disease.Received his M.D. from Stanford University and pediatric training at Stanford University Hospital. Main research interests are growth disorders and adolescent development.Studied psychology at Dartmouth College and Oxford University before coming to Stanford University, where he is currently completing his Ph.D. in social psychology. Main research interests are the social determinants of motivation.Chief of the Allergy and Pulmonary Disease Service at Children's Hospital at Stanford and Assistant Professor of Pediatrics at Stanford University. Received his M.D. from University of Iowa; pediatric training at Yale-New Haven Hospital and Stanford University Hospital; and allergy, immunology, and respiratory postdoctoral training at Stanford University Hospital. Main research interest is cystic fibrosis.