A majorization comparison of apportionment methods in proportional representation

From the inception of the proportional representation movement it has been an issue whether larger parties are favored at the expense of smaller parties in one apportionment of seats as compared to another apportionment. A number of methods have been proposed and are used in countries with a proportional representation system. These apportionment methods exhibit a regularity of order, as discussed in the present paper, that captures the preferential treatment of larger versus smaller parties. This order, namely majorization, permits the comparison of seat allocations in two apportionments. For divisor methods, we show that one method is majorized by another method if and only if their signpost ratios are increasing. This criterion is satisfied for the divisor methods with power-mean rounding, and for the divisor methods with stationary rounding. Majorization places the five traditional apportionment methods in the order as they are known to favor larger parties over smaller parties: Adams, Dean, Hill, Webster, and Jefferson. Received: 5 August 2000/Accepted: 24 October 2001     

Behavior, Belonging, and Belief: A Theory of Ritual Practice

A new model of ritual based on Durkheim's ([1912] 1995) theory is developed. It is argued that ritual practices generate belief and belonging in participants by activating multiple social–psychological mechanisms that interactively create the characteristic outcomes of ritual. Specifically, the distinctive elements of ritual practice are shown to induce altered subjective states and effortful and/or anomalous behaviors, which are subsequently misattributed in such a way that belief and belonging are created or maintained around the focus of ritual attention. These processes are traced in detail, and the resulting model is shown to be empirically credible, comprehensive, and theoretically fertile.     

Constituents’ economic interests and senator support for spending limitations

Peltzman [Peltzman, S., 1984. Constituent interest and congressional voting. Journal of Law and Economics 27, 181–210] argues that if constituents’ economic interests have well-defined “winners and losers” and are appropriately measured, then constituents’ economic interests, and not legislator ideology, are the most important determinates of legislator voting. We test Peltzman's theory by examining senatorial voting on three mandated spending limitation bills. We find, consistent with Peltzman's theory, that the ratio of federal spending in a senator's state to federal taxes paid by that state, and not a senator's personal ideology, matters on legislation where there are well-defined economic “winners and losers.” This is particularly important because unlike other constituents’ economic interest measures that only impact a fraction of the constituency, the ratio of federal spending to federal taxes in a state represents the economic interests of all the constituents in a state.     

Pivotal partings: Forced termination with a sexually abused boy

The termination phase of therapy is an integral part of the treatment process engendering its own unique set of dynamics. However, the potential eruption of new material dislodged by the trauma of the impending loss may in some cases require a reassessment of discharge goals and consequent alteration of treatment modality. The likelihood of new material surfacing at this critical juncture is perhaps highest among the caseloads of therapist trainees, wherein the termination date is forced by the time-limited nature of the learning contract. In the following article, supervisor and trainee detail the process of therapeutic shift from a dynamic to a crisis-oriented modality in the case of a young boy whose central trauma emerged during termination.     

Group therapists' countertransference reactions to multiple deaths from aids

Group therapists for those with HIV Related Diseases are becoming the “professional” survivors of this world-wide epidemic. From their experiences we may learn a great deal more about the effects of multiple deaths on mental health care professionals. As therapists they are constantly eliciting and listening to the fears, hopes, agonies and terrors of those with this disease. They become the bereaved. Witnesses to the deaths of many of their group members, they struggle with a wide range of emotional responses while at the same time assisting surviving group members in their struggle to live with these deaths. Mourning reactions and countertransference phenomena are in abundance as these therapists grapple with these group processes. This article identifies and examines these therapists' responses by focusing on clinical illustrations drawn from their bi-weekly supervision sessions.     

Triangular empathy: “The other” in psychotherapy with individuals

This paper seeks to explore triangular dimensions in individual psychotherapy. In addition to serving as the dyadic object of transference projection and/or as selfobject for a person in psychotherapy, the therapist may be called upon to help the patient work on relationships with certain early, important people or their representations and on the interplay between such relationships and the therapeutic one, that is, in a triangular configuration. Because patients' attempts to introduce others into individual psychotherapy are sometimes experienced by therapists as resistant rather than as integral to the therapeutic process, I propose an empathic reconsideration of such patient efforts to get us to help with the complicated dimensions of human relatedness.     

A model of numbers of births in three countries,with persistent forty-year cycles

This paper describes a model which relates fertility to partner availability, an aspect of relative cohort size. Partner availability is affected by the tendency for males to reproduce at a later age than females. For women born at a time of rising birth rates, there is a shortage of slightly older men as potential partners. Women born when birthrates are falling enjoy a surplus of older men from which to choose. This model is believed to be the first non-linear demographic feedback model involving feedbacks through marriage squeezes in which empirically estimated values of the parameters imply persistent limit cycles. The deterministic model makes births in each five-year period a function of births in previous five-year periods. The form of the function is chosen to model the effect of partner availability upon entry into reproductive relationships, and therefore on age-specific fertility. Marriage rates are not modeled directly. The model was developed from data for more than a century from England and Wales, New Zealand, and the US. The demographic transition is modeled with a logistic function and age-specific fertility rates are estimated using lognormal distributions. The stepwise inclusion of a partner availability estimate in the model showed that it accounts for 29% of otherwise unexplained variance. Projected future births stabilize in sustained or limit cycles with periods a little longer than 40 years, and amplitudes of at least 7% of the mean. The necessary conditions for cycle persistence are outlined on a graph of maximum and minimum fertility parameters.