Seat Biases in Proportional Representation Systems with Thresholds

In proportional representation systems, apportionment methods are used to convert the number of votes of a party into the number of seats allocated to this party. An interesting characteristic of any such method are the seat biases, that is, the expected differences between the actual seat allocation and the ideal share of seats, separately for each party, when parties are ordered from largest to smallest. For electoral systems with a threshold, that is, with a minimum percentage of votes that parties must reach in order to be eligible to participate in the apportionment process, we show that seat biases decrease from their maximum to zero, as the threshold increases from zero to its maximum, and that all seat biases decrease linearly.     

Ethical inequality measures and the redistribution of income when needs differ

The paper considers nested social welfare functions and ethical inequality measures when households may differ in needs. Several principles of transfers between different household types are introduced and systematically examined. Their implications for the form of welfare functions and inequality measures are derived. The corresponding classes are completely described.      

Social welfare,inequality, and poverty when needs differ

The paper examines income distributions of a finite population consisting of households which may differ with respect to needs. Since observed incomes are not directly comparable, income distributions have to be adjusted. Incomes are transformed to equivalent incomes interpreted as living standards and measured for a reference type, and the latter are supplemented by weights depending on needs. A general class of social welfare orderings (being based on adjusted rank-ordered income distributions) is characterized by a set of properties. Severe limitations for the form of the adjustment process are implied. The consequences for the measurement of inequality and poverty are demonstrated, and corresponding orderings are derived.     

Mixed Methods – Stand der Debatte und aktuelle Problemlagen

While mixed methods research is already much advanced and institutionalized in textbooks, handbooks and its own journal on an international level, the German-language debate on mixed methods lags behind. Thus, this introductory paper starts with outlining the history and key concepts of mixed methods designs as well as the current state of the international debate. Next, we explain the aims and concept of this special issue as well as the crucial arguments of the single papers in the overall context of the special issues. Namely, the debate in this special issue of the Kölner Zeitschrift für Soziologie und Sozialpsychologie circles around the following four topics: philosophical, methodological and methodical foundations of mixed methods research; mixed methods designs and mixed methods sampling; modes of combining data and issues of validity; and process-oriented analysis, longitudinal analysis and evaluation. Based on the observations that, firstly, both the international social science research community and social problems are globalizing and, secondly, that social research itself is changing, especially by the increasing relevance of social media and big data, the paper concludes with suggestions for future research.     

Household decisions and equivalence scales

Considering an economy with a private good and a household good with a variable degree of publicness, we examine the consequences of two extreme decision rules: (1) the cooperative model, where households maximize the welfare of their members, and (2) the noncooperative model, where each household’s member maximizes her own utility. While publicness of the household good is necessary and sufficient for economies of size to exist and to increase with family size under cooperation, it is shown that this no longer holds in the absence of cooperation. On the other hand, the cooperative rule leads to less generous scales than the noncooperative one.      

Global stability of stochastic systems with Poisson distributed random time-delay

This paper gives global stability criteria for a controlled stochastic system with randomly distributed time-delay. The delay function is governed by a homogeneous Poisson process and is independent of the stochastic perturbation on the system. A delay-dependent gain controller is constructed and used to develop a stabilization criterion for the system. Based on the Lyapunov-Krasovskii functional method and stochastic analysis theory, notions of stochastic stability are examined in terms of linear matrix inequality and global stability criteria derived.     

Equivalence Scales Reconsidered

The paper proposes a new and normative approach for adjusting households’ incomes in order to account for the heterogeneity of needs across income recipients when measuring inequality and welfare. We derive the implications for the structure of the adjustment method of two conditions concerned with the way the ranking of situations is modified by a change in the reference household type and by more equally distributed living standards across households. Our results suggest that concern for greater equality in living standards conflicts with the basic welfarist principle of symmetrical treatment of individuals that is at the core of the standard equivalence scale approach.     

Making sense of the self: an integrative framework for moral agency

The self is conceptualized in a multitude of ways in different scholarly fields; at the same time moral agency appears to presuppose a unitary conception of the self. This paper explores this tension by introducing ‘moral senses’ which inform the normative evaluations of a person. The moral senses are featured as innate dispositions, but they inevitably recruit discursive categorizations in order to function. These senses forward both an ‘individual self’, by experiencing a unitary body, mind and character, and a ‘social self’, that is similarly experienced as a body, a mind, and a character. This social self is enabled by the capacity to internalize other people's feelings and intentions and the need to have otherworldly explanations for observable reality. This integrative framework of moral senses provides an understanding that helps to address the challenge of moral heterogeneity and plurality.