Bd. 1. Genese und Systematik der Methodenreflexion.

How can different individuals' probability assignments to some events be aggregated into a collective probability assignment? Classic results on this problem assume that the set of relevant events -- the agenda -- is a sigma-algebra and is thus closed under disjunction (union) and conjunction (intersection). We drop this demanding assumption and explore probabilistic opinion pooling on general agendas. One might be interested in the probability of rain and that of an interest-rate increase, but not in the probability of rain or (...) an interest-rate increase. We characterize linear pooling and neutral pooling for general agendas, with classic results as special cases for agendas that are sigma-algebras. As an illustrative application, we also consider probabilistic preference aggregation. Finally, we compare our results with existing results on binary judgment aggregation and Arrovian preference aggregation. This paper is the first of two self-contained, but technically related companion papers inspired by binary judgment-aggregation theory. (shrink)

How can different individuals' probability functions on a given sigma-algebra of events be aggregated into a collective probability function? Classic approaches to this problem often require 'event-wise independence': the collective probability for each event should depend only on the individuals' probabilities for that event. In practice, however, some events may be 'basic' and others 'derivative', so that it makes sense first to aggregate the probabilities for the former and then to let these constrain the probabilities for the latter. We formalize (...) this idea by introducing a 'premise-based' approach to probabilistic opinion pooling, and show that, under a variety of assumptions, it leads to linear or neutral opinion pooling on the 'premises'. This paper is the second of two self-contained, but technically related companion papers inspired by binary judgment-aggregation theory. (shrink)

Commonsense reasoning often relies on the perception of similarity as well as dissimilarity between objects or situations.

Über medizinische Fragen hat sich Popper nur sehr wenig geäußert. Aber es liegt nahe, seine erkenntnis- und wissenschaftstheoretischen Grundprinzipien auf die Medizin und ihre Methodologie anzuwenden. Auch das Wissen in der Medizin ist zunächst in der Hauptsache nur Vermutungswissen, welches einer ständigen Verbesserung und Korrektur bedarf. Auch in der Medizin passieren Fehler. Die Fehler gilt es zu erkennen, zu analysieren und in Zukunft zu vermeiden. Arzt und Patient wollen Sicherheit – in der Diagnose und in der Therapie. Absolute Sicherheit kann (...) es aber nicht geben. Die kritische Fehleranalyse und die darauf beruhende Fehlerkorrektur helfen allerdings, den Sicherheitsgrad beständig zu steigern. Daraus ergeben sich auch entscheidende Konsequenzen für die medizinische Ethik. (shrink)

Ranking functions have been introduced under the name of ordinal conditional functions in Spohn (1988; 1990). They are representations of epistemic states and their dynamics. The most comprehensive and up to date presentation is Spohn (manuscript).