TL;DR: A procedure for estimating local weights is described and a set of plausible properties that impose systematic ordinal relationships among local weights are introduced that accounts for nearly all of the variance in the probability judgments in these empirical tests.
TL;DR: In this paper, a stochastic model of the calibration of subjective probabilities based on support theory is presented, which can account for the common finding of overconfidence, and also predicts the form of the relationship between overconfidence and item difficulty.
TL;DR: In this paper, the continuity of the measure of the epigraphs of a preference relation over lotteries was shown to be inconsistent with the assumption that the measure is a product measure.
Abstract: Wakker (1991) and Puppe (1990) point out a mistake in theorem 1 in Segal (1989). This theorem deals with representing preference relations over lotteries by the measure of their epigraphs. An error in the theorem is that it gives wrong conditions concerning the continuity of the measure. This article corrects the error. Another problem is that the axioms do not imply that the measure is bounded; therefore, the measure representation applies only to subsets of the space of lotteries, although these subsets can become arbitrarily close to the whole space of lotteries. Some additional axioms (Segal, 1989, 1990) implying that the measure is a product measure (and hence anticipated utility) also guarantee that the measure is bounded.
TL;DR: The aim is to reduce partition dependence, a judgmental bias that arises from the particular way in which a state space is partitioned for the purposes of making probability judgments, by exploring a property of subjective probabilities called interior additivity (IA).
Abstract: One of the goals of psychological research on subjective probability judgment is to develop prescriptive procedures that can improve such judgments. In this paper, our aim is to reduce partition dependence, a judgmental bias that arises from the particular way in which a state space is partitioned for the purposes of making probability judgments. We explore a property of subjective probabilities called interior additivity (IA). Our story begins with a psychological model of subjective probability judgment that exhibits IA. The model is a linear combination of underlying support for the event in question and a term that reflects a prior belief that all elements in the state space partition are equally likely. The model is consistent with known properties of subjective probabilities, such as binary complementarity, subadditivity, and partition dependence, and has several additional properties related to IA. We present experimental evidence to support our model. The model further suggests a simple prescriptive method based on IA that decision and risk analysts can use to reduce partition dependence, and we present preliminary empirical evidence demonstrating the effectiveness of the method.
TL;DR: In this article, the geometric structure of the support of stable measures with index $p > 1$ is described, and the tail behavior of a stable measure with respect to a seminorm is determined.
Abstract: The tail behavior of a stable measure with respect to a seminorm is determined. Bounds are obtained for the measure of small spheres. The geometric structure of the support of stable measures with index $p > 1$ is described.