Theoretical units of interest often do not align with the spatial units at which data are available. This problem is pervasive in political science, particularly in subnational empirical research that requires integrating data across incompatible geographic units (e.g., administrative areas, electoral constituencies, and grid cells). Overcoming this challenge requires researchers not only to align the scale of empirical and theoretical units, but also to understand the consequences of this change of support for measurement error and statistical inference. We show how the accuracy of transformed values and the estimation of regression coefficients depend on the degree of nesting (i.e., whether units fall completely and neatly inside each other) and on the relative scale of source and destination units (i.e., aggregation, disaggregation, and hybrid). We introduce simple, nonparametric measures of relative nesting and scale, as ex ante indicators of spatial transformation complexity and error susceptibility. Using election data and Monte Carlo simulations, we show that these measures are strongly predictive of transformation quality across multiple change-of-support methods. We propose several validation procedures and provide open-source software to make transformation options more accessible, customizable, and intuitive.

A central aim of animal welfare science is to be able to compare the effects of different ways of keeping, managing or treating animals based on welfare indicators. A system to aggregate the different indicators is therefore needed. However, developing such a system gives rise to serious challenges. Here, we focus specifically on the ethical aspects of this problem, taking as our starting point the ambitious efforts to set up an aggregation system within the project Welfare Quality® (WQ). We first consider the distinction between intra- and inter-individual aggregation. These are of a very different nature, with inter-individual aggregation potentially giving rise to much more serious ethical disagreement than intra-individual aggregation. Secondly, we look at the idea of aggregation with a focus on how to compare different levels and sorts of welfare problems. Here, we conclude that animal welfare should not be understood as a simple additive function of negative or positive states. We also conclude that there are significant differences in the perceived validity and importance of different kinds of welfare indicators. Based on this, we evaluate how aggregation is undertaken in WQ. The main conclusion of this discussion is that the WQ system lacks transparency, allows important problems to be covered up, and has severe shortcomings when it comes to the role assigned to experts. These shortcomings may have serious consequences for animal welfare when the WQ scheme at farm or group level is applied. We conclude by suggesting ways to overcome some of these shortcomings.

Most prior research on the external validity of mixed-motive games has studied only one single game version and/or one specific type of real-life prosocial behavior. The present study employs a different approach. We used multiple game trials — with different payoff structures — to measure participants’ behavior in the Prisoner’s Dilemma, the Commons Dilemma, and the Public Goods Dilemma. We then examined the associations between these aggregated game behaviors and a wide set of self-reported prosocial behaviors such as donations, commuting, and environmental behaviors. We also related these prosocial behavior measures to a dispositional measure of prosociality, social value orientation. We report evidence that the weak statistical relationships routinely observed in prior studies are at least partially a consequence of failures to aggregate. More specifically, our results show that aggregation over multiple game trials was especially effective for the Prisoner’s Dilemma, whereas it was somewhat effective for the Public Goods Dilemma. Yet, aggregation on the side of the prosocial behaviors was effective for both these games, as well as for social value orientation. The Commons Dilemma, however, turned out to yield invariably poor relationships with prosocial behavior, regardless of the level of aggregation. Based on these findings, we conclude that the use of multiple instances of game behavior and prosocial behavior is preferable to the use of only a single measurement.

We propose a new method to facilitate comparison of aggregated forecasts based on different aggregation, elicitation and calibration methods. Aggregates are evaluated by their relative position on the cumulative distribution of the corresponding individual scores. This allows one to compare methods using different measures of quality that use different scales. We illustrate the use of the method by re-analyzing various estimates from Budescu and Du (Management Science, 2007).

People are often more likely to accept risky monetary gambles with positive expected values when the gambles will be played more than once. We investigated whether this distinction between single-play and multiple-play gambles extends to medical treatments for individual patients and groups of patients. Resident physicians and medical students (n = 69) and undergraduates (n = 99) ranked 9 different flu shots and a no-flu-shot option in 1 of 4 combinations of perspective (individual patient vs. group of 1000 patients) and uncertainty frame (probability vs. frequency). The rank of the no-flu-shot option (a measure of preference for treatment vs. no treatment) was not significantly related to perspective or participant population. The main effect of uncertainty frame and the interaction between perspective and uncertainty frame approached significance (0.1 > p > 0.05), with the no-flu-shot option faring particularly poorly (treatment faring particularly well) when decisions about many patients were based on frequency information. Undergraduate participants believed that the no-flu-shot option would be less attractive (treatment would be more attractive) in decisions about many patients, but these intuitions were inconsistent with the actual ranks. These results and those of other studies suggest that medical treatments for individuals and groups are not analogous to single-play and multiple-play monetary gambles, perhaps because many people are unwilling to aggregate treatment outcomes over patients in the same way that they would compute net gains or losses over monetary gambles.

This paper presents two studies on narrow bracketing and myopic loss aversion. The first study shows that the tendency to segregate multiple gambles is eliminated if subjects face a certainty equivalent or a probability equivalent task instead of a binary choice. The second study argues that the behavioral differences previously attributed entirely to myopic loss aversion are partly because long-term return properties are simply easier to grasp if the return information is already provided in the form of long-term returns rather than one-year returns. Both results may be related to recent failures to replicate myopic loss aversion. When the choice situation is structured in such a way that it draws respondents’ attention to the final outcome distribution and/or if severe misestimations of long-term returns based on short-term return information are unlikely, behavioral differences consistent with myopic loss aversion are less likely to be observed.

A routine part of intelligence analysis is judging the probability of alternative hypotheses given available evidence. Intelligence organizations advise analysts to use intelligence-tradecraft methods such as Analysis of Competing Hypotheses (ACH) to improve judgment, but such methods have not been rigorously tested. We compared the evidence evaluation and judgment accuracy of a group of intelligence analysts who were recently trained in ACH and then used it on a probability judgment task to another group of analysts from the same cohort that were neither trained in ACH nor asked to use any specific method. Although the ACH group assessed information usefulness better than the control group, the control group was a little more accurate (and coherent) than the ACH group. Both groups, however, exhibited suboptimal judgment and were susceptible to unpacking effects. Although ACH failed to improve accuracy, we found that recalibration and aggregation methods substantially improved accuracy. Specifically, mean absolute error (MAE) in analysts’ probability judgments decreased by 61% after first coherentizing their judgments (a process that ensures judgments respect the unitarity axiom) and then aggregating their judgments. The findings cast doubt on the efficacy of ACH, and show the promise of statistical methods for boosting judgment quality in intelligence and other organizations that routinely produce expert judgments.

In this paper, we study the optimal multiple stopping problem under the filtration-consistent nonlinear expectations. The reward is given by a set of random variables satisfying some appropriate assumptions, rather than a process that is right-continuous with left limits. We first construct the optimal stopping time for the single stopping problem, which is no longer given by the first hitting time of processes. We then prove by induction that the value function of the multiple stopping problem can be interpreted as the one for the single stopping problem associated with a new reward family, which allows us to construct the optimal multiple stopping times. If the reward family satisfies some strong regularity conditions, we show that the reward family and the value functions can be aggregated by some progressive processes. Hence, the optimal stopping times can be represented as hitting times.

The good of those who are worse off matters more to the overall good than the good of those who are better off does. But being worse off than one’s fellows is not itself bad; nor is inequality itself bad; nor do differences in well-being matter more when well-being is lower in an absolute sense. Instead, the good of the relatively worse-off weighs more heavily in the overall good than the good of the relatively better-off does, in virtue of the fact that the former are relatively worse off. This paper articulates and defends the view just described.

This paper presents a dilemma for the additive model of reasons. Either the model accommodates disjunctive cases in which one ought to perform some act $$\phi $$ just in case at least one of two factors obtains, or it accommodates conjunctive cases in which one ought to $$\phi $$ just in case both of two factors obtains. The dilemma also arises in a revised additive model that accommodates imprecisely weighted reasons. There exist disjunctive and conjunctive cases. Hence the additive model is extensionally inadequate. The upshot of the dilemma is that one of the most influential accounts of how reasons accrue to determine what we ought to do is flawed.