Drawing on Sen (1973) and Yitzhaki (1979), we display a core measure of relative deprivation and, thereafter, configure variants of this measure. The core measure of the relative deprivation of an individual is obtained by aggregating the income excesses arising from comparisons with the higher incomes of other individuals in the individual’s reference (comparison) group or population and dividing this sum by the size of the population. Although the core measure of relative deprivation is based on a comparison of absolute incomes (cardinality), we show that it has a pure rank preference component embedded in it (ordinality): built into the core measure is a term that expresses the rank distance of an individual from the top rank, where “distance” is measured by the number of higher ranks. This attribute is revealing in the sense that the distress from trailing behind others can be decomposed into a distress that results from occupying a rank other than the top rank and a distress arising from the income differences between the higher incomes of others and one’s own income. Drawing on this observation, we subsequently construct a composite relative income formula as a “weighted” representation that encompasses both components. In that formula, we incorporate an exponential parameter to account for the relative importance of a measure of the rank term in comparison with the importance of a measure of the cardinal term. We illustrate our formulas with numerical examples. We conclude this paper with a thought experiment on how we might infer from an observed behavior of individuals whether their underlying preferences are purely cardinal, purely ordinal, or joint.
Overconfidence refers to the overestimation of one’s own abilities, and it is generally measured as the difference between the expected (or subjective) and actual results in a task. We propose an alternative way to measure overconfidence using psychometric tools. Participants are asked to answer a Multiple Choice Test (MCT), and the data obtained are used to fit an Item Response Theory (IRT) model which allows us to take into account test features such as the degree of difficulty and the discrimination power of each item in the test. These features, which are not even considered in the classical measures of overconfidence, open up the opportunity to provide a more reliable measure of overconfidence.
The Basic Local Independence Model (BLIM) is the most frequently used probabilistic model in knowledge structure theory. One of its fundamental assumptions is that the item-specific probabilities of a lucky guess and a careless error are constant across individual knowledge states. This assumption has been challenged on theoretical and empirical grounds. The development of a generalized yet parsimonious model can be founded upon measuring how far an item is from a knowledge state. The paper examines such a previously suggested item-state discrepancy based on the notions of inner and outer layer, and introduces a novel kind of discrepancy induced by a canonical metric on the knowledge states. This so-called minimum discrepancy reflects the minimal length of a possible learning path. The discrepancies are compared theoretically, and conditions for their equality are provided. The advantages that minimum discrepancy offers for generalizing the BLIM are discussed.
We consider the widely used Mazur hyperbolic delay discounting model. Our scientific contributions are two-fold. First, we provide a novel linearized version of the Mazur model that leads to an analytic estimator of the delay discount rate. Our novel estimator bypasses an outstanding problem: the instability in the numerical optimization to compute the nonlinear estimator. As a result, a simulation study shows that when compared to the conventional nonlinear estimator, our novel estimator more accurately estimates the discount rate. Second, we propose a linearized Mazur random effects model and develop a related F-test for the comparison of the impact of different experimental conditions on the delay discount rate. Because our approach does not suffer from numerical instability, all observations can be used in the computation of the F-statistic. As a result, when compared to the conventional approach, our F-test provides much higher statistical power to detect nonnull effect sizes. Analysis of a previously published dataset examining the effects of a brief intervention to reduce delay discounting provides empirical support for the utility of our proposed linearized methods.
Artificial neural networks are widely used in modeling sentence processing but often exhibit overconfident point estimates in their output behavior, even in the presence of ambiguous or conflicting linguistic cues. This limitation is illustrated by reversal anomalies—sentences with unexpected role reversals inducing a conflict between syntactic and semantic information, and has been observed in established models such as the Sentence Gestalt (SG) model. To address this, we introduce a Bayesian formulation of the SG model by applying an extension of the ensemble Kalman filter for Bayesian inference at the level of model parameters. Framing sentence comprehension as a Bayesian inverse problem allows us to characterize posterior predictive uncertainty in the model’s output representations, rather than relying on point estimates. Through numerical experiments and comparisons with a standard maximum likelihood-trained SG model, we show that the Bayesian approach yields systematically less overconfident output activations under cue conflict, reflecting increased uncertainty when processing linguistic ambiguities.
