Journal of Mathematical Psychology最新文献

A central component of human intelligence is the ability to make abstractions, to gloss over some details in favor of drawing out higher-order structure. Clustering stimuli together is a classic example of this. However, the crucial question remains of how one should make these abstractions—what details to retain and what to throw away? How many clusters to form? We provide an analysis of how a rational agent with limited cognitive resources should approach this problem, considering not only how well a clustering fits the data but also by how ‘complex’ it is, i.e. how cognitively expensive it is to represent. We show that the solution to this problem provides a way to reinterpret a wide range of psychological models that are based on principles from non-parametric Bayesian statistics. In particular, we show that the Chinese Restaurant Process prior, ubiquitous in rational models of human and animal clustering behavior, can be interpreted as minimizing an intuitive formulation of representational complexity.

We extend to a certain class of compound concepts the binary model classically used for the representation of simple concepts. This class consists of concepts that are determined or modified by a single feature. The treatment of such a mixed composition shows the need to differentiate between exceptional and non exceptional modifiers. In the first case, typicality is easily retrieved from the components of the composition, while, in the second case, it is necessary to isolate the characteristic features of the initial concept that contradict the modifier. The distinction between exceptional and non exceptional modifiers plays a key role in the evaluation of resemblance with mixed compositions.

A major argument for positional-coding over associative chaining models of immediate serial recall has been the high probability that an error from a prior list will appear in its correct serial-position, so-called “protrusions.” Here we show that a chaining model can produce protrusions if it includes three characteristics that have been incorporated into published chaining models: (a) a “start-signal” item is associated with all first list-items, (b) memory is not cleared following each list, and (c) the retrieval cue for each item is always the full non-redintegrated retrieved information, regardless of the response. The model covertly recalls all studied lists in parallel (weighted by recency), such that when prior-list items intrude, they predominantly occur at the correct output position. In addition to fitting prior protrusion data, we report two new data sets that question the ubiquity of the simple protrusion-dominance characteristic. These findings show that protrusions cannot falsify an associative basis for serial-order memory and speak to the plausibility of mixture models.

In 1999, Richard Gonzalez and George Wu proposed an axiomatization for the widely used Goldstein–Einhorn probability weighting functions. Our present study analyzes the preference conditions in the axioms, leading to the discovery of a larger family of weighting functions. Furthermore, we present a new preference condition which is necessary and sufficient for the Goldstein–Einhorn weighting functions.

In this work we introduce and study multiple properties and conditions related to the modeling of student knowledge in knowledge space theory (KST). We begin by looking at a property called forgetting consistency, which enforces a systematic way of forgetting within a knowledge structure. Next, we analyze in detail a concept we call positive knowledge correlation. This concept postulates that knowing more should not make it less likely that a student knows a particular concept. Among other things, we find that satisfying positive knowledge correlation implies the knowledge structure is closed under both union and intersection, and we also perform an empirical evaluation to assess the validity of the property. Finally, in the context of an adaptive assessment, we conclude with an analysis of the related concept of a positively correlated updating rule.

This note axiomatically proposes a social choice rule called majority approval, which coincides with the simple majority rule when the latter is decisive (i.e., contains no top cycles), and otherwise coincides with approval voting (Brams and Fishburn, 1978) defined on the top cycle set. We compare our rule to other social choice rules that prioritize preference information over approval information, and show that it stands out for its appealing properties. In addition, we provide axiomatization for a version of majority approval that satisfies the Pareto criterion.

Stefanutti et al. (2020) and Heller (2021) have recently done significant work on the polytomous extensions of knowledge space theory (KST), which opens the field for systematically generalizing many KST concepts to the polytomous case. Following these developments, the paper provides a first counterexample showing that the assumptions in Heller (2021) do not guarantee component-directed joins to be defined item-wise. This leads to an incomplete characterization of the closed elements of the Galois connection in Proposition 8 of Heller (2021), an issue which is resolved in the present paper. A second counterexample in the paper shows that the equivalence between atoms and $⨆$-irreducible elements of the polytomous structure stated in Stefanutti et al. (2020) may not hold in general. This paper provides theoretical results showing that the equivalence still holds if the response categories form a linear order or the structure happens to be factorial.

We propose a two-stage choice model in which decision makers first filter out alternatives (consideration stage) before choosing their preferred alternative among the considered options (choice stage). The model accounts for heterogeneity in consideration screening by allowing respondents to have different thresholds for accepting attribute levels. By utilizing a conjunctive consideration rule, the model can capture well-known non-compensatory screening heuristics. The decision stage is modelled with a compensatory utility model. We compare our two-stage approach with the mixed logit model on simulated choice data, and conclude that both models can be distinguished based on the pattern of opt-out responses they produce. If such responses are the result of screening behaviour, the two-stage model is always selected in favour of a single-stage model. In addition, we evaluated several models on empirical choice data concerning preferences towards cinemas. Our results show that the data is best explained by the proposed model, suggesting that 73% of the participants used a screening rule before making a final choice.

The Mnemonic Similarity Task (MST: Stark et al., 2019) is a modified recognition memory task designed to place strong demand on pattern separation. The sensitivity and reliability of the MST make it an extremely valuable tool in clinical settings, where it has been used to identify hippocampal dysfunction associated with healthy aging, dementia, schizophrenia, depression, and other disorders. As with any test used in a clinical setting, it is especially important for the MST to be administered as efficiently as possible. We apply adaptive design optimization methods (Lesmes et al.,2015; Myung et al., 2013) to optimize the presentation of test stimuli in accordance with previous responses. This optimization is based on a signal detection model of an individual’s memory capabilities and decision-making processes. We demonstrate that the adaptive design optimization approach generally reduces the number of test stimuli needed to measure recognition memory.

Animal interval timing is often studied through the peak interval (PI) procedure. In this procedure, the animal is rewarded for the first response after a fixed delay from the stimulus onset, but on some trials, the stimulus remains and no reward is given. The standard methods and models to analyse the response pattern describe it as break-run-break, a period of low rate response followed by rapid responding, followed by a low rate of response. The study of the pattern has found correlations between start, stop, and duration of the run period that hold across species and experiments.

It is commonly assumed that to achieve the statistics with a pacemaker accumulator model, it is necessary to have start and stop thresholds. In this paper, we will develop a new model that varies response rate in relation to the likelihood of event occurrence, as opposed to a threshold, for changing the response rate. The new model reproduced the start and stop statistics that have been observed in 14 different PI experiments from 3 different papers. The developed model is also compared to the two-threshold Time-adaptive Drift–diffusion Model (TDDM), and the latest accumulator model subsuming the scalar expectancy theory (SET) on all 14 datasets. The results show that it is unnecessary to have explicit start and stop thresholds or an internal equivalent to break-run-break states to reproduce the individual trials statistics, the average behaviour, and the break-run-break analysis results. The new model also produces more realistic individual trials compared to TDDM.