Journal of Mathematical Psychology最新文献

{"title":"Regret theory, Allais’ paradox, and Savage’s omelet","authors":"V.G. Bardakhchyan,&nbsp;A.E. Allahverdyan","doi":"10.1016/j.jmp.2023.102807","DOIUrl":"https://doi.org/10.1016/j.jmp.2023.102807","url":null,"abstract":"<div><p>We study a sufficiently general regret criterion for choosing between two probabilistic lotteries. For independent lotteries, the criterion is consistent with stochastic dominance and can be made transitive by a unique choice of the regret function. Together with additional (and intuitively meaningful) super-additivity property, the regret criterion resolves the Allais’ paradox including the cases were the paradox disappears, and the choices agree with the expected utility. This super-additivity property is also employed for establishing consistency between regret and stochastic dominance for dependent lotteries. Furthermore, we demonstrate how the regret criterion can be used in Savage’s omelet, a classical decision problem in which the lottery outcomes are not fully resolved. The expected utility cannot be used in such situations, as it discards important aspects of lotteries.</p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"117 ","pages":"Article 102807"},"PeriodicalIF":1.8,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50189498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"How averaging individual curves transforms their shape: Mathematical analyses with application to learning and forgetting curves","authors":"Jaap M.J. Murre","doi":"10.1016/j.jmp.2023.102816","DOIUrl":"https://doi.org/10.1016/j.jmp.2023.102816","url":null,"abstract":"<div><p>This paper demonstrates how averaging over individual learning and forgetting curves gives rise to transformed averaged curves. In an earlier paper (Murre and Chessa, 2011), we already showed that averaging over exponential functions tends to give a power function. The present paper expands on the analyses with exponential functions. Also, it is shown that averaging over power functions tends to give a log power function. Moreover, a general proof is given how averaging over logarithmic functions retains that shape in a specific manner. The analyses assume that the learning rate has a specific statistical distribution, such as a beta, gamma, uniform, or half-normal distribution. Shifting these distributions to the right, so that there are no low learning rates (censoring), is analyzed as well and some general results are given. Finally, geometric averaging is analyzed, and its limits are discussed in remedying averaging artefacts.</p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"117 ","pages":"Article 102816"},"PeriodicalIF":1.8,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50189499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A variation of the cube model for best–worst choice","authors":"Keivan Mallahi-Karai ,&nbsp;Adele Diederich","doi":"10.1016/j.jmp.2023.102820","DOIUrl":"https://doi.org/10.1016/j.jmp.2023.102820","url":null,"abstract":"<div><p>In this paper, we propose a dynamical model<span><span> for the best–worst choice task. The proposed model is a modification of the multi-episode Cube model proposed and studied in so-called (Mallahi-Karai and Diederich, 2019, 2021). This model postulates that best–worst choice (or more generally, ranking) task is the outcome of sequential choices made in a number of episodes. The underlying model is a multivariate Wiener process with drift issued from a point in the unit cube, where episodes are defined in terms of a sequence of </span>stopping times. This model can also be extended to an attention-switching framework in a standard way.</span></p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"117 ","pages":"Article 102820"},"PeriodicalIF":1.8,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138136298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On delineating forward- and backward-graded knowledge structures from fuzzy skill maps","authors":"Bochi Xu ,&nbsp;Jinjin Li ,&nbsp;Wen Sun ,&nbsp;Bo Wang","doi":"10.1016/j.jmp.2023.102819","DOIUrl":"https://doi.org/10.1016/j.jmp.2023.102819","url":null,"abstract":"<div><p>Forward-graded and backward-graded structures of knowledge are two important classes of knowledge structures. Spoto and Stefanutti (2020) establish necessary and sufficient conditions for skill maps to delineate these structures. We introduce fuzzy skills to describe varying levels of proficiency in skills and extend the theoretical results of Spoto and Stefanutti (2020) for delineating forward- and backward-graded knowledge structures using fuzzy skill maps. The paper establishes necessary and sufficient conditions for fuzzy skill maps to delineate a backward-graded simple closure space, a forward-graded knowledge space, and a forward-graded simple closure space. Furthermore, the competence-based local independence model (CBLIM) with fuzzy skills is introduced and its unidentifiability is discussed.</p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"117 ","pages":"Article 102819"},"PeriodicalIF":1.8,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91987533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"How do people build up visual memory representations from sensory evidence? Revisiting two classic models of choice","authors":"Maria M. Robinson,&nbsp;Isabella C. DeStefano,&nbsp;Edward Vul,&nbsp;Timothy F. Brady","doi":"10.1016/j.jmp.2023.102805","DOIUrl":"https://doi.org/10.1016/j.jmp.2023.102805","url":null,"abstract":"<div><p><span>In many decision tasks, we have a set of alternative choices and are faced with the problem of how to use our latent beliefs and preferences about each alternative to make a single choice. Cognitive and decision models typically presume that beliefs and preferences are distilled to a scalar latent strength for each alternative, but it is also critical to model how people use these latent strengths to choose a single alternative. Most models follow one of two traditions to establish this link. Modern psychophysics<span> and memory researchers make use of signal detection theory, assuming that latent strengths are perturbed by noise, and the highest resulting signal is selected. By contrast, many modern decision theoretic modeling and machine learning approaches use the softmax function (which is based on Luce’s choice axiom; Luce, 1959) to give some weight to non-maximal-strength alternatives. Despite the prominence of these two theories of choice, current approaches rarely address the connection between them, and the choice of one or the other appears more motivated by the tradition in the relevant literature than by theoretical or empirical reasons to prefer one theory to the other. The goal of the current work is to revisit this topic by elucidating which of these two models provides a better characterization of latent processes in </span></span><span><math><mi>m</mi></math></span>-alternative decision tasks, with a particular focus on memory tasks. In a set of visual memory experiments, we show that, within the same experimental design, the softmax parameter <span><math><mi>β</mi></math></span> varies across <span><math><mi>m</mi></math></span>-alternatives, whereas the parameter <span><math><msup><mrow><mi>d</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span><span> of the signal-detection model is stable. Together, our findings indicate that replacing softmax with signal-detection link models would yield more generalizable predictions across changes in task structure. More ambitiously, the invariance of signal detection model parameters across different tasks suggests that the parametric<span> assumptions of these models may be more than just a mathematical convenience, but reflect something real about human decision-making.</span></span></p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"117 ","pages":"Article 102805"},"PeriodicalIF":1.8,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50189496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Experiment-based calibration in psychology: Optimal design considerations","authors":"Dominik R. Bach","doi":"10.1016/j.jmp.2023.102818","DOIUrl":"https://doi.org/10.1016/j.jmp.2023.102818","url":null,"abstract":"<div><p>Psychological theories are often formulated at the level of latent, not directly observable, variables. Empirical measurement of latent variables ought to be valid. Classical psychometric validity indices can be difficult to apply in experimental contexts. A complementary validity index, termed retrodictive validity, is the correlation of theory-derived predicted scores with actually measured scores, in specifically designed calibration experiments. In the current note, I analyse how calibration experiments can be designed to maximise the information garnered and specifically, how to minimise the sample variance of retrodictive validity estimators. First, I harness asymptotic limits to analytically derive different distribution features that impact on estimator variance. Then, I numerically simulate various distributions with combinations of feature values. This allows deriving recommendations for the distribution of predicted values, and for resource investment, in calibration experiments. Finally, I highlight cases in which a misspecified theory is particularly problematic.</p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"117 ","pages":"Article 102818"},"PeriodicalIF":1.8,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022249623000743/pdfft?md5=67d69b64184de497db1e3d6b51cc26d6&pid=1-s2.0-S0022249623000743-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92039597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multi-Attribute Gain Loss (MAGL) method to predict choices","authors":"Ram Kumar Dhurkari","doi":"10.1016/j.jmp.2023.102804","DOIUrl":"10.1016/j.jmp.2023.102804","url":null,"abstract":"<div><p>A better method named MAGL (Multi-Attribute Gain Loss) is proposed to predict choices made by consumers in a multi-attribute setting. The MAGL method uses the tenets of prospect theory, Kauffman’s complexity theory, norm theory, and context-dependent choice theory. Since the choice processes are often found to be affected by the context or the choice set, the proposed MAGL method is able to model and predict the context-dependent choice behavior of consumers. The predictions of the MAGL method are useful to marketing/product managers in designing new products. The output of the MAGL method can be analyzed to determine which combination of attribute values is outperforming in a specific competitive market condition. A decision support system can be designed and developed for marketing/product managers where they can experiment by introducing, redesigning, or removing products and simulate the market share of various products for a similar consumer population.</p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"117 ","pages":"Article 102804"},"PeriodicalIF":1.8,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46212892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Structure of single-peaked preferences","authors":"Alexander Karpov","doi":"10.1016/j.jmp.2023.102817","DOIUrl":"10.1016/j.jmp.2023.102817","url":null,"abstract":"<div><p>The paper studies a variety of domains of preference orders that are closely related to single-peaked preferences. We develop recursive formulas for the number of single-peaked preference profiles and the number of preference profiles that are single-peaked on a circle. The number of Arrow’s single-peaked preference profiles is found for three, four, and five alternatives. Random sampling applications are discussed. For restricted tier preference profiles, a forbidden subprofiles characterization and an exact enumeration formula are obtained. It is also shown that each Fishburn’s preference profile is single-peaked on a circle preference profile, and Fishburn’s preference profiles cannot be characterized by forbidden subprofiles.</p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"117 ","pages":"Article 102817"},"PeriodicalIF":1.8,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135962830","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bayesian stopping","authors":"Igor Douven","doi":"10.1016/j.jmp.2023.102794","DOIUrl":"10.1016/j.jmp.2023.102794","url":null,"abstract":"<div><p>Stopping rules are criteria for determining when data collection can or should be terminated, allowing for inferences to be made. While traditionally discussed in the context of classical statistics, Bayesian<span> statisticians have also begun exploring stopping rules. Kruschke proposed a Bayesian stopping rule utilizing the concept of Highest Density Interval, where data collection can cease once enough probability mass (or density) accumulates in a sufficiently small region of parameter space. This paper presents an alternative to Kruschke’s approach, introducing the novel concept of Relative Importance Interval and considering the distribution of probability mass within parameter space. Using computer simulations, we compare these proposals to each other and to the widely-used Bayes factor-based stopping method. Our results do not indicate a single superior proposal but instead suggest that different stopping rules may be appropriate under different circumstances.</span></p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"116 ","pages":"Article 102794"},"PeriodicalIF":1.8,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42806782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A new type of polytomous surmise system","authors":"Bo Wang ,&nbsp;Jinjin Li ,&nbsp;Zhuoheng Chen ,&nbsp;Bochi Xu ,&nbsp;Xiaoxian Xie","doi":"10.1016/j.jmp.2023.102803","DOIUrl":"10.1016/j.jmp.2023.102803","url":null,"abstract":"<div><p>Doignon and Falmagne (1985) introduced a surmise system, which generalized the precedence relation, allowing multiple possible learning paths for an item. Heller (2021) took into account precedence relations on an extended set of (virtual) items and further generalized quasi-ordinal knowledge spaces to polytomous items. Wang et al. (2022) proposed CD-polytomous knowledge space and provided its corresponding polytomous surmise system. Following these developments and drawing upon the so-called extended polytomous knowledge structure, this paper presents two concepts: weak polytomous structure and extended surmise system. Via setting up a Galois connection, a one-to-one correspondence is established between the collection of all extended surmise functions and the collection of certain weak polytomous structures. This paper also comprehensively discusses the relationships among the precedence relations, the polytomous surmise systems, and the extended surmise systems.</p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"116 ","pages":"Article 102803"},"PeriodicalIF":1.8,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44134288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}