Journal of Mathematical Psychology最新文献

{"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":"2023-09-09","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":"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":"2023-09-06","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":"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}

{"title":"Sparse attentional subsetting of item features and list-composition effects on recognition memory","authors":"Jeremy B. Caplan","doi":"10.1016/j.jmp.2023.102802","DOIUrl":"10.1016/j.jmp.2023.102802","url":null,"abstract":"<div><p><span>Although knowledge is extremely high-dimensional, human episodic memory performance appears extremely low-dimensional, focused largely on stimulus-features that distinguish list items from one another. A cognitively plausible way this tension could be addressed is if selective attention selects a small number of features from each item. I consider an ongoing debate about whether stronger items (better encoded) interfere more than weaker items (less well encoded) with probe items during old/new episodic recognition judgements. This is called the list-strength effect, concerning whether or not effects of encoding strength are larger in lists of mixed strengths than in pure lists of a single strength. Analytic derivations with Anderson’s (1970) matched filter model show how storing only a small subset of features within high-dimensional representations, and assuming those same subsets tend to reiterate themselves item-wise at test, can support high recognition performance. In the sparse regime, the model produces a list-strength effect that is small in magnitude, resembling previous findings of so-called </span>null list-strength effects. When the attended feature space is compact, such as for phonological features, attentional subsetting cannot be sparse. This introduces non-negligible cross-talk from other list items, producing a large-magnitude list-strength effect, similar to what is observed for the production effect (better recognition when reading aloud). This continuum-based account implies the existence of a continuous range of magnitudes of list-composition effects, including occasional inverted list-strength effects. This lays the foundation for propagating effects of task-relevant attention to sparse subsets of features through a broad range of models of memory behaviour.</p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"116 ","pages":"Article 102802"},"PeriodicalIF":1.8,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44228331","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":"Mathematical self-determination theory II: Affine space representation","authors":"Ali Ünlü","doi":"10.1016/j.jmp.2023.102793","DOIUrl":"10.1016/j.jmp.2023.102793","url":null,"abstract":"<div><p><span><span>Self-determination theory is a well-established theory of motivation. This theory provides for fundamental concepts related to human motivation, including self-determination. The mathematization of this theory has been envisaged in a series of two papers by the author. The first paper entitled “Mathematical self-determination theory I: Real representation” addressed the representation of the theory in reals. This second paper is in continuation of it. The representation of the first part allows to abstract the results in more general mathematical structures, namely, </span>affine spaces<span>. The simpler real representation is reobtained as a special instance. We take convexity as the pivotal starting point to generalize the whole exposition and represent self-determination theory in abstract affine spaces. This includes the affine space analogs of the notions of internal locus, external locus, and impersonal locus, of regulated and graded motivation, and self-determination. We also introduce polar coordinates in Euclidean affine motivation spaces to study self-determination on radial and angular line segments. We prove the distributivity of the </span></span>lattice<span> of general self-determination in the affine space formulation. The representation in an affine space is free in the choice of primitives. However, the different representations, in reals or affine, are shown to be unique up to canonical isomorphism. The aim of this paper is to extend on the results obtained in the first paper, thereby to further lay the mathematical foundations of self-determination motivation theory.</span></p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"116 ","pages":"Article 102793"},"PeriodicalIF":1.8,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42987897","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":"Mathematical self-determination theory I: Real representation","authors":"Ali Ünlü","doi":"10.1016/j.jmp.2023.102792","DOIUrl":"10.1016/j.jmp.2023.102792","url":null,"abstract":"<div><p><span>In two parts, MSDT1 this paper and MSDT2 the follow-up paper, we treat the topic of mathematical self-determination theory. MSDT1 considers the real representation, MSDT2 the affine space representation. The aim of the two papers is to lay the mathematical foundations of self-determination motivation theory. Self-determination theory was proposed by Deci and Ryan, which is a popular theory of motivation. The fundamental concepts are extrinsic and intrinsic motivation, amotivation, their type of regulation, locus of causality, and especially, self-determination. First, we give a geometric description of its concepts for the regulated case (no amotivation), as the unit 1-simplex. Thereby, we derive a symmetric definition of self-determination. Second, we extend the geometric description to the regulated and unregulated case, based on a more general ternary model, in internal motivation, external motivation, and amotivation. We define gradations of amotivation (and motivation), as 1-simplexes parallel to the unit 1-simplex. The ternary representation implies the types of strong, weak, and general self-determination, as partial orders on the motivation space. Third, we study the order, </span>lattice<span>, and algebraic properties of self-determination. In a version of polar coordinates, strong self-determination turns out to be a complete lattice<span> on angular line segments, weak self-determination is a complete lattice on radial line<span> segments, and general self-determination entails a complete lattice on the entire motivation space. In addition, the modified polar coordinates are employed to obtain necessary and sufficient conditions for strong, weak, and general self-determination. We propose measures for the strength of an ordinal dependency in self-determination, which are partial metrics on the motivation space.</span></span></span></p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"116 ","pages":"Article 102792"},"PeriodicalIF":1.8,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46293911","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 characterization of two-agent Pareto representable orderings","authors":"Juan C. Candeal","doi":"10.1016/j.jmp.2023.102806","DOIUrl":"10.1016/j.jmp.2023.102806","url":null,"abstract":"<div><p>Partial orders defined on a nonempty set <span><math><mi>X</mi></math></span> admitting a two-agent Pareto representation are characterized. The characterization is based upon the fulfillment of two axioms. The first one entails the existence, for any point <span><math><mrow><mi>x</mi><mo>∈</mo><mi>X</mi></mrow></math></span>, of a very particular decomposition of the points which are incomparable to <span><math><mi>x</mi></math></span>. The second one encodes a separability condition. Our approach is then applied to show that if the cardinality of <span><math><mi>X</mi></math></span> is, at most, 5, then a two-agent Pareto representation always exists whereas this need not be the case otherwise. The connection with the concept of the dimension of a poset is also discussed. Certain examples are also presented that illustrate the scope of our tools.</p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"116 ","pages":"Article 102806"},"PeriodicalIF":1.8,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46404460","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":"Subjective expected utility with signed threshold","authors":"Yutaka Nakamura","doi":"10.1016/j.jmp.2023.102777","DOIUrl":"https://doi.org/10.1016/j.jmp.2023.102777","url":null,"abstract":"<div><p>This paper generalizes subjective expected utility by incorporating signed threshold, whose positive (respectively, negative) value enhances (respectively, reduces) subjective expected utility of chosen alternative against unchosen one. It can be interpreted, for example, that positivity of the signed threshold reflects domination of rejoicing feeling against regret feeling. Since the signed threshold representation is a special case of skew-symmetric additive (SSA) representation, we prove that in addition to SSA axiomatization, restriction of probabilistic sophistication to pairs of acts which are regret-free separates subjective expected utility and signed threshold. It is assumed that regret-freeness is measured by monetary differences or ex post strength of preferences.</p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"115 ","pages":"Article 102777"},"PeriodicalIF":1.8,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49864109","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":"The standard relationship between choice frequency and choice time is violated in multi-attribute preferential choice","authors":"Guy E. Hawkins,&nbsp;Gavin Cooper,&nbsp;Jon-Paul Cavallaro","doi":"10.1016/j.jmp.2023.102775","DOIUrl":"10.1016/j.jmp.2023.102775","url":null,"abstract":"<div><p>Many decision making theories assume a principle of sequentially sampling decision-relevant evidence from the stimulus environment, where sampled evidence is dynamically accumulated toward a threshold to trigger a decision in favour of the threshold-crossing option. A core prediction of sequential sampling models is that options more likely to be chosen are chosen more quickly. This result has been empirically supported hundreds of times for low-level speeded perceptual decisions — the traditional domain of sequential sampling models. More recently, sequential sampling models have been generalised and applied to higher-level preferential, or value-based, decisions — decisions for which there is no objectively correct option. Preferential options are typically composed of multiple attributes, like a phone defined by its price, camera quality, memory capacity, and so on. Here, we show that decisions for such multi-attribute preferential options with defined features violate the core prediction of sequential sampling models: options more likely to be chosen are not chosen more quickly. We find this invariance across 4 data sets spanning multi-attribute choices made in unconstrained conditions, under time pressure, and for multi-attribute options with artificial or marketplace compositions. The result remains whether the relationship between choice frequency and choice time is inspected at the lower level of component attributes or the higher level of whole options. Our finding places critical constraints on the capacity to generalise sequential sampling models from low-level perceptual decisions to high-level multi-attribute preferential choice.</p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"115 ","pages":"Article 102775"},"PeriodicalIF":1.8,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41924256","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}