Journal of Mathematical Psychology最新文献_第5页

Mathematical self-determination theory II: Affine space representation 数学自决理论II：仿射空间表示

IF 1.8 4区心理学

Journal of Mathematical Psychology Pub Date : 2023-09-01 DOI: 10.1016/j.jmp.2023.102793

Ali Ünlü

{"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":null,"pages":null},"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}

引用次数: 1

Mathematical self-determination theory I: Real representation 数学自我决定理论1:实表示

IF 1.8 4区心理学

Journal of Mathematical Psychology Pub Date : 2023-09-01 DOI: 10.1016/j.jmp.2023.102792

Ali Ünlü

{"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":null,"pages":null},"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}

引用次数: 1

A characterization of two-agent Pareto representable orderings 双主体Pareto可表征排序的表征

IF 1.8 4区心理学

Journal of Mathematical Psychology Pub Date : 2023-09-01 DOI: 10.1016/j.jmp.2023.102806

Juan C. Candeal

引用次数: 0

Subjective expected utility with signed threshold 带符号阈值的主观期望效用

IF 1.8 4区心理学

Journal of Mathematical Psychology Pub Date : 2023-08-01 DOI: 10.1016/j.jmp.2023.102777

Yutaka Nakamura

引用次数: 0

Speeded response tasks with unpredictable deadlines 快速响应截止日期不可预测的任务

IF 1.8 4区心理学

Journal of Mathematical Psychology Pub Date : 2023-08-01 DOI: 10.1016/j.jmp.2023.102776

Steven P. Blurton , Jan Feifel , Matthias Gondan

{"title":"Speeded response tasks with unpredictable deadlines","authors":"Steven P. Blurton , Jan Feifel , Matthias Gondan","doi":"10.1016/j.jmp.2023.102776","DOIUrl":"10.1016/j.jmp.2023.102776","url":null,"abstract":"<div><p>In response time (RT) research, it is common to instruct participants to respond as fast and as accurately as possible, which is easily conceived as a contradiction. Participants may overcome this dilemma using a two-fold strategy, with (A) delaying their response until they feel confident that enough information has been sampled, and (B) scheduling the response right before the end of the response window to avoid omissions. The purpose of this strategy is to satisfy the contradictory requirements of the task instructions, but both (A) and (B) may yield a distorted picture of the processing times under investigation. We asked participants to discriminate random dot motion with fixed and variable deadlines for responding. With the exponentially distributed variable deadline, strategic responding is useless because it is impossible to schedule an optimal time point for the response. We present two analyses, a model-free approach that investigates the effect of an unpredictable deadline on standard RT measures, and the fit of an RT model testing for effects of the deadline on specific parameters. Compared to the fixed deadline, faster responses that were less variable across participants were observed under the variable deadline, suggesting that the new paradigm can reduce strategic responding. We demonstrate how to deal with omitted responses and conclude that variable deadlines are a promising tool to exert time pressure in RT experiments and potentially yield better estimates of the underlying processing times.</p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41246001","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}

引用次数: 0

The standard relationship between choice frequency and choice time is violated in multi-attribute preferential choice 多属性优先选择违反了选择频率与选择时间的标准关系

IF 1.8 4区心理学

Journal of Mathematical Psychology Pub Date : 2023-08-01 DOI: 10.1016/j.jmp.2023.102775

Guy E. Hawkins, Gavin Cooper, Jon-Paul Cavallaro

{"title":"The standard relationship between choice frequency and choice time is violated in multi-attribute preferential choice","authors":"Guy E. Hawkins, Gavin Cooper, 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":null,"pages":null},"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}

引用次数: 1

Sufficient conditions making lexicographic rules over the power set satisfy extensibility 幂集上词典编纂规则满足可扩展性的充分条件

IF 1.8 4区心理学

Journal of Mathematical Psychology Pub Date : 2023-08-01 DOI: 10.1016/j.jmp.2023.102780

Takashi Kurihara

{"title":"Sufficient conditions making lexicographic rules over the power set satisfy extensibility","authors":"Takashi Kurihara","doi":"10.1016/j.jmp.2023.102780","DOIUrl":"10.1016/j.jmp.2023.102780","url":null,"abstract":"<div><p>This study aims to clarify sufficient conditions for weak orders on the existing and null alternatives to make <em>leximax</em> and <em>leximin rules</em> over the power set satisfy <em>extensibility</em>. Each null alternative indicates ‘choosing not to choose the corresponding existing alternative’. Extensibility requires that a preference order of any two alternatives is equivalent to that of their singleton sets. Then, the leximax (alternatively, leximin) rule ranks any two subsets by comparing the same-ranked (null) alternatives in the two <em>transformed</em> subsets (which include the existing alternatives in each subset and the null alternatives of other existing alternatives) from top to bottom (alternatively, bottom to top). We then introduce the following two new properties: <em>Semi-inversion desirability</em> requires that a preference of any two null alternatives is not identical to that of their existing alternatives. <em>Consistent desirability</em> requires that a preference order of ‘a null alternative and a non-paired existing alternative’ is not identical to that of their paired (null) alternatives. We show that semi-inversion desirability implies extensibility, and the combination of semi-inversion desirability and consistent desirability is weaker than a traditional property, namely self-reflecting. Furthermore, we clarify the sufficient condition to make the leximax and leximin rules equivalent.</p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45102326","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}

引用次数: 0

Towards a competence-based polytomous knowledge structure theory 基于能力的多元论知识结构理论

IF 1.8 4区心理学

Journal of Mathematical Psychology Pub Date : 2023-08-01 DOI: 10.1016/j.jmp.2023.102781

Luca Stefanutti , Andrea Spoto , Pasquale Anselmi , Debora de Chiusole

引用次数: 0

A representation of interval orders through a bi-utility function 通过双效用函数表示区间阶

IF 1.8 4区心理学

Journal of Mathematical Psychology Pub Date : 2023-08-01 DOI: 10.1016/j.jmp.2023.102778

Yann Rébillé

引用次数: 2

Modelling constituent order despite symmetric associations in memory 尽管在内存中存在对称关联，但对组成顺序进行建模

IF 1.8 4区心理学

Journal of Mathematical Psychology Pub Date : 2023-08-01 DOI: 10.1016/j.jmp.2023.102774

Jeremy J. Thomas , Jeremy B. Caplan

引用次数: 0