[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81578-en":3,"doc-seo-81578-105":30,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},81578,962075006959,"Anda","https://ap-avatar.wpscdn.com/avatar/e0002397efbe92a78e?_k=1776741047341049297",8,"Research & Report","Minimal Decision Dynamics and Contextual Probability: A Quantum Tug-of-War Model","Decision making often depends on context in ways that classical probability cannot represent. The paper proposes a quantum-like extension of the Tug-of-War (QTOW) decision model to determine when such context dependence can be captured by a single minimal internal state. Using a qutrit internal state, conservation-preserving updates, and measurement-induced disturbance, the model unifies decision, learning, and probing within one coherent state space. KCBS-type probing contexts yield a witness of non-contextual classical non-embeddability, implying contextual probability as a compact resource signature.","arXiv :2601 . 10034v2 [ quant-ph] 9 Jul 2026  \nMinimal Decision Dynamics and Contextual Probability: A Quantum Tug-of-War Model  \nSong-Ju Kim  \nSOBIN Institute LLC, 3-38-7 Keyakizaka, Kawanishi, Hyogo 666-0145, Japan  \n[kim@sobin.org](kim@sobin.org)  \nAbstract  \nDecision making often exhibits context dependence that challenges classical probability theory. This paper develops a quantum-like extension of the Tug-of-War (QTOW) decision-making model to clarify when such context dependence can be represented by a single minimal internal state. The QTOW construction uses a qutrit internal state, conservation-preserving updates, and measurement-induced disturbance to model decision, learning, and probing operations within one coherent state space. Within this minimal representation, KCBS-type probing contexts can be constructed, yielding a witness of non-contextual classical non-embeddability. The main claim is not that quantum theory is uniquely or assumption-freely derived from decision making. Rather, a classical reconstruction of the same operation family requires additional contextual memory, history dependence, or an enlarged hidden-state representation. Thus, contextual probability appears as a resource signature of minimal decision dynamics, while quantum probability provides a compact, memory-efficient realization of this structure.  \nKeywords: Decision Making; Contextuality; Quantum Cognition; Human Intelligence; Natural Intelligence  \n1 Introduction  \nHuman decision making exhibits robust deviations from classical probability theory. A particularly simple and well-documented example is the question order effect: the probability assigned to a judgment depends systematically on the sequence in which questions are posed. For instance, when individuals are asked whether a given person is honest and whether the  \nsame person is competent, the joint and conditional response probabilities differ depending on which attribute is evaluated first [1, 2, 3] . Such order dependence directly contradicts classical probability theory, in which joint probabilities are invariant under permutation and measurement is assumed not to alter the underlying state.  \nRelated violations appear in the form of context dependence and failures of the law of total probability. Empirically, the probability of a response cannot always be decomposedas a weighted sum of conditional probabilities across mutually exclusive alternatives,  \nP (B) =X P (Ai)P (B | Ai) , (1)  \ni  \nindicating that conditioning on one judgment actively changes the cognitive context in which subsequent judgments are made [4, 5] . These effects suggest that human decision processes are not governed by a single, fixed probability space, but instead involve state changes induced by the act of evaluation itself.  \nOver the past two decades, these phenomena have motivated the development of quantum cognition, where the mathematical formalism of quantum theory—most notably Hilbert spaces and non-commuting observables—is employed to model cognitive processes [2, 6] . A substantial body of work has demonstrated that quantum-inspired models can successfully reproduce experimental data in psychology and decision science. However, a fundamental question remains unresolved: Why should quantum probability appear in decision making at all?  \nIn many existing approaches, the quantum formalism is introduced a priori as a modeling choice. Consequently, it has often been argued that the same behavioral data could, in principle, be explained by sufficiently complex classical models with hidden states or nonMarkovian dynamics [7] . This criticism has limited the interpretational force of quantum cognition, reducing it to a convenient—but not necessary—descriptive framework.  \nA particularly clear articulation of this concern appears in the work of Khrennikov, who emphasizes that quantum cognition should be understood as a theory of contextual probability, rather than as evidence for quantum physical pro","cbCaisTHhmoQH1pV","https://ap.wps.com/l/cbCaisTHhmoQH1pV","pdf",471490,5,1,47,"English","en",105,"# Introduction\n## From descriptive models to generative structure","[{\"question\":\"What problem does the paper address about classical probability in decision making?\",\"answer\":\"It addresses context dependence that produces order effects and violates classical assumptions such as invariant joint probabilities and the law of total probability. The work targets when those contextual effects can or cannot be embedded into a single classical probability space.\"},{\"question\":\"How does the QTOW model represent decision, learning, and probing?\",\"answer\":\"It uses a qutrit internal state with conservation-preserving update rules and measurement-induced disturbance. These mechanisms let multiple operations act within one coherent state space rather than separate probability models.\"},{\"question\":\"What is the main claim regarding quantum probability in decision dynamics?\",\"answer\":\"Quantum probability is not asserted to be uniquely or assumption-freely derived from decision making. Instead, reproducing the same operation family classically requires extra contextual memory, history dependence, or an enlarged hidden-state representation, so contextual probability functions as a resource signature.\"}]",1784174438,118,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":28},"minimal-decision-dynamics-and-contextual-probability-a-quantum-tug-of-war-model","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/minimal-decision-dynamics-and-contextual-probability-a-quantum-tug-of-war-model/81578/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-07-25","2026-07-16",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What problem does the paper address about classical probability in decision making?","Question",{"text":76,"@type":77},"It addresses context dependence that produces order effects and violates classical assumptions such as invariant joint probabilities and the law of total probability. The work targets when those contextual effects can or cannot be embedded into a single classical probability space.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does the QTOW model represent decision, learning, and probing?",{"text":81,"@type":77},"It uses a qutrit internal state with conservation-preserving update rules and measurement-induced disturbance. These mechanisms let multiple operations act within one coherent state space rather than separate probability models.",{"name":83,"@type":74,"acceptedAnswer":84},"What is the main claim regarding quantum probability in decision dynamics?",{"text":85,"@type":77},"Quantum probability is not asserted to be uniquely or assumption-freely derived from decision making. Instead, reproducing the same operation family classically requires extra contextual memory, history dependence, or an enlarged hidden-state representation, so contextual probability functions as a resource signature.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":93},[94,98,102,106,110,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":20,"slug":138},19,"General","general"]