[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81558-en":3,"doc-seo-81558-105":29,"detail-sidebar-cat-0-en-105":90},{"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":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},81558,549758146520,"Patrick","https://ap-avatar.wpscdn.com/avatar/80002397d8c0411e94?_k=1775819394049821470",8,"Research & Report","Explaining Human Choice Probabilities with Simple Vector Representations","Explains human choice behavior in a probabilistic hide-and-seek task using a geometric, vector-based construction. Choice frequencies are represented with vectors that encode probability matching and maximizing strategies for seeking, and an avoidance counterpart for hiding. The model defines probability antimatching as a vector reflection across the uniform distribution, then derives analogous minimizing and antimatching strategies. Fits participant frequencies with linear combinations of two basis vectors and applies the approach to up to seven rooms, attributing strategy diversity to changing weights.","arXiv :2511 .03643v3 [ q-bio .NC] 10 Jul 2026  \n Manuscript Submission  \nExplaining Human Choices with Simple Vector Representations  \nAn Investigation of Hiding and Seeking  \nPeter A. V. DiBerardino1 | Britt Anderson1,2  \n1 Dept. of Psychology,University of Waterloo,Waterloo, ON Canada | 2 Centre for Theoretical Neuroscience,University of Waterloo,Waterloo, ON Canada |  \n[Correspondence:](Correspondence: Britt Anderson britt@uwaterloo.ca)[ Britt Anderson britt@uwaterloo.ca](Correspondence: Britt Anderson britt@uwaterloo.ca)  \n[Received:](Received: 00 | Revised: 00 | Accepted: 00)[ 00](Received: 00 | Revised: 00 | Accepted: 00)[ |](Received: 00 | Revised: 00 | Accepted: 00)[ Revised:](Received: 00 | Revised: 00 | Accepted: 00)[ 00](Received: 00 | Revised: 00 | Accepted: 00)[ |](Received: 00 | Revised: 00 | Accepted: 00)[ Accepted:](Received: 00 | Revised: 00 | Accepted: 00)[ 00](Received: 00 | Revised: 00 | Accepted: 00)  \n[Funding:](Funding: NSERC)[ NSERC](Funding: NSERC)  \nKeywords: choice, probability matching, vector representations, computational model  \nWe formalize human choice behavior in a probabilistic hide-and-seek task. In our geometric construction, vectors represent participant choice frequencies as well as probability matching and maximizing strategies. We measured choice behavior not just in the well-studied scenario of pursuing an objective (seeking), but also the rarely studied scenario of avoiding consequences (hiding). We used our geometric construction to define the avoidance counterpart of probability matching, probability antimatching, as a vector reflection across the uniform distribution. Decomposing the behavior of participants when they were seeking into matching and maximizing components, we could mathematically derive the analogous antimatching and minimizing strategies for hiding.  \nParticipants did change their choice frequencies between hiding and seeking conditions. In both cases, we found that a linear combination of just two vectors did an excellent job of fitting participant choice frequencies: matching + maximizing for seeking, antimatching + minimizing for hiding. We could account for diversity in participant strategy usage by varying the coefficients of the two relevant basis strategy vectors. We successfully applied this model in scenarios of up to 7 rooms. We conclude that an apparent diversity of human conduct in stochastic environments can, in some cases, be explained by varying the weighting of two principle strategies: whether to match/antimatch or  \nmaximize/minimize.  \n, 2026;v0:1–30  \n[https://doi.org/10.1002/0000](https://doi.org/10.1002/0000) 1 of 30  \n1  Introduction  \nWe implicitly learn to exploit the statistical structure of our environments. We do this to build context-dependent conceptual structures (e.g. in language the transition probabilities between syllables are dependent on the language (Saffran, Aslin, & Newport, 1996)) . We do this to optimize the match between circumstance and action (this is the basis for reinforcement learning as a model for behavior (Sutton & Barto, 2018)) . It might be tempting to assume that the way we do this is by representing the underlying probability distributions directly. However, this account seems at odds with our computational and storage limitations, and all the probability fallacies that we are heir to (nicely reviewed by (Huang, Busemeyer, Ebelt, & Pothos, 2024) in their introduction) .  \nDespite these fallacies and limits we do seem to have the ability to track frequencies for modest numbers of options, suggesting some representation of the generating distribution. But this represention of the generating distribution cannot be the sole determinant of behavior, because the same person behaves differently in different circumstances with same underlying distribution, and different people behave differently in the same circumstance with the same underlying distribution. We propose this behavioral variety within and between individu","cbCaitn4yPAGRleV","https://ap.wps.com/l/cbCaitn4yPAGRleV","pdf",1015809,1,32,"English","en",105,"# Introduction\n## Probabilistic Structure and Behavioral Variety\n## Hide-and-Seek Setup and Roles\n## Prior Focus on Probability Matching\n## Maximizing vs Matching Illustration","[{\"question\":\"How does the paper represent human choice behavior in the hide-and-seek task?\",\"answer\":\"It uses a geometric construction where vectors represent participant choice frequencies and encode probability matching and maximizing strategies (for seeking) as well as avoidance strategies (for hiding).\"},{\"question\":\"What is probability antimatching in the context of hiding?\",\"answer\":\"Probability antimatching is defined as a vector reflection across the uniform distribution, serving as the avoidance counterpart to probability matching in the seeking condition.\"},{\"question\":\"How well does the proposed model fit participants’ behavior and what drives strategy diversity?\",\"answer\":\"A linear combination of two vectors fits participant choice frequencies well in both conditions, using matching + maximizing for seeking and antimatching + minimizing for hiding; diversity is explained by varying the coefficients (weights) of the two basis strategy vectors.\"}]",1784174308,81,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"explaining-human-choice-probabilities-with-simple-vector-representations","",{"@graph":35,"@context":84},[36,53,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/explaining-human-choice-probabilities-with-simple-vector-representations/81558/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"How does the paper represent human choice behavior in the hide-and-seek task?","Question",{"text":74,"@type":75},"It uses a geometric construction where vectors represent participant choice frequencies and encode probability matching and maximizing strategies (for seeking) as well as avoidance strategies (for hiding).","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"What is probability antimatching in the context of hiding?",{"text":79,"@type":75},"Probability antimatching is defined as a vector reflection across the uniform distribution, serving as the avoidance counterpart to probability matching in the seeking condition.",{"name":81,"@type":72,"acceptedAnswer":82},"How well does the proposed model fit participants’ behavior and what drives strategy diversity?",{"text":83,"@type":75},"A linear combination of two vectors fits participant choice frequencies well in both conditions, using matching + maximizing for seeking and antimatching + minimizing for hiding; diversity is explained by varying the coefficients (weights) of the two basis strategy vectors.","https://schema.org",{"og:url":51,"og:type":86,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":88,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":91},[92,96,100,104,109,114,119,122,127,130,134],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":101,"show_sort_weight":102,"slug":103},"Exam",70,"exam",{"id":105,"doc_module":4,"doc_module_name":45,"category_name":106,"show_sort_weight":107,"slug":108},5,"Comic",60,"comic",{"id":110,"doc_module":4,"doc_module_name":45,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":45,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":45,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":45,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":45,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":45,"category_name":136,"show_sort_weight":105,"slug":137},19,"General","general"]