{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T06:55:32Z","timestamp":1790751332102,"version":"4.1.0"},"reference-count":61,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T00:00:00Z","timestamp":1790726400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Psychol."],"abstract":"<jats:p>Non-symbolic proportion judgments require relational information to be extracted from perceptual input, yet the computational principles governing the contribution of continuous visual magnitude remain unclear. The present study examined whether perceptual influences on proportion judgments vary with relational context and whether their contribution increases linearly with cue strength or is subject to functional constraints. Across four experiments, participants compared non-symbolic proportions while continuous perceptual magnitude was manipulated through area scaling without altering the underlying proportional relationships. Experiments 1 and 2 showed that unilateral enlargement and contraction both influenced proportion judgments, indicating that perceptual effects were not specific to a single direction of physical scaling. Experiment 3 further showed that performance varied according to the alignment between perceptual and relational information, with perceptually congruent conditions generally facilitating performance and incongruent conditions producing interference. Experiment 4 manipulated perceptual cue strength at two scaling levels and found that increasing cue magnitude did not produce proportional increases in behavioral influence; this constraint was more evident in response-time dynamics than in categorical accuracy. Hierarchical drift-diffusion modeling provided converging computational evidence: a model incorporating a bounded transformation of perceptual input showed better predictive performance than a purely linear integration model. Together, these findings indicate that non-symbolic proportion judgments are not fully insulated from continuous perceptual variation. Instead, perceptual information contributes to decision formation in a context-sensitive manner, and its influence is better characterized by a constrained computational framework than by unrestricted linear cue accumulation.<\/jats:p>","DOI":"10.3389\/fpsyg.2026.1904042","type":"journal-article","created":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T06:00:41Z","timestamp":1790748041000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["When more is not more: evidence for bounded perceptual-relational integration in non-symbolic proportion judgments"],"prefix":"10.3389","volume":"17","author":[{"given":"Qiang","family":"Wu","sequence":"first","affiliation":[{"name":"School of Psychology, Guizhou Normal University","place":["Guiyang, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Di","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Psychology, Guizhou Normal University","place":["Guiyang, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lei","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Literature and Communication, Qiannan Normal University for Nationalities","place":["Duyun, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liang Zhi","family":"Jia","sequence":"additional","affiliation":[{"name":"School of Psychology, Guizhou Normal University","place":["Guiyang, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yun","family":"Pan","sequence":"additional","affiliation":[{"name":"School of Psychology, Guizhou Normal University","place":["Guiyang, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1965","published-online":{"date-parts":[[2026,9,30]]},"reference":[{"key":"B1","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1037\/amp0000191","article-title":"Journal article reporting standards for quantitative research in psychology: The APA publications and communications board task force report.","volume":"73","author":"Appelbaum","year":"2018","journal-title":"Am. Psychol"},{"key":"B2","doi-asserted-by":"publisher","first-page":"e13305","DOI":"10.1111\/desc.13305","article-title":"No intrinsic number bias: Evaluating the role of perceptual discriminability in magnitude categorization.","volume":"26","author":"Aulet","year":"","journal-title":"Dev. Sci"},{"key":"B3","doi-asserted-by":"publisher","first-page":"1125925","DOI":"10.3389\/fpsyg.2023.1125925","article-title":"Visual adaptation reveals multichannel coding for numerosity.","volume":"14","author":"Aulet","year":"","journal-title":"Front. Psychol"},{"key":"B4","doi-asserted-by":"publisher","first-page":"390","DOI":"10.1016\/j.jml.2007.12.005","article-title":"Mixed-effects modeling with crossed random effects for subjects and items.","volume":"59","author":"Baayen","year":"2008","journal-title":"J. Mem. Lang"},{"key":"B5","doi-asserted-by":"publisher","first-page":"328","DOI":"10.3389\/fpsyg.2013.00328","article-title":"Random effects structure for testing interactions in linear mixed-effects models [Opinion].","volume":"4","author":"Barr","year":"2013","journal-title":"Front. Psychol."},{"key":"B6","doi-asserted-by":"publisher","first-page":"624","DOI":"10.1037\/0033-295x.108.3.624","article-title":"Conflict monitoring and cognitive control.","volume":"108","author":"Botvinick","year":"2001","journal-title":"Psychol. Rev"},{"key":"B7","doi-asserted-by":"publisher","first-page":"516","DOI":"10.1016\/j.jecp.2011.11.001","article-title":"Child proportional scaling: Is 1\/3=2\/6=3\/9=4\/12?","volume":"111","author":"Boyer","year":"2012","journal-title":"J. Exp. Child. Psychol"},{"key":"B8","doi-asserted-by":"publisher","first-page":"615","DOI":"10.1037\/a0039010","article-title":"Prompting children to reason proportionally: Processing discrete units as continuous amounts.","volume":"51","author":"Boyer","year":"2015","journal-title":"Dev. Psychol"},{"key":"B9","doi-asserted-by":"publisher","first-page":"1478","DOI":"10.1037\/a0013110","article-title":"Development of proportional reasoning: Where young children go wrong.","volume":"44","author":"Boyer","year":"2008","journal-title":"Dev. Psychol."},{"key":"B10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.18637\/jss.v080.i01","article-title":"brms: An R package for bayesian multilevel models using stan.","volume":"80","author":"B\u00fcrkner","year":"2017","journal-title":"J. Stat. Softw."},{"key":"B11","doi-asserted-by":"publisher","first-page":"e125","DOI":"10.1371\/journal.pbio.0040125","article-title":"Functional imaging of numerical processing in adults and 4-y-old children.","volume":"4","author":"Cantlon","year":"2006","journal-title":"PLoS Biol"},{"key":"B12","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1038\/nrn3136","article-title":"Normalization as a canonical neural computation.","volume":"13","author":"Carandini","year":"2011","journal-title":"Nat. Rev. Neurosci"},{"key":"B13","doi-asserted-by":"publisher","first-page":"1484","DOI":"10.1016\/j.visres.2011.04.012","article-title":"Visual attention: The past 25 years.","volume":"51","author":"Carrasco","year":"2011","journal-title":"Vision Res"},{"key":"B14","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1016\/j.cognition.2015.05.016","article-title":"Modeling the approximate number system to quantify the contribution of visual stimulus features.","volume":"142","author":"DeWind","year":"2015","journal-title":"Cognition"},{"key":"B15","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1038\/415429a","article-title":"Humans integrate visual and haptic information in a statistically optimal fashion.","volume":"415","author":"Ernst","year":"2002","journal-title":"Nature"},{"key":"B16","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1016\/j.tics.2004.02.002","article-title":"Merging the senses into a robust percept.","volume":"8","author":"Ernst","year":"2004","journal-title":"Trends Cogn. Sci"},{"key":"B17","doi-asserted-by":"publisher","first-page":"175","DOI":"10.3758\/bf03193146","article-title":"G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences.","volume":"39","author":"Faul","year":"2007","journal-title":"Behav. Res. Methods"},{"key":"B18","doi-asserted-by":"publisher","first-page":"641","DOI":"10.1146\/annurev-psych-122414-033645","article-title":"Sequential sampling models in cognitive neuroscience: Advantages, applications, and extensions.","volume":"67","author":"Forstmann","year":"2016","journal-title":"Annu. Rev. Psychol"},{"key":"B19","doi-asserted-by":"publisher","first-page":"1481","DOI":"10.1111\/j.1469-8986.2012.01461.x","article-title":"Continuous visual properties explain neural responses to nonsymbolic number.","volume":"49","author":"Gebuis","year":"","journal-title":"Psychophysiology"},{"key":"B20","doi-asserted-by":"publisher","first-page":"642","DOI":"10.1037\/a0026218","article-title":"The interplay between nonsymbolic number and its continuous visual properties.","volume":"141","author":"Gebuis","year":"","journal-title":"J. Exp. Psychol. Gen"},{"key":"B21","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/j.actpsy.2016.09.003","article-title":"Sensory-integration system rather than approximate number system underlies numerosity processing: A critical review.","volume":"171","author":"Gebuis","year":"2016","journal-title":"Acta. Psychol"},{"key":"B22","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1016\/B978-0-12-801637-4.00018-4","article-title":"Sensory integration theory: An alternative to the approximate number system","volume-title":"Continuous Issues in Numerical Cognition","author":"Gevers","year":"2016"},{"key":"B23","doi-asserted-by":"publisher","first-page":"741","DOI":"10.1136\/bmj.327.7417.741","article-title":"Simple tools for understanding risks: From innumeracy to insight.","volume":"327","author":"Gigerenzer","year":"2003","journal-title":"BMJ"},{"key":"B24","doi-asserted-by":"publisher","first-page":"923","DOI":"10.1080\/20445911.2016.1221828","article-title":"Congruency effects in dot comparison tasks: Convex hull is more important than dot area.","volume":"28","author":"Gilmore","year":"2016","journal-title":"J. Cogn. Psychol"},{"key":"B25","doi-asserted-by":"publisher","first-page":"535","DOI":"10.1146\/annurev.neuro.29.051605.113038","article-title":"The neural basis of decision making.","volume":"30","author":"Gold","year":"2007","journal-title":"Annu. Rev. Neurosci"},{"key":"B26","doi-asserted-by":"publisher","first-page":"665","DOI":"10.1038\/nature07246","article-title":"Individual differences in non-verbal number acuity correlate with maths achievement.","volume":"455","author":"Halberda","year":"2008","journal-title":"Nature"},{"key":"B27","doi-asserted-by":"publisher","first-page":"389","DOI":"10.3758\/bf03202431","article-title":"Is three greater than five: The relation between physical and semantic size in comparison tasks.","volume":"10","author":"Henik","year":"1982","journal-title":"Mem. Cognit"},{"key":"B28","doi-asserted-by":"publisher","first-page":"4652","DOI":"10.1523\/JNEUROSCI.0651-09.2009","article-title":"Notation-independent representation of fractions in the human parietal cortex.","volume":"29","author":"Jacob","year":"","journal-title":"J. Neurosci"},{"key":"B29","doi-asserted-by":"publisher","first-page":"1432","DOI":"10.1111\/j.1460-9568.2009.06932.x","article-title":"Tuning to non-symbolic proportions in the human frontoparietal cortex.","volume":"30","author":"Jacob","year":"","journal-title":"Eur. J. Neurosci"},{"key":"B30","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1016\/j.tics.2012.02.002","article-title":"Relating magnitudes: The brain\u2019s code for proportions.","volume":"16","author":"Jacob","year":"2012","journal-title":"Trends Cogn. Sci"},{"key":"B31","doi-asserted-by":"publisher","first-page":"101288","DOI":"10.1016\/j.cogpsych.2020.101288","article-title":"Modeling the interaction of numerosity and perceptual variables with the diffusion model.","volume":"120","author":"Kang","year":"2020","journal-title":"Cogn. Psychol"},{"key":"B32","doi-asserted-by":"publisher","first-page":"712","DOI":"10.1016\/j.tins.2004.10.007","article-title":"The bayesian brain: The role of uncertainty in neural coding and computation.","volume":"27","author":"Knill","year":"2004","journal-title":"Trends Neurosci"},{"key":"B33","doi-asserted-by":"publisher","first-page":"244","DOI":"10.1038\/nature02169","article-title":"Bayesian integration in sensorimotor learning.","volume":"427","author":"K\u00f6rding","year":"2004","journal-title":"Nature"},{"key":"B34","doi-asserted-by":"publisher","first-page":"e943","DOI":"10.1371\/journal.pone.0000943","article-title":"Causal inference in multisensory perception.","volume":"2","author":"K\u00f6rding","year":"2007","journal-title":"PLoS One"},{"key":"B35","doi-asserted-by":"publisher","first-page":"e164","DOI":"10.1017\/S0140525X16000960","article-title":"From \u201csense of number\u201d to \u201csense of magnitude\u201d: The role of continuous magnitudes in numerical cognition.","volume":"40","author":"Leibovich","year":"2017","journal-title":"Behav. Brain. Sci"},{"key":"B36","doi-asserted-by":"publisher","first-page":"6139","DOI":"10.1073\/pnas.1217854110","article-title":"Normalization is a general neural mechanism for context-dependent decision making.","volume":"110","author":"Louie","year":"2013","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"B37","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1037\/rev0000380","article-title":"A theory of perceptual number encoding.","volume":"130","author":"Lourenco","year":"2023","journal-title":"Psychol. Rev"},{"key":"B38","doi-asserted-by":"publisher","first-page":"1432","DOI":"10.1038\/nn1790","article-title":"Bayesian inference with probabilistic population codes.","volume":"9","author":"Ma","year":"2006","journal-title":"Nat. Neurosci"},{"key":"B39","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1016\/j.cogpsych.2015.01.006","article-title":"Fractions as percepts? Exploring cross-format distance effects for fractional magnitudes.","volume":"78","author":"Matthews","year":"2015","journal-title":"Cogn. Psychol"},{"key":"B40","doi-asserted-by":"publisher","first-page":"1656","DOI":"10.1111\/cogs.12419","article-title":"Fractions we cannot ignore: The nonsymbolic ratio congruity effect.","volume":"41","author":"Matthews","year":"2017","journal-title":"Cogn. Sci"},{"key":"B41","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1177\/0956797615617799","article-title":"Individual differences in nonsymbolic ratio processing predict symbolic math performance.","volume":"27","author":"Matthews","year":"2016","journal-title":"Psychol. Sci"},{"key":"B42","doi-asserted-by":"publisher","first-page":"740","DOI":"10.1111\/j.1467-9280.2007.01969.x","article-title":"Ratio abstraction by 6-month-old infants.","volume":"18","author":"McCrink","year":"2007","journal-title":"Psychol. Sci"},{"key":"B43","doi-asserted-by":"publisher","first-page":"e13043","DOI":"10.1111\/desc.13043","article-title":"More than the sum of its parts: Exploring the development of ratio magnitude versus simple magnitude perception.","volume":"24","author":"Park","year":"2021","journal-title":"Dev. Sci"},{"key":"B44","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1111\/j.1467-9280.2006.01720.x","article-title":"Numeracy and decision making.","volume":"17","author":"Peters","year":"2006","journal-title":"Psychol. Sci"},{"key":"B45","doi-asserted-by":"publisher","first-page":"547","DOI":"10.1016\/j.neuron.2004.10.014","article-title":"Tuning curves for approximate numerosity in the human intraparietal sulcus.","volume":"44","author":"Piazza","year":"2004","journal-title":"Neuron"},{"key":"B46","doi-asserted-by":"publisher","first-page":"983","DOI":"10.1016\/s0896-6273(04)00107-2","article-title":"Distributed and overlapping cerebral representations of number, size, and luminance during comparative judgments.","volume":"41","author":"Pinel","year":"2004","journal-title":"Neuron"},{"key":"B47","volume-title":"R: The R Project for Statistical Computing.","year":"2023"},{"key":"B48","doi-asserted-by":"publisher","first-page":"873","DOI":"10.1162\/neco.2008.12-06-420","article-title":"The diffusion decision model: Theory and data for two-choice decision tasks.","volume":"20","author":"Ratcliff","year":"2008","journal-title":"Neural. Comput"},{"key":"B49","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1016\/j.tics.2010.07.001","article-title":"Causal inference in perception.","volume":"14","author":"Shams","year":"2010","journal-title":"Trends Cogn. Sci"},{"key":"B50","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1016\/j.neuron.2013.07.007","article-title":"The expected value of control: An integrative theory of anterior cingulate cortex function.","volume":"79","author":"Shenhav","year":"2013","journal-title":"Neuron"},{"key":"B51","doi-asserted-by":"publisher","first-page":"909","DOI":"10.1037\/edu0000025","article-title":"Conceptual knowledge of fraction arithmetic.","volume":"107","author":"Siegler","year":"2015","journal-title":"J. Educ. Psychol."},{"key":"B52","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1016\/j.cogpsych.2011.03.001","article-title":"An integrated theory of whole number and fractions development.","volume":"62","author":"Siegler","year":"2011","journal-title":"Cogn Psychol"},{"key":"B53","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1016\/j.tics.2014.11.005","article-title":"Do humans make good decisions?","volume":"19","author":"Summerfield","year":"2015","journal-title":"Trends Cogn. Sci"},{"key":"B54","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/0010-0285(80)90005-5","article-title":"A feature-integration theory of attention.","volume":"12","author":"Treisman","year":"1980","journal-title":"Cogn. Psychol"},{"key":"B55","doi-asserted-by":"publisher","first-page":"1420","DOI":"10.1016\/j.cub.2008.08.042","article-title":"Behavioral and prefrontal representation of spatial proportions in the monkey.","volume":"18","author":"Vallentin","year":"2008","journal-title":"Curr. Biol"},{"key":"B56","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1037\/a0021765","article-title":"Hierarchical diffusion models for two-choice response times.","volume":"16","author":"Vandekerckhove","year":"2011","journal-title":"Psychol. Methods"},{"key":"B57","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1016\/j.tics.2003.09.002","article-title":"A theory of magnitude: Common cortical metrics of time, space and quantity.","volume":"7","author":"Walsh","year":"2003","journal-title":"Trends Cogn. Sci"},{"key":"B58","article-title":"Magnitudes, metaphors, and modalities: A theory of magnitude revisited","volume-title":"Oxford Handbook of Synesthesia","author":"Walsh","year":"2013"},{"key":"B59","first-page":"3571","article-title":"Asymptotic equivalence of bayes cross validation and widely applicable information criterion in singular learning theory.","volume":"11","author":"Watanabe","year":"2010","journal-title":"J. Machine Learn. Res"},{"key":"B60","doi-asserted-by":"publisher","first-page":"14","DOI":"10.3389\/fninf.2013.00014","article-title":"HDDM: Hierarchical bayesian estimation of the drift-diffusion model in python [methods].","volume":"7","author":"Wiecki","year":"2013","journal-title":"Front. Neuroinformatics"},{"key":"B61","doi-asserted-by":"publisher","first-page":"931","DOI":"10.1037\/0033-295x.111.4.939","article-title":"The neural basis of error detection: Conflict monitoring and the error-related negativity.","volume":"111","author":"Yeung","year":"2004","journal-title":"Psychol. Rev"}],"container-title":["Frontiers in Psychology"],"original-title":[],"link":[{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/fpsyg.2026.1904042\/full","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T06:00:43Z","timestamp":1790748043000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/fpsyg.2026.1904042\/full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,30]]},"references-count":61,"alternative-id":["10.3389\/fpsyg.2026.1904042"],"URL":"https:\/\/doi.org\/10.3389\/fpsyg.2026.1904042","relation":{},"ISSN":["1664-1078"],"issn-type":[{"value":"1664-1078","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,30]]},"article-number":"1904042"}}