{"title":"A test of attribute normalization via a double decoy effect","authors":"Remi Daviet , Ryan Webb","doi":"10.1016/j.jmp.2022.102741","DOIUrl":"10.1016/j.jmp.2022.102741","url":null,"abstract":"<div><p>We report a “Double Decoy” experiment designed to separate two competing accounts of the asymmetric dominance effect. The experiment places an additional decoy alternative within the range of existing alternatives, which should leave choice behaviour unaltered if attributes are weighted by their range. Instead, we observe a decrease in the relative proportion of targets chosen, particularly for subjects who exhibited an initial decoy effect. We also observe considerably more variation in individual behaviour than expected. We therefore consider an alternative theory in which attributes values are compared with diminishing sensitivity (via divisive normalization) and assess its performance in an additional discrete choice experiment previously used in the discrete choice literature. We find that divisive normalization captures behaviour better than range normalization and the linear additive Logit model typically used in applied settings. We therefore propose divisive normalization as both a neuro-computational explanation for context effects and a useful empirical tool for applied researchers.</p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"113 ","pages":"Article 102741"},"PeriodicalIF":1.8,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47408056","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":"Semiorders and continuous Scott–Suppes representations. Debreu’s Open Gap Lemma with a threshold","authors":"A. Estevan","doi":"10.1016/j.jmp.2023.102754","DOIUrl":"https://doi.org/10.1016/j.jmp.2023.102754","url":null,"abstract":"","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"1 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"54597673","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":"Cultural consensus theory for two-dimensional location judgments","authors":"Maren Mayer , Daniel W. Heck","doi":"10.1016/j.jmp.2022.102742","DOIUrl":"10.1016/j.jmp.2022.102742","url":null,"abstract":"<div><p>Cultural consensus theory is a model-based approach for analyzing responses of informants when correct answers are unknown. The model provides aggregate estimates of the latent consensus knowledge at the group level while accounting for heterogeneity in informant competence and item difficulty. We develop a new version of cultural consensus theory for two-dimensional continuous judgments which are obtained when asking informants to locate a set of unknown sites on a geographic map. The new model is fitted using hierarchical Bayesian modeling. A simulation study shows satisfactory parameter recovery for realistic numbers of informants and items. We also assess the accuracy of the aggregate location estimates by comparing the new model against simply computing the unweighted average of the informants’ judgments. A simulation study shows that, due to weighing judgments by the inferred competence of the informants, cultural consensus theory provides more accurate location estimates than unweighted averaging. The new model also showed a higher accuracy in an empirical study in which individuals judged the location of 57 European cities on maps.</p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"113 ","pages":"Article 102742"},"PeriodicalIF":1.8,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47092091","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 statistical foundation for derived attention","authors":"Samuel Paskewitz , Matt Jones","doi":"10.1016/j.jmp.2022.102728","DOIUrl":"10.1016/j.jmp.2022.102728","url":null,"abstract":"<div><p><span>According to the theory of derived attention, organisms attend to cues with strong associations. Prior work has shown that – combined with a Rescorla–Wagner style learning mechanism – derived attention explains phenomena such as learned predictiveness, inattention to blocked cues, and value-based salience. We introduce a Bayesian derived attention model that explains a wider array of results than previous models and gives further insight into the principle of derived attention. Our approach combines Bayesian linear regression with the assumption that the associations of any cue with various outcomes share the same prior variance, which can be thought of as the inherent importance of that cue. The new model simultaneously estimates cue–outcome associations and prior variance through approximate Bayesian learning. A significant cue will develop large associations, leading the model to estimate a high prior variance and hence develop larger associations from that cue to novel outcomes. This provides a normative, statistical explanation for derived attention. Through simulation, we show that this Bayesian derived attention model not only explains the same phenomena as previous versions, but also </span>retrospective revaluation<span>. It also makes a novel prediction: inattention after backward blocking. We hope that further development of the Bayesian derived attention model will shed light on the complex relationship between uncertainty and predictiveness effects on attention.</span></p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"112 ","pages":"Article 102728"},"PeriodicalIF":1.8,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10004174/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9118519","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Nondistributivity of human logic and violation of response replicability effect in cognitive psychology","authors":"Masanao Ozawa , Andrei Khrennikov","doi":"10.1016/j.jmp.2022.102739","DOIUrl":"10.1016/j.jmp.2022.102739","url":null,"abstract":"<div><p>The aim of this paper is to promote quantum logic as one of the basic tools for analyzing human reasoning. We compare it with classical (Boolean) logic and highlight the role of violation of the distributive law for conjunction and disjunction. It is well known that nondistributivity is equivalent to incompatibility of logical variables — the impossibility to assign jointly the two-valued truth values to these variables. A natural question arises as to whether quantum logical nondistributivity in human logic can be tested experimentally. We show that testing the response replicability effect (RRE) in cognitive psychology is equivalent to testing nondistributivity — under the prevailing conjecture that the mental state update generated by observation is described as orthogonal projection of the mental state vector (the projective update conjecture of Wang and Busemeyer). A simple test of RRE is suggested. In contrast to the previous works in quantum-like modeling, we proceed in the state-dependent framework; in particular, distributivity, compatibility, and RRE are considered in a fixed mental state. In this framework, we improve the previous result on the impossibility to combine question order and response replicability effects by using (von Neumann–Lüders) projective measurements.</p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"112 ","pages":"Article 102739"},"PeriodicalIF":1.8,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44027357","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 note on the relation between the Contextual Fraction and CNT2","authors":"Víctor H. Cervantes","doi":"10.1016/j.jmp.2022.102726","DOIUrl":"https://doi.org/10.1016/j.jmp.2022.102726","url":null,"abstract":"<div><p>Contextuality (or lack thereof) is a property of systems of random variables. Among the measures of the degree of contextuality, two have played important roles. One of them, Contextual Fraction (<span><math><mtext>CNTF</mtext></math></span>) was proposed within the framework of the sheaf-theoretic approach to contextuality, and extended to arbitrary systems in the Contextuality-by-Default approach. The other, denoted <span><math><msub><mrow><mtext>CNT</mtext></mrow><mrow><mn>2</mn></mrow></msub></math></span>, was proposed as one of the measures within the Contextuality-by-Default approach. In this note, I prove that <span><math><mrow><mtext>CNTF</mtext><mo>=</mo><mn>2</mn><msub><mrow><mtext>CNT</mtext></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span> within a class of systems, called cyclic, that have played a prominent role in contextuality research.</p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"112 ","pages":"Article 102726"},"PeriodicalIF":1.8,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49856654","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":"Using diverging predictions from classical and quantum models to dissociate between categorization systems","authors":"Gunnar P. Epping, Jerome R. Busemeyer","doi":"10.1016/j.jmp.2022.102738","DOIUrl":"https://doi.org/10.1016/j.jmp.2022.102738","url":null,"abstract":"<div><p>Quantum probability theory has successfully provided accurate descriptions of behavior in the areas of judgment and decision making, and here we apply the same principles to two category learning tasks, one task using information-integration categories and the other using rule-based categories. Since information-integration categories lack verbalizable descriptions, unlike rule-based ones, we assert that an information-integration categorization decision results from an intuitive probabilistic reasoning system characterized by quantum probability theory, whereas a rule-based categorization decision results from a logical, rational probabilistic reasoning system characterized classical probability theory. In our experiment, participants learn to categorize simple, visual stimuli as members of either category S or category K during an acquisition phase, and then rate the likelihood on a scale of 0 to 5 that a stimulus belongs to one category and subsequently perform the same likelihood rating for the other category during a transfer phase. Following the principle of complementarity in quantum theory, we expect the category likelihood ratings to exhibit order effects in the information-integration task, but not in the rule-based task. In the information-integration task, we found definitive order effects in the likelihood ratings. But, in the rule-based task, we found that the order effects in the likelihood ratings are not significant.</p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"112 ","pages":"Article 102738"},"PeriodicalIF":1.8,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49856657","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 note on the relation between the Contextual Fraction and CNT2","authors":"Víctor H. Cervantes","doi":"10.1016/j.jmp.2022.102726","DOIUrl":"https://doi.org/10.1016/j.jmp.2022.102726","url":null,"abstract":"","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45361902","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":"Do cognitive and physical effort costs affect choice behavior similarly?","authors":"Li Xin Lim , Madison Fansher , Sébastien Hélie","doi":"10.1016/j.jmp.2022.102727","DOIUrl":"10.1016/j.jmp.2022.102727","url":null,"abstract":"<div><p>Performing an action often incurs a cost, such as exerting effort for a reward. Previous studies used the Effort Expenditure for Reward Task (EEfRT) to show devaluation of reward with physical effort. However, it is unclear if a similarly structured attentional task would produce a similar devaluation with cognitive effort. In the present work, we propose a new task called the “shell game task” (SGT) as a cognitive effort-based decision-making paradigm. Participants performed both the EEfRT and SGT in a within-subject design. Using computational models of choice behavior, we showed that effort cost induced by the variability of task demands in the SGT is similar to the effort cost from the existing EEfRT in the devaluation of a given outcome in action choice selection. This result suggests that effort cost may be a stable idiosyncratic trait across the two tasks and shows how computational approaches can be used to estimate and compare measures of effort. In addition, the results suggest that the SGT can be used as an alternative to the EEfRT with subject populations with motor deficits.</p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"112 ","pages":"Article 102727"},"PeriodicalIF":1.8,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48503811","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":"Assessment-based correct rates in learning spaces","authors":"Jürgen Heller","doi":"10.1016/j.jmp.2022.102740","DOIUrl":"10.1016/j.jmp.2022.102740","url":null,"abstract":"<div><p>The basic local independence model (BLIM) is the standard probabilistic model in knowledge structure theory. It assumes that the probability of a correct response to a problem is constant for all individuals that master the problem, and accordingly, for all individuals that do not master it, irrespective of the mastering of other problems. Recently published data on the problem correct rate as inferred from a response-based assessment of the mastering of the problem seem to contradict this assumption. The analysis presented in this paper, however, reveals that deviations from constancy in the observed direction are to be expected under the BLIM. They are mainly due to the inaccuracy inherent in any response-based assessment. The implications of these results for the empirical validation of the BLIM are discussed.</p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"112 ","pages":"Article 102740"},"PeriodicalIF":1.8,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49631882","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}