Audiovisual congruency drives confidence in presence and absence

Reviewer #1 (Public review):

Porte et al. investigate how observers form confidence judgments about the presence vs absence of near-threshold audiovisual stimuli. In two psychophysical detection experiments, human participants judged whether a stimulus (visual, auditory, or audiovisual) was present or absent, reported amodal confidence, and then gave modality-specific detection and confidence ratings using a bidimensional scale. The authors report that audiovisual (AV) stimuli are detected more accurately than unimodal stimuli, but that multisensory stimulation does not improve metacognitive efficiency. Participants are more confident in absence than in presence judgments. They extend a previously proposed model to an audiovisual setting, assuming evidence is available only for presence and that absence is inferred via counterfactual detectability. Detection is modeled with a disjunctive integration rule across modalities, while confidence is explained by a combination of conjunctive (for presence) and disjunctive/negation-of-disjunction (for absence) rules.

There are several points I wish to have clarified, outlined below:

(1) Framing of bimodal vs unimodal detection

On p.3, the introduction states that "Adults typically show higher detection rates and faster reaction times for bimodal than for unimodal stimuli." This is broadly consistent with the literature, but as written, it obscures the fact that these effects depend critically on experimenter-defined stimulus strengths. It is trivial to construct cases where a strong unimodal stimulus is more detectable than a bimodal stimulus made of two very weak unimodal stimuli. If "bimodal" is understood as the co-presentation of two unimodal components matched in detectability, then Bayes-rule-based arguments indeed predict better detection for the bimodal case; how much better is theoretically interesting, but not quantified in this paper. There is an entire literature on the combination of two unimodal stimuli, which is not touched on. For a pertinent reference, see Ernst & Banks 2002. I recommend clarifying that the statement assumes comparable unimodal intensities.

(2) Relationship to signal detection theory and counterfactual perceptibility

In the introduction, the authors write, "If sensory evidence is only available for presence," motivating counterfactual perceptibility as a necessary ingredient to infer absence. However, standard signal detection theory (SDT) already provides a widely accepted framework in which a continuous internal response is present on both signal and noise (absent) trials, with absence corresponding to the noise distribution and decisions implemented by a criterion.

Thus, there is no logical need to invoke counterfactual perceptibility simply to define absence; rather, the Mazor-style framework adds an explicit belief model about detectability and an optimal stopping policy. It would strengthen the paper to more clearly state how the proposed model goes beyond SDT conceptually, acknowledge that SDT can account for presence/absence decisions without counterfactuals, and position the counterfactual account as a hypothesis about how observers actually compute absence/confidence, not as a necessity. One of the central claims of the paper is that detection in the case of absence requires counterfactual reasoning. The authors should demonstrate whether or not an SDT-based generative model can describe these amodal and uni- and bi-modal stimulus decisions. In such an SDT model, an SDT-based generative model in which the noise distribution is shared across conditions, and unimodal vs bimodal differences are captured by changes in the mean or variance of the signal+noise distribution.

(3) Confidence vs performance: is AV confidence special?

The paper's central claims about multisensory confidence and metacognition would be stronger if the authors showed that AV confidence deviates from what is expected given performance alone. From the reported results, AV accuracy is around 80%, with visual and auditory at about 60% and 40%, respectively. Given that confidence typically monotonically scales with accuracy, the first question is whether AV confidence is entirely explained by improved performance, or whether there is an additional multisensory contribution. A simple, informative analysis would be for each subject, plot mean confidence vs per cent correct for AV, V, A, and absent conditions, and to test whether AV confidence lies above the trend predicted by accuracy alone.

(4) Metacognitive measures: logistic regression slopes vs meta-d′/d′

In the "Multisensory effects on metacognitive performance" section, the authors define "metacognitive sensitivity" as the slope of a Bayesian logistic regression predicting accuracy from confidence. There is substantial literature showing that logistic-slope measures of metacognitive sensitivity are criterion-dependent and can be affected by both task and confidence criteria (for one example, see Rausch & Zehetleitner, 2017). In contrast, meta-d′/d′ was specifically developed to provide a bias-invariant measure of metacognitive efficiency. Though this, too, is dated (see Boundy-Singer et al., 2023). Given that the authors already estimate HMeta-d-based M-ratios, it is unclear why they rely on logistic regression slopes as their primary "metacognitive sensitivity" metric in Figure 4A. I suggest either replacing the logistic-slope metric with SDT-based measures (meta-d′, meta-d′/d′) or providing a clear justification for using logistic slopes, along with a discussion of their known limitations.

Additionally, Figure 3 reports M-ratios without showing the corresponding d′ or meta-d′ for judge-present vs judge-absent conditions. Presenting these would help contextualize the metacognitive efficiency results and clarify whether differences are driven mainly by changes in metacognitive sensitivity, changes in task performance, or both. The d' values per condition could be added to Figure 2A.

(5) Interpretation of confidence in absence vs presence

The authors emphasise that it is surprising subjects are more confident in absence than in presence judgments, both at amodal and modality-specific levels. However, Figure 2B suggests that absent responses are very accurate: absent is reported as present only in about 10% of absent trials, implying a high correct rejection rate. If confidence tracks outcome probability, higher confidence for absence may be at least partly expected. Before attributing this asymmetry primarily to counterfactual reasoning, it would be important to explicitly relate confidence to accuracy for hits, misses, false alarms, and correct rejections and show whether absence confidence remains elevated relative to presence after controlling for accuracy differences across judgment types and conditions. Without this, the interpretation that higher absence confidence is inherently "unexpected" seems overstated.

(6) Model: integration rules, confidence, and evidence strength

The modeling section extends the Mazor et al. ideal observer to two modality-specific sensors, with disjunctive integration for detection and then disjunctive vs conjunctive integration rules for confidence. I have a few comments.

First, the detection rule is disjunctive and is reported as a finding. However, the conclusion that detection relies on a disjunctive rule ("present if A or V") closely mirrors the task instructions-participants are explicitly told to respond "present" if they detect the stimulus in any modality. As such, this seems more like a sanity check than a novel empirical finding.

Relatedly, the conjunctive detection is a weak null. The conjunctive rule ("present only if both A and V") is behaviorally implausible given the task instructions. A more informative baseline would be an SDT-style scalar-evidence model (see comment 2), rather than a conjunctive rule that participants would have to actively violate the instructions to follow.

Second, confidence in the model is defined as the probability of being correct at the time of the detection decision. However, this implies a fixed amount of evidence at decision time unless additional mechanisms are invoked. This issue is well known in diffusion modeling (see Kiani et al. 2014) and deserves explicit discussion; otherwise, it is unclear how the model produces graded confidence from a bound-crossing rule alone.

Third, the authors do not consider a straightforward evidence-strength account of confidence. When both modalities indicate presence, there is, on average, more total sensory evidence than in unimodal trials, making correct decisions more likely and, under most frameworks, confidence higher. Likewise, weak evidence in both modalities can be stronger evidence for absence than moderate in one and weak in the other. Many of the patterns that motivate the presence-conjunctive/absence-disjunctive mix could arise from a model where confidence simply reflects the amount of evidence for the chosen option, without positing distinct logical integration rules for presence vs absence. As the authors note, purely disjunctive or purely conjunctive confidence rules fail to capture the trends in confidence reports in Figure 7, leading them to adopt a combined presence-conjunctive / absence-disjunctive rule. A more parsimonious alternative-that confidence scales with evidence magnitude and cross-modal agreement-should be explicitly considered and, ideally, implemented as a competing model.


Finally, if the model is intended as a good account of the data, it would be useful to report whether it also reproduces the metacognitive efficiency patterns (M-ratios) beyond the mean confidence patterns shown in Figures 7-8. At present, the model appears systematically over-confident, which should be acknowledged and quantified.

(7) Confidence asymmetry index (CAI) and modality weighting

The confidence asymmetry index (CAI) is defined as the difference between auditory and visual confidence on AV vs absent trials, and the authors report strong correlations between observed and simulated CAI across participants. They interpret this as evidence that subjects place different weights on auditory vs visual signals. Several questions arise. First, does CAI capture asymmetries beyond what is expected from accuracy differences between modalities and conditions? Second, because the simulated data are generated from model fits to the observed data, a correlation between observed and simulated CAI is expected: the model is built to reproduce the individual patterns it is then compared to. A stronger test would compare CAI from data simulated with modality-specific belief parameters, versus CAI from data simulated with constrained equal belief parameters (same θs). Relatedly, the paper would benefit from a plot showing the distribution of θs for A and V- present stimuli across subjects. These values could also be related to unimodal sensitivity measured in the calibration/training phases. A natural prediction is that higher unimodal sensitivity should correspond to higher belief parameters for presence.

Reviewer #2 (Public review):

Summary:

In this study, across two experiments, the authors wrestle with the question: What is the profile of confidence judgments in presence/absence decisions for audiovisual stimuli? After thresholding observers to 50% target detection rates in each modality, the authors conducted one experiment that included 75% target presence (spread equally across bimodal, auditory, and visual targets) and one experiment with 50% overall target presence. Results showed that, overall, detection performance was higher for audiovisual stimuli compared to unimodal ones, and that a recent model for stimulus detection could be extended to this multisensory scenario. By incorporating a disjunctive rule for absence judgments and a conjunctive rule for presence judgments, the model was able to qualitatively reproduce some of the trends observed in the human data regarding confidence.

Strengths:

(1) The paper makes novel contributions to the study of multisensory confidence judgments for yes/no target detection.

(2) The paper further extends the use of a leading model of stimulus detection (from Mazor et al., 2025).

(3) Pre-registration of the study was implemented, and the code is publicly available (although the GitLab link requires registration to access the materials).

(4) One of the empirical results (higher confidence for absence compared to presence judgments) is especially interesting, contributing another empirical finding to a very mixed literature on this topic (as the authors note).

Weaknesses:

(1) Page 5 - I have concerns about the use of the equal-variance model from Signal Detection Theory to analyze the data. For example, the authors should read the recent paper by Miyoshi, Rahnev, and Lau in iScience, found at this link: https://www.cell.com/iscience/fulltext/S2589-0042(26)00373-1. In this paper, the authors note how the equal variance model should be used with caution in yes/no detection tasks, since the variances of the "stimulus present" and "stimulus absent" distributions are often different from one another. In a revision, I highly recommend that the authors explicitly discuss this paper and review whether the assumptions for the equal-variance model have been met (e.g., since they have confidence data, one way to do this would be to evaluate if the slope of the line in zROC space differs from 1). The authors may also want to incorporate methods from this iScience paper into the current manuscript, or potentially move to using an unequal variance SDT model and compute d'a and c'a.

(2) Related to the computation/measurement of the response criterion, the authors note on page 18 in the Methods that for Experiment 1, signals are actually present on 75% of trials, since a bimodal stimulus is present on 25% of trials, the visual circle only occurs on 25% of trials, the sinusoidal tone occurs on 25% of trials, and then only noise is present on 25% of trials. Did the authors have any a priori hypotheses about the response criteria that participants would exhibit in Experiment 1, considering the unbalanced target presentation rate in this task? Also, in Experiment 2, what did it mean to equate target present and target absent trials? Is it that they broke 50% target present trials down into 16.67% bimodal targets, 16.67% visual targets, and 16.67% auditory targets? A few more details would be good to explicitly note for those trying to replicate the task.

(3) It is important to plot the individual data for Figure 2. If the authors didn't match detection performance for the visual and auditory modalities, it would be good to see the individual data to know why. Is it that the thresholding procedure didn't work for some of the participants in the visual modality, and that's why the "yes" response rate is (on average) ~60% or higher across the two experiments? Similarly, in the auditory domain, do the authors have participants that are at floor? Or is it simply that the staircases failed to successfully target 50% detection on average?

(4) The authors mentioned that data were collected on the Prolific platform. What checks did they conduct to ensure that this data wasn't produced by bots? There are recent high-profile publications in PNAS and Behavioral Research Methods that indicate how online data collection is problematic (e.g., https://www.pnas.org/doi/10.1073/pnas.2535585123 and https://link.springer.com/article/10.3758/s13428-025-02852-7). What analyses or quality checks are there to ensure that humans were the ones completing the task?

(5) Page 7 - Since confidence was collected on a continuous scale, the authors should say a bit more about how they were able to compute measures of metacognitive efficiency. My understanding is that to compute meta-d', the data has to be binned. How was the binning implemented? With whatever bin size the authors chose, would it make any difference to the results if they changed the number of the bins in the analysis?

(6) Page 8 - Is there a prior precedent for using slope of the Bayesian logistic regression predicting accuracy from confidence as a measure of metacognitive sensitivity? If so, can the authors cite those papers as a reference? If not, can they place this analysis within the context of other measures of metacognitive sensitivity that exist? (meta-d', AUROC (Type 2), etc.)

(7) Page 8 - Another one of the results on page 8 is worth reflecting further upon: the authors note how in Experiment 1, no credible difference was found between unimodal and bimodal trials (DeltaM = -0.25 [-0.59, 0.10]), but in Experiment 2, "we observed higher metacognitive efficiency in unimodal compared to bimodal trials (DeltaM = -0.28 [-0.54, -0.02]. Those DeltaM values are nearly identical, so without a power analysis motivating the number of participants the authors collected, how certain are they that the results from these two experiments are really that distinct? It reminds me a bit of the Andrew Gelman blog post, "The difference between significance and non-significance is not significant".

(8) Is there any way to look at whether the presence of multisensory hallucinations (or perhaps that word is too strong, and we should simply consider them miscategorizations) increased as the task progressed? That is, the authors have repeated presentations of audiovisual stimuli for at least some percentage of the trials. Since the percentages for auditory stimuli being correctly categorized as auditory are at 85% in Experiment 1 and 79% in Experiment 2, were the trials where they miscategorized these stimuli equally spread throughout the task? Or did they come later in the experiment, after being repeatedly exposed to multisensory trials?

(9) Would the authors obtain the same results if they got rid of the amodal confidence judgment in their task, and simply had participants report the bimodal confidence following the presence/absence judgment? Part of the reason for asking this is that, according to page 11, the model is only fitted to amodal detection accuracy and response time data. This surprised me. I would have expected that the bimodal confidence would provide more useful information for the model fit. The authors should further explain this rationale in the paper. It seems odd to me to have the multisensory confidence ratings and not have them play a central role in the modeling work.

(10) In Figure 6, it appears the model is a bit off in its estimate of auditory responses (panel B, E) in the AV condition. Do the authors have any intuitions about why this might be happening?

(11) The authors talk about how the model is reproducing effects in the human data, but there's no systematic comparison, quantitatively, of how the two things relate. The authors should include some quantitative measure that reflects this.

(12) Related to this, I am not sure I agree with the characterization in Figure 7 that "when confidence followed a disjunctive rule, the model failed to capture important aspects of the data. On the other hand, when confidence followed a conjunctive rule, it reproduced confidence in presence judgments but failed to capture variability in confidence ratings for absence judgments." What, quantitatively, is the basis of this claim? This applies to Figure 8, too. I am not clear how, specifically, and quantitatively, the authors are justifying their claims about model fits. I don't think the confidence asymmetry index in Figure 8 is enough to quantify the quality of the model fitting procedure.

(13) Is there any chance the higher metacognitive efficiency for auditory trials is simply driven by differences in the d' values across the modalities? It might be good to probe this effect further.

(14) Lastly, I think it would be interesting to look at how instructions about modality-specific attention could modulate these findings, in terms of how unimodal (unimodal visual, unimodal auditory) or bimodal attention might modulate these effects. This is an idea for future work.

Reviewer #3 (Public review):

Summary:

This study used a pre-registered novel behavioural paradigm and computational modelling to investigate multi-sensory influences on detection and confidence. Participants performed amodal detection of auditory and visual stimuli (indicating that a stimulus was there when either an auditory stimulus or a visual stimulus or both were present), followed by amodal and unimodal confidence ratings. Detection was higher when both stimuli were present, and the presence of one modality increased the confidence in the presence of the other modality. In contrast to previous detection studies, confidence was higher for absent than for present judgements, but metacognitive efficiency was higher for present judgements. Metacognitive sensitivity was higher for bimodal stimuli, but this was not the case for metacognitive efficiency, suggesting that the sensitivity might be driven by first-order performance. The computational model showed that both detection and confidence in absence followed a disjunctive evidence integration rule, while confidence in presence followed a conjunctive integration rule.

Strengths:

The paper has several major strengths. Firstly, it addresses a novel research question using an innovative and well-controlled paradigm. Furthermore, the paradigm and analyses were pre-registered, and all effects that were interpreted were replicated in two independent samples. Finally, the paper uses an advanced computational model to capture counterintuitive patterns in the data.

Weaknesses:

The major weakness of the paper is the narrative structure. It is not always clear how the different analyses relate to the main research question. Many different effects are reported in terms of detection accuracy, bias, confidence and metacognition, as well as cross-modal and unimodal versus bimodal effects. It would help readability if the paper were streamlined in terms of the research question that is being answered, which I believe is specifically about multimodal absence judgements. Relatedly, for a reader not intimately familiar with the metacognition literature, the difference between MRatio, metacognitive sensitivity and metacognitive efficiency is not obvious. It would be good to clarify this more in the manuscript.

In general, the conclusions drawn by the authors seem to be supported by the results. However, I was missing quantitative model comparisons between the conjunctive and the disjunctive models and an explanation of why the models systematically overestimated the confidence ratings. Furthermore, the 'perceptual multisensory interference' section reports on very interesting effects, but these are not supported by statistical tests in the main text. It would help to assess the strength of the claims if the statistical evidence in favour of these claims were presented together in the main text.

One other concern is that in real-world multi-sensory perception, such as the mosquito example in the introduction, the auditory and visual signals have a strong natural association, which means that if you hear the auditory signal, you expect that you will see the visual signal soon and vice versa. As far as I understood, this association was not present in the current paradigm, which might influence the type of effects that one would expect to see.

Author response:

Reviewer 1:

Porte et al. investigate how observers form confidence judgments about the presence vs absence of near-threshold audiovisual stimuli. In two psychophysical detection experiments, human participants judged whether a stimulus (visual, auditory, or audiovisual) was present or absent, reported amodal confidence, and then gave modality-specific detection and confidence ratings using a bidimensional scale. The authors report that audiovisual (AV) stimuli are detected more accurately than unimodal stimuli, but that multisensory stimulation does not improve metacognitive efficiency. Participants are more confident in absence than in presence judgments. They extend a previously proposed model to an audiovisual setting, assuming evidence is available only for presence and that absence is inferred via counterfactual detectability. Detection is modeled with a disjunctive integration rule across modalities, while confidence is explained by a combination of conjunctive (for presence) and disjunctive/negation-of-disjunction (for absence) rules.

We thank the reviewer for thoroughly evaluating our work.

There are several points I wish to have clarified, outlined below:

(1) Framing of bimodal vs unimodal detection

On p.3, the introduction states that "Adults typically show higher detection rates and faster reaction times for bimodal than for unimodal stimuli." This is broadly consistent with the literature, but as written, it obscures the fact that these effects depend critically on experimenter-defined stimulus strengths. It is trivial to construct cases where a strong unimodal stimulus is more detectable than a bimodal stimulus made of two very weak unimodal stimuli. If "bimodal" is understood as the co-presentation of two unimodal components matched in detectability, then Bayes-rule-based arguments indeed predict better detection for the bimodal case; how much better is theoretically interesting, but not quantified in this paper. There is an entire literature on the combination of two unimodal stimuli, which is not touched on. For a pertinent reference, see Ernst & Banks 2002. I recommend clarifying that the statement assumes comparable unimodal intensities.

We will clarify that when discussing bimodal stimuli, we mean the co-presentation of two unimodal stimuli of similar intensity. We will add references to the literature during discrimination tasks that have shown that multisensory cue-combination followed Bayes rule integration (e.g., Ernst & Banks, 2002; Battaglia et al., 2003; Alais & Burr, 2004) and clarify in which ways our work differs from this rich body of work and provides novel contributions.

(2) Relationship to signal detection theory and counterfactual perceptibility

In the introduction, the authors write, "If sensory evidence is only available for presence," motivating counterfactual perceptibility as a necessary ingredient to infer absence. However, standard signal detection theory (SDT) already provides a widely accepted framework in which a continuous internal response is present on both signal and noise (absent) trials, with absence corresponding to the noise distribution and decisions implemented by a criterion. Thus, there is no logical need to invoke counterfactual perceptibility simply to define absence; rather, the Mazor-style framework adds an explicit belief model about detectability and an optimal stopping policy. It would strengthen the paper to more clearly state how the proposed model goes beyond SDT conceptually, acknowledge that SDT can account for presence/absence decisions without counterfactuals, and position the counterfactual account as a hypothesis about how observers actually compute absence/confidence, not as a necessity.

One of the central claims of the paper is that detection in the case of absence requires counterfactual reasoning. The authors should demonstrate whether or not an SDT-based generative model can describe these amodal and uni- and bi-modal stimulus decisions. In such an SDT model, an SDT-based generative model in which the noise distribution is shared across conditions, and unimodal vs bimodal differences are captured by changes in the mean or variance of the signal+noise distribution.

We will clarify that our framework explains how absence judgments (and related confidence) are formed, and what it adds to SDT models, including the reproduction of reaction times and a normative explanation of criterion placement (results about RTs are available in the supplementary materials).We will also run additional model comparisons assessing how an SDT-based generative model performs compared to our Bayesian model based on counterfactual perceivability.

(3) Confidence vs performance: is AV confidence special?

The paper's central claims about multisensory confidence and metacognition would be stronger if the authors showed that AV confidence deviates from what is expected given performance alone. From the reported results, AV accuracy is around 80%, with visual and auditory at about 60% and 40%, respectively. Given that confidence typically monotonically scales with accuracy, the first question is whether AV confidence is entirely explained by improved performance, or whether there is an additional multisensory contribution. A simple, informative analysis would be for each subject, plot mean confidence vs per cent correct for AV, V, A, and absent conditions, and to test whether AV confidence lies above the trend predicted by accuracy alone.

This is an excellent suggestion, and we will conduct the proposed analysis.

(4) Metacognitive measures: logistic regression slopes vs meta-d′/d′

In the "Multisensory effects on metacognitive performance" section, the authors define "metacognitive sensitivity" as the slope of a Bayesian logistic regression predicting accuracy from confidence. There is substantial literature showing that logistic-slope measures of metacognitive sensitivity are criterion-dependent and can be affected by both task and confidence criteria (for one example, see Rausch & Zehetleitner, 2017). In contrast, meta-d′/d′ was specifically developed to provide a bias-invariant measure of metacognitive efficiency. Though this, too, is dated (see Boundy-Singer et al., 2023). Given that the authors already estimate HMeta-d-based M-ratios, it is unclear why they rely on logistic regression slopes as their primary "metacognitive sensitivity" metric in Figure 4A. I suggest either replacing the logistic-slope metric with SDT-based measures (meta-d′, meta-d′/d′) or providing a clear justification for using logistic slopes, along with a discussion of their known limitations.

Additionally, Figure 3 reports M-ratios without showing the corresponding d′ or meta-d′ for judge-present vs judge-absent conditions. Presenting these would help contextualize the metacognitive efficiency results and clarify whether differences are driven mainly by changes in metacognitive sensitivity, changes in task performance, or both. The d' values per condition could be added to Figure 2A.

All typical measures of metacognitive sensitivity are influenced by metacognitive bias and task performance to some extent, and none of them is a pure measure of type-2 sensitivity (e.g., see Rahnev, 2025). Here, we chose logistic regression because it enables modeling interactions with other predictors in a factorial design with a limited number of trials.

We will clarify the limitations of metacognitive sensitivity measures and better explain why we then used Mratio to estimate metacognitive performance while controlling for underlying task performance.

Thank you for this suggestion. We will add the d’ values per condition to Figure 2A.

(5) Interpretation of confidence in absence vs presence

The authors emphasise that it is surprising subjects are more confident in absence than in presence judgments, both at amodal and modality-specific levels. However, Figure 2B suggests that absent responses are very accurate: absent is reported as present only in about 10% of absent trials, implying a high correct rejection rate. If confidence tracks outcome probability, higher confidence for absence may be at least partly expected. Before attributing this asymmetry primarily to counterfactual reasoning, it would be important to explicitly relate confidence to accuracy for hits, misses, false alarms, and correct rejections and show whether absence confidence remains elevated relative to presence after controlling for accuracy differences across judgment types and conditions. Without this, the interpretation that higher absence confidence is inherently "unexpected" seems overstated.

This higher confidence for absence judgments than for presence judgments was observed while controlling for response accuracy. We will clarify this in the main text.

(6) Model: integration rules, confidence, and evidence strength

The modeling section extends the Mazor et al. ideal observer to two modality-specific sensors, with disjunctive integration for detection and then disjunctive vs conjunctive integration rules for confidence. I have a few comments.

First, the detection rule is disjunctive and is reported as a finding. However, the conclusion that detection relies on a disjunctive rule ("present if A or V") closely mirrors the task instructions-participants are explicitly told to respond "present" if they detect the stimulus in any modality. As such, this seems more like a sanity check than a novel empirical finding. Relatedly, the conjunctive detection is a weak null. The conjunctive rule ("present only if both A and V") is behaviorally implausible given the task instructions. A more informative baseline would be an SDT-style scalar-evidence model (see comment 2), rather than a conjunctive rule that participants would have to actively violate the instructions to follow.

Second, confidence in the model is defined as the probability of being correct at the time of the detection decision. However, this implies a fixed amount of evidence at decision time unless additional mechanisms are invoked. This issue is well known in diffusion modeling (see Kiani et al. 2014) and deserves explicit discussion; otherwise, it is unclear how the model produces graded confidence from a bound-crossing rule alone.

Third, the authors do not consider a straightforward evidence-strength account of confidence. When both modalities indicate presence, there is, on average, more total sensory evidence than in unimodal trials, making correct decisions more likely and, under most frameworks, confidence higher. Likewise, weak evidence in both modalities can be stronger evidence for absence than moderate in one and weak in the other. Many of the patterns that motivate the presence-conjunctive/absence-disjunctive mix could arise from a model where confidence simply reflects the amount of evidence for the chosen option, without positing distinct logical integration rules for presence vs absence. As the authors note, purely disjunctive or purely conjunctive confidence rules fail to capture the trends in confidence reports in Figure 7, leading them to adopt a combined presence-conjunctive/absence-disjunctive rule. A more parsimonious alternative-that confidence scales with evidence magnitude and cross-modal agreement-should be explicitly considered and, ideally, implemented as a competing model. Finally, if the model is intended as a good account of the data, it would be useful to report whether it also reproduces the metacognitive efficiency patterns (M-ratios) beyond the mean confidence patterns shown in Figures 7-8. At present, the model appears systematically over-confident, which should be acknowledged and quantified.

Indeed, the disjunctive rule was expected, given our design; we will clarify this. As mentioned above, we will directly compare the results of our current model with those of a more traditional SDT-based generative model, as suggested by the reviewer.

Contrary to a classical drift diffusion model, the model does not assume a fixed decision boundary, but derives an optimal stopping policy per time point and belief state. As a result, and depending on beliefs about perceptual evidence and the temporal discounting factor, optimal decision boundaries can be asymmetric and may collapse asymmetrically toward 0. Furthermore, given the asymmetry in the information value between sensor activations and inactivations, and differences in the information value of sensor activations of the two modalities, boundary crossing can lead to belief states that are far or close to the decision boundary, depending on the nature of the evidence. Together, even without an explicit modeling of post-decisional evidence, the model can account for variability in the total accumulated evidence at decision time.

From our understanding, the proposed alternative is equivalent to our current model, in which confidence scales with evidence magnitude.

The model was not fitted to confidence data, which could explain its overall overconfidence. To further test our model, we will assess its ability to reproduce patterns of metacognitive efficiency (M-ratios).

(7) Confidence asymmetry index (CAI) and modality weighting

The confidence asymmetry index (CAI) is defined as the difference between auditory and visual confidence on AV vs absent trials, and the authors report strong correlations between observed and simulated CAI across participants. They interpret this as evidence that subjects place different weights on auditory vs visual signals. Several questions arise. First, does CAI capture asymmetries beyond what is expected from accuracy differences between modalities and conditions? Second, because the simulated data are generated from model fits to the observed data, a correlation between observed and simulated CAI is expected: the model is built to reproduce the individual patterns it is then compared to. A stronger test would compare CAI from data simulated with modality-specific belief parameters, versus CAI from data simulated with constrained equal belief parameters (same θs). Relatedly, the paper would benefit from a plot showing the distribution of θs for A and V- present stimuli across subjects. These values could also be related to unimodal sensitivity measured in the calibration/training phases. A natural prediction is that higher unimodal sensitivity should correspond to higher belief parameters for presence.

The model was not fitted to either the modality-specific responses or the confidence ratings, so the correlation between observed and simulated CAI was not expected and provides a good test of our model's ability to reproduce the observed patterns. We will test whether the same correlations hold when using the difference in accuracy instead of the confidence.

We found that the best model is the one with the same belief across the visual and auditory sensors. Given this, we cannot investigate how modality-specific belief parameters are linked to unimodal sensitivity for each participant.

Reviewer 2:

Summary:

In this study, across two experiments, the authors wrestle with the question: What is the profile of confidence judgments in presence/absence decisions for audiovisual stimuli? After thresholding observers to 50% target detection rates in each modality, the authors conducted one experiment that included 75% target presence (spread equally across bimodal, auditory, and visual targets) and one experiment with 50% overall target presence. Results showed that, overall, detection performance was higher for audiovisual stimuli compared to unimodal ones, and that a recent model for stimulus detection could be extended to this multisensory scenario. By incorporating a disjunctive rule for absence judgments and a conjunctive rule for presence judgments, the model was able to qualitatively reproduce some of the trends observed in the human data regarding confidence.

Strengths:

(1) The paper makes novel contributions to the study of multisensory confidence judgments for yes/no target detection.

(2) The paper further extends the use of a leading model of stimulus detection (from Mazor et al., 2025).

(3) Pre-registration of the study was implemented, and the code is publicly available (although the GitLab link requires registration to access the materials).

(4) One of the empirical results (higher confidence for absence compared to presence judgments) is especially interesting, contributing another empirical finding to a very mixed literature on this topic (as the authors note).

We thank the reviewer for the positive evaluation of our work.

Weaknesses:

(1) Page 5 - I have concerns about the use of the equal-variance model from Signal Detection Theory to analyze the data. For example, the authors should read the recent paper by Miyoshi, Rahnev, and Lau in iScience, found at this link: https://www.cell.com/iscience/fulltext/S2589-0042(26)00373-1 . In this paper, the authors note how the equal variance model should be used with caution in yes/no detection tasks, since the variances of the "stimulus present" and "stimulus absent" distributions are often different from one another. In a revision, I highly recommend that the authors explicitly discuss this paper and review whether the assumptions for the equal-variance model have been met (e.g., since they have confidence data, one way to do this would be to evaluate if the slope of the line in zROC space differs from 1). The authors may also want to incorporate methods from this iScience paper into the current manuscript, or potentially move to using an unequal variance SDT model and compute d'a and c'a.

This is an excellent suggestion. We will run this analysis and refit the d’ and criterion response using unequal-variance models to see whether we observe the same results.

(2) Related to the computation/measurement of the response criterion, the authors note on page 18 in the Methods that for Experiment 1, signals are actually present on 75% of trials, since a bimodal stimulus is present on 25% of trials, the visual circle only occurs on 25% of trials, the sinusoidal tone occurs on 25% of trials, and then only noise is present on 25% of trials. Did the authors have any a priori hypotheses about the response criteria that participants would exhibit in Experiment 1, considering the unbalanced target presentation rate in this task? Also, in Experiment 2, what did it mean to equate target present and target absent trials? Is it that they broke 50% target present trials down into 16.67% bimodal targets, 16.67% visual targets, and 16.67% auditory targets? A few more details would be good to explicitly note for those trying to replicate the task

We will clarify this point in the manuscript. In Experiment 2, the stimulus was absent on 50% of the trials. As a result, the 50% of stimulus present trials were split into the three possible conditions, resulting in a sixth of the trials being auditory, a sixth visual, and a sixth audiovisual; we will make these proportions clearer in the text.

We did not have any a priori hypotheses about the response criteria for Experiment 1. The reviewer is right, the proportion of absent versus present trials can indeed have an impact on response bias. In fact, one of the goals of Experiment 2 was to test whether the low frequency of absent trials compared to present ones could explain both response bias and higher confidence in absence observed in Experiment 1, which we found was not the case, as we did not observe a difference between the two experiments. We will clarify this in our revision.

(3) It is important to plot the individual data for Figure 2. If the authors didn't match detection performance for the visual and auditory modalities, it would be good to see the individual data to know why. Is it that the thresholding procedure didn't work for some of the participants in the visual modality, and that's why the "yes" response rate is (on average) ~60% or higher across the two experiments? Similarly, in the auditory domain, do the authors have participants that are at floor? Or is it simply that the staircases failed to successfully target 50% detection on average?

We will add individual data to Figure 2.

Indeed, staircases failed to achieve 50% detection on average; participants for whom psychometric curves did not converge were excluded, as were those at floor level in one of the two modalities.

(4) The authors mentioned that data were collected on the Prolific platform. What checks did they conduct to ensure that this data wasn't produced by bots? There are recent high-profile publications in PNAS and Behavioral Research Methods that indicate how online data collection is problematic (e.g., https://www.pnas.org/doi/10.1073/pnas.2535585123and https://link.springer.com/article/10.3758/s13428-025-02852-7 ). What analyses or quality checks are there to ensure that humans were the ones completing the task?

Data were collected on the Prolific platform, which has been shown to yield high-quality data (Kay, 2025). However, we agree that this is a potential concern and will add a note of caution in the revised manuscript, even if the risk that the data do not come from humans but from bots is low (Huskey et al., 2026; Chetverikov, 2026).

(5) Page 7 - Since confidence was collected on a continuous scale, the authors should say a bit more about how they were able to compute measures of metacognitive efficiency. My understanding is that to compute meta-d', the data has to be binned. How was the binning implemented? With whatever bin size the authors chose, would it make any difference to the results if they changed the number of the bins in the analysis?

We will clarify this aspect of the analysis. Data were binned into four quartiles based on the overall distribution of confidence values across participants, based on the binning used in the example in Fleming (2017). We will examine whether changing the number of bins changes the results (Dayan, 2023).

(6) Page 8 - Is there a prior precedent for using slope of the Bayesian logistic regression predicting accuracy from confidence as a measure of metacognitive sensitivity? If so, can the authors cite those papers as a reference? If not, can they place this analysis within the context of other measures of metacognitive sensitivity that exist? (meta-d', AUROC (Type 2), etc.)

Yes, logistic regression has been used to quantify metacognitive sensitivity before. We will add the relevant papers as references (e.g., Sandberg et al., 2010; Norman et al., 2011; Siedlecka et al., 2016; Wierzchoń et al., 2012; Faivre et al., 2018; Pereira et al., 2023)

(7) Page 8 - Another one of the results on page 8 is worth reflecting further upon: the authors note how in Experiment 1, no credible difference was found between unimodal and bimodal trials (DeltaM = -0.25 [-0.59, 0.10]), but in Experiment 2, "we observed higher metacognitive efficiency in unimodal compared to bimodal trials (DeltaM = -0.28 [-0.54, -0.02]. Those DeltaM values are nearly identical, so without a power analysis motivating the number of participants the authors collected, how certain are they that the results from these two experiments are really that distinct? It reminds me a bit of the Andrew Gelman blog post, "The difference between significance and non-significance is not significant".

The number of participants was determined using a Bayesian optional stopping rule, as preregistered. The reviewer is right that the delta values are very similar in the two experiments. Given that a difference was found in only one experiment, we decided not to draw conclusions from it.

(8) Is there any way to look at whether the presence of multisensory hallucinations (or perhaps that word is too strong, and we should simply consider them miscategorizations) increased as the task progressed? That is, the authors have repeated presentations of audiovisual stimuli for at least some percentage of the trials. Since the percentages for auditory stimuli being correctly categorized as auditory are at 85% in Experiment 1 and 79% in Experiment 2, were the trials where they miscategorized these stimuli equally spread throughout the task? Or did they come later in the experiment, after being repeatedly exposed to multisensory trials?

We will examine how the proportion of miscategorisation changed throughout the task.

(9) Would the authors obtain the same results if they got rid of the amodal confidence judgment in their task, and simply had participants report the bimodal confidence following the presence/absence judgment? Part of the reason for asking this is that, according to page 11, the model is only fitted to amodal detection accuracy and response time data. This surprised me. I would have expected that the bimodal confidence would provide more useful information for the model fit. The authors should further explain this rationale in the paper. It seems odd to me to have the multisensory confidence ratings and not have them play a central role in the modeling work.

Our main goal was to investigate how participants form integrated, supramodal confidence judgments on the basis of multisensory sources of information. Therefore, the amodal confidence judgments are required here.

Moreover, the model was fitted to response times that corresponded to the amodal judgment. Because we had no meaningful response times for the modality-specific judgment, we could not use them to fit the model.

(10) In Figure 6, it appears the model is a bit off in its estimate of auditory responses (panel B, E) in the AV condition. Do the authors have any intuitions about why this might be happening?

Indeed, the model does not capture the full behavioral effects reflecting multisensory interference in the modality-specific responses. We suppose that the model does not reproduce these interferences, as it is only fitted to amodal detection accuracy, and as the two sensors are completely independent from one another. We will clarify this aspect in the text.

(11) The authors talk about how the model is reproducing effects in the human data, but there's no systematic comparison, quantitatively, of how the two things relate. The authors should include some quantitative measure that reflects this

In addition to the d’ and criterion comparison between the observed and simulated data, we will compare modality-specific d’ and the correlations between observed and simulated confidence.

(12) Related to this, I am not sure I agree with the characterization in Figure 7 that "when confidence followed a disjunctive rule, the model failed to capture important aspects of the data. On the other hand, when confidence followed a conjunctive rule, it reproduced confidence in presence judgments but failed to capture variability in confidence ratings for absence judgments." What, quantitatively, is the basis of this claim? This applies to Figure 8, too. I am not clear how, specifically, and quantitatively, the authors are justifying their claims about model fits. I don't think the confidence asymmetry index in Figure 8 is enough to quantify the quality of the model fitting procedure.

To further support this claim, we will add a quantitative comparison of the different confidence fits.

(13) Is there any chance the higher metacognitive efficiency for auditory trials is simply driven by differences in the d' values across the modalities? It might be good to probe this effect further.

Thank you for this remark. Indeed, the difference in metacognitive efficiency may be driven by differences in the d’ values, and so a lower d’ for auditory stimuli can lead to higher metacognitive efficiency for a similar metacognitive sensitivity.

Reviewer 3:

This study used a pre-registered novel behavioural paradigm and computational modelling to investigate multi-sensory influences on detection and confidence. Participants performed amodal detection of auditory and visual stimuli (indicating that a stimulus was there when either an auditory stimulus or a visual stimulus or both were present), followed by amodal and unimodal confidence ratings. Detection was higher when both stimuli were present, and the presence of one modality increased the confidence in the presence of the other modality. In contrast to previous detection studies, confidence was higher for absent than for present judgements, but metacognitive efficiency was higher for present judgements. Metacognitive sensitivity was higher for bimodal stimuli, but this was not the case for metacognitive efficiency, suggesting that the sensitivity might be driven by first-order performance. The computational model showed that both detection and confidence in absence followed a disjunctive evidence integration rule, while confidence in presence followed a conjunctive integration rule.

We thank the reviewer for engaging with our work.

Strengths:

The paper has several major strengths. Firstly, it addresses a novel research question using an innovative and well-controlled paradigm. Furthermore, the paradigm and analyses were pre-registered, and all effects that were interpreted were replicated in two independent samples. Finally, the paper uses an advanced computational model to capture counterintuitive patterns in the data.

Weaknesses:

The major weakness of the paper is the narrative structure. It is not always clear how the different analyses relate to the main research question. Many different effects are reported in terms of detection accuracy, bias, confidence and metacognition, as well as cross-modal and unimodal versus bimodal effects. It would help readability if the paper were streamlined in terms of the research question that is being answered, which I believe is specifically about multimodal absence judgements. Relatedly, for a reader not intimately familiar with the metacognition literature, the difference between MRatio, metacognitive sensitivity and metacognitive efficiency is not obvious. It would be good to clarify this more in the manuscript.

We will improve the narrative structure so that each result clearly relates to the research question.

We will also add a clearer definition of the various metacognition metrics to improve readability.

In general, the conclusions drawn by the authors seem to be supported by the results. However, I was missing quantitative model comparisons between the conjunctive and the disjunctive models and an explanation of why the models systematically overestimated the confidence ratings. Furthermore, the 'perceptual multisensory interference' section reports on very interesting effects, but these are not supported by statistical tests in the main text. It would help to assess the strength of the claims if the statistical evidence in favour of these claims were presented together in the main text.

The model was not fitted to confidence data, which could explain its overall overconfidence. As stated in previous responses, we will perform additional analyses to evaluate the model’s ability to reproduce confidence ratings. As some of the results were not replicated across experiments, we decided to put all statistical results related to multisensory interference in the supplementary materials and to focus only on consistent results across experiments.

One other concern is that in real-world multi-sensory perception, such as the mosquito example in the introduction, the auditory and visual signals have a strong natural association, which means that if you hear the auditory signal, you expect that you will see the visual signal soon and vice versa. As far as I understood, this association was not present in the current paradigm, which might influence the type of effects that one would expect to see.

The relation here is indeed artificial; we try to reinforce it as much as possible in the instructions of the task by indicating to the participants that they have to “detect a mosquito” that could be present auditory, visually, or both. But we acknowledge that the association between the visual and auditory stimuli is artificial, which may indeed influence our results.

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