Does Confidence Use a Common Currency Across Two Visual Tasks?

Observers typically know about their own uncertainty during simple perceptual decisions: Better performance is linked to greater confidence in being correct (e.g., Fleming, Dolan, & Frith, 2012; Peirce & Jastrow, 1884; Yeung & Summerfield, 2012). However, there are many outstanding issues concerning how observers evaluate their confidence, an ability we refer to here as metacognition. At the processing level, computation of confidence could take place early (Baranski & Petrusic, 1994; Zylberberg, Barttfeld, & Sigman, 2012) or late (Pleskac & Busemeyer, 2010) during the decision process. Here, we focus on the representation level of confidence. More specifically, we report an experiment in which we investigated whether confidence is represented in a task-specific or a generic (task-independent) format.

Although conceptually very different, these two possibilities (task-specific vs. generic format) are not easily distinguishable via confidence ratings. Consider an orientation discrimination task: Observers judge the tilt of a bar as clockwise or counterclockwise relative to vertical and then rate their confidence in that judgment. The confidence rating could reflect the absolute tilt estimated in degrees (task-specific format) or, alternatively, the probability of success given this estimate (task-independent confidence). Critically, however, according to traditional signal detection theory (Green & Swets, 1966), these two quantities are perfectly correlated and indistinguishable (see Mathematical Appendix in the Supplemental Material available online). We therefore took another approach to address this question.

In a computerized experiment, observers (N = 35) performed two visual tasks (orientation and spatial-frequency discrimination) on Gabor stimuli (for details on the method, see Supplementary Methods in the Supplemental Material). On each trial, two Gabor stimuli were presented in succession, and observers judged the second orientation as clockwise or counterclockwise relative to the first orientation, or judged the spatial frequency of the second stimulus as higher or lower than the spatial frequency of the first stimulus. The tasks were known in advance and manipulated across blocks. After every pair of trials, observers made a comparative judgment of their confidence (Barthelmé & Mamassian, 2009, 2010), indicating the trial on which they felt they were more likely to have been correct. In two blocks, the same task was performed on all trials, so that confidence comparisons were for the same task (within-task condition); in the other two blocks, the task alternated between trials, so that confidence comparisons were for pairs of trials involving different tasks (across-task condition). If confidence is task-specific, then comparing confidence across two different tasks should be harder (i.e., observers should be less able to separate high-performance from low-performance trials) than comparing confidence across two instances of the same task. Alternatively, if confidence is accessed as an abstract and task-independent quantity (e.g., success probability), then comparing confidence in two decisions should not depend on whether the same task was performed.

We constructed psychometric curves describing the proportion of responses indicating counterclockwise rotations in the orientation task or increase in spatial frequency in the frequency task, as a function of the angular difference between the two orientations or the log-ratio of the two spatial frequencies. We quantified performance via sensitivity (i.e., the slope of the psychometric curve; see Psychometric Analyses in the Supplemental Material). We measured metacognitive ability as the change in sensitivity from low-confidence to high-confidence trials, by using the observers’ confidence-comparison response for each trial pair to classify one trial as high confidence and the other as low confidence. As expected, sensitivity increased with confidence (see Fig. 1a) in both tasks—orientation: 0.35 versus 0.71 deg⁻¹, t(34) = 15.43, p < .001; frequency: 27.5 versus 49.7 log-units⁻¹, t(34) = 14.58, p < .001. In other words, observers were able to track their own uncertainty above and beyond its variance due to the stimulus.

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Fig. 1.

Experimental results. The graphs in (a) show 1 participant’s psychometric curves for low- and high-confidence trials in the orientation and frequency tasks. For the orientation task, the proportion of trials on which the observer reported that the second orientation (O2) was rotated counterclockwise relative to the first (O1) is plotted as a function of the angular difference between the two orientations (in degrees). For the frequency task, the proportion of trials on which the observer reported that the second spatial frequency (F2) was higher than the first (F1) is plotted as a function of the logarithm of the ratio of the two spatial frequencies. The data have been fitted with cumulative Gaussian curves. The graphs in (b) show mean sensitivity (the inverse of the standard deviation of the fitted cumulative Gaussian curve) for the entire sample, calculated separately for each combination of confidence level and comparison type for each task. Error bars represent 1 SEM. The percentages correspond to the average confidence modulation indices (calculated as the sensitivity difference between low- and high-confidence trials divided by the average sensitivity across both confidence levels).

Critically, we assessed whether this metacognitive ability (i.e., the increase in sensitivity with confidence) was stronger in the within-task condition than in the across-task condition, as predicted by the task-specific-format hypothesis, or showed no effect of comparison type, as predicted by the generic-format hypothesis. Our data (Fig. 1b) supported the latter hypothesis: For both tasks, the Confidence (higher vs. lower) × Comparison Type (within-task vs. across-task) analysis of variance revealed main effects of confidence, both Fs(1, 34) > 106, ps < .001, but no main effect of comparison type, both Fs(1, 34) < 1, ps > .33. Critically, there was no interaction for either the orientation task, F(1, 34) = 0.01, p = .91, or the frequency task, F(1, 34) = 0.08, p = .78. Bayesian analyses (Masson, 2011) indicated positive evidence for the absence of an interaction (null hypothesis, H0) in both tasks—orientation: p(H0) = .85; frequency: p(H0) = .85. Thus, if an interaction exists, it is likely to be extremely weak.

To pool observations across tasks, we defined a confidence modulation index (CMI) quantifying metacognitive ability as the sensitivity increase for high- relative to low-confidence trials (as a percentage of the average sensitivity; see Psychometric Analyses in the Supplemental Material). A Comparison Type × Task analysis of variance on these values indicated a main effect of task, F(1, 34) = 4.93, p = .033; metacognitive ability was greater for the orientation task than for the frequency task. However, there was no main effect of comparison type, F(1, 34) = 0.50, p = .48, and no interaction, F(1, 34) = 0.19, p = .66. Again, Bayesian analyses indicated positive evidence for the absence of a difference between within-task and across-tasks comparisons (H0)—orientation: p(H0) = .85; frequency: p(H0) = .80; pooled: p(H0) = .82.

Overall, our results indicated that observers can compare confidence across tasks and access perceptual uncertainty in an abstract format, without losing information. We next investigated whether this conversion to an abstract format was costly in terms of processing time. The latency of confidence-comparison responses provided no evidence for such costs: These latencies did not differ between within-task and across-task comparisons (511 ms vs. 503 ms), t(34) = 0.50, p = .51. However, perceptual responses were slower in the across-task condition than in the within-task condition (654 ms vs. 532 ms), t(34) = 6.70, p < .001, presumably because of task-switching costs unrelated to confidence per se (e.g., changing perceptual filters and response mappings between trials), although a confidence-conversion cost taking place during the perceptual decision might have contributed to the effect as well. Finally, additional analyses confirmed that this latency difference was not due to the variation of perceptual stimuli across trials (for further information on the response time analyses, see Supplementary Methods and Supplementary Results in the Supplemental Material). However, despite the time costs associated with the across-task condition, the precision of the metacognitive evaluation and the confidence-comparison judgments (as assessed by our psychometric analyses) was unchanged in our observers.

To summarize, we investigated the representational format of confidence during perceptual decisions and found that whether confidence comparisons were made within the same task (and could be based on estimates of the stimuli themselves) or across two different tasks (and necessarily involved an abstract format), the discrimination between high- and low-performance trials was equally good. Thus, observers could metacognitively access their own uncertainty on an abstract, task-independent scale with no loss of information, although possibly with a small time cost. This common currency for metacognitive confidence judgments could be a success probability scale, or any monotonic transformation of such a scale (e.g., log-odds; see, e.g., Zhang & Maloney, 2012). An important question for future research is whether the metacognitive system can access and compare any measures of perceptual uncertainty, even across sensory modalities (Hillis, Ernst, Banks, & Landy, 2002).