Dual strategies in human confidence judgments

Abstract

Although confidence is commonly believed to be an essential element in decision-making, it remains unclear what gives rise to one's sense of confidence. Recent Bayesian theories propose that confidence is computed, in part, from the degree of uncertainty in sensory evidence. Alternatively, observers can use physical properties of the stimulus as a heuristic to confidence. In the current study, we developed ideal observer models for either hypothesis and compared their predictions against human data obtained from psychophysical experiments. Participants reported the orientation of a stimulus, and their confidence in this estimate, under varying levels of internal and external noise. As predicted by the Bayesian model, we found a consistent link between confidence and behavioral variability for a given stimulus orientation. Confidence was higher when orientation estimates were more precise, for both internal and external sources of noise. However, we observed the inverse pattern when comparing between stimulus orientations: although observers gave more precise orientation estimates for cardinal orientations (a phenomenon known as the oblique effect), they were more confident about oblique orientations. We show that these results are well explained by a strategy to confidence that is based on the perceived amount of noise in the stimulus. Altogether, our results suggest that confidence is not always computed from the degree of uncertainty in one's perceptual evidence but can instead be based on visual cues that function as simple Heuristics to confidence.

Figure 1.

Schematic representation of a single trial in Experiments 1 and 2. The number, size, and position of the elements in the stimulus, as well as the size of the bar and spiral, are not an exact copy but were adapted for illustrative purposes. On each trial, subjects first reported the mean orientation across 36 Gabor patches by rotating a bar that appeared around fixation. They then reported their confidence in this orientation estimate by rotating a dot within a spiral. In Experiment 1, sensory uncertainty (orientation variability) was manipulated using five noise levels. In Experiment 2, a single level of orientation noise was used, and the mean orientation of the stimulus was manipulated.

Figure 2.

Predictions for the Bayesian and Heuristics model observers. (a–d) Variability in behavioral orientation estimates and mean reported confidence as a function of external (a–b) and internal (c–d) noise, for the Bayesian (a, c) and Heuristics (b, d) model observer. For both observers, behavioral variability increases with increasing levels of external and internal noise. In addition, confidence decreases with increasing levels of external noise. Thus either model observer predicts lower levels of confidence when behavioral performance worsens because of external sources of noise. The predictions of the two models diverge when internal sources of noise are considered. The Bayesian observer reports lower confidence when internal noise increases, such that confidence and behavioral variability remain inversely linked. In contrast, the Heuristics observer paradoxically becomes more confident when internal noise increases, even though behavioral performance deteriorates. (e–f) Predictions when trials are sorted with respect to reported confidence. For each level of external noise, trials were sorted into three bins of increasing confidence, and behavioral variability was computed across all trials in each bin. For the Bayesian observer (e), confidence correctly predicts behavioral variability: when the observer reports high confidence, orientation estimates tend to be less variable. For the Heuristics observer (f), the relationship between confidence and behavioral performance is less straightforward, because the effects of external and internal noise compete. In all figures, the x-axis is plotted using a logarithmic scale.

Figure 3.

Variability in human behavioral orientation estimates, and associated levels confidence, across various levels of external noise. (a) Behavioral variability (blue) increases with increasing levels of orientation noise in the stimulus, whereas reported confidence (green) decreases. (b) For each level of external noise, the data were divided into three bins of increasing confidence (black, brown, and yellow lines), and behavioral variability was computed across all the trials in each bin. Data were averaged over (base) orientations. As can be seen in the figure, behavioral variability decreased when reported confidence increased (the yellow line generally lies below the brown and black lines). Error bars represent ± 1 SEM.

Figure 4.

Behavioral variability (blue) and reported confidence (green) across orientation stimuli (Experiment 2), for both model and human observers. Top: Bayesian model observer who computes confidence from the degree of uncertainty in their orientation estimates. Confidence decreases when behavioral variability increases (oblique orientations). Middle: Heuristics model observer who computes confidence from the amount of perceived noise in the stimulus. Confidence is positively linked to behavioral variability: when behavioral variability increases (oblique orientations), so does confidence. Bottom: Human observers expressed greater levels of confidence for oblique compared to cardinal orientation stimuli, whereas their orientation estimates were less precise for oblique stimuli. These results are most consistent with the predictions of the Heuristics model observer. Shaded area represents ± 1 SEM.

Figure 5.

Internal noise, predicted confidence, and actual confidence. (a) Recovered internal noise values for different orientation stimuli, using Equation 10 and the data from the noise discrimination task (Experiment 3). Human observers are better able to discriminate small changes in stimulus variance for cardinal than oblique orientation stimuli, which indicates that internal noise values are higher for oblique than cardinal orientations (r = 0.48, t(87) = 5.12, p < 0.001). (b) Predicted confidence for the Heuristics model observer (black) using realistic levels of internal noise (from a), shown alongside the actual levels of confidence reported by human observers (green). Predicted confidence nicely matches reported confidence, suggesting that human observers use heuristic strategies to confidence based on the amount of perceived noise in the stimulus. Shaded area represents ±1 SEM.