Optimal decision making requires both perceptual evidence and an estimation of the reliability of such evidence. Importantly, judgment difficulty and confidence (the subjective sense of the likelihood of success) may be separate components of an overall sense of reliability. In the present experiment, we investigated how observers represent discrimination difficulty in the context of numerical discrimination judgments. In our first experiment, we presented participants with a display of blue and yellow dots that varied in ratio and, hence, discrimination difficulty (e.g., discriminating 20:4 dots is easier than 20:9 dots while both decision are highly accurate). Participants had to click on a line to indicate how difficult they thought the trial was. We found that participants had representations of difficulty that were not merely based on the confidence or response time of their decision a?? even with discrimination performance at 100%, participants continued to reliably discriminate one easy trial from an even easier one. Given this differentiation, we sought to characterize the psychophysical signatures of difficulty representations (e.g., the precision, the relationship of variance to the mean, etc.). In the second experiment, participants were shown two trials of blue and yellow dots, and had to judge whether the first or second trial was easier. We found that observersa?? judgment of difficulty obeys Webera??s law and scalar variability: the ability to successfully determine the easier trial depends on the magnitude of the difference between the ratios, suggesting that representations of task difficulty are continuous and probabilistic in format. Furthermore, we measured and established the internal noise associated with difficulty representations, and found them to be close and correlated, but not exactly equivalent, to the noise associated with representations of number used in the task. We discuss these results in the context of theories of decision making, confidence, and optimal behavior.
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