Confidence in absence as confidence in counterfactual visibility

When things are perceived clearly they can be detected with confidence. But under what conditions can one be confident that something is absent? Here we use a meta-perceptual illusion to show that confidence in absence scales not with visibility itself, but with the subjective belief that a stimulus would have been visible, if present. In two pre-registered experiments, participants detected the presence or absence of letters in frames of dynamic noise, and rated their decision confidence. Across trials, stimuli could appear bigger or smaller. Critically, while perceptual sensitivity was increased for smaller stimuli, participants' meta-perceptual beliefs (measured with post-experiment debriefing and prospective confidence ratings) were that larger letters were easier to detect. Accordingly, while confidence in presence scaled with objective visibility (and was therefore higher for smaller stimuli), confidence in absence scaled with beliefs about counterfactual visibility (and was therefore higher for bigger stimuli). This dissociation between the effect of stimulus size on confidence in presence and absence diminished as the experiment progressed: a sign of meta-perceptual learning. Furthermore, the effect of size on confidence in absence, but not in presence, correlated with a meta-perceptual parameter from an ideal observer model of perceptual detection, fitted to decision and response time data alone. Overall, we conclude that confidence in absence closely tracked participants' model-derived expectations about the visibility of counterfactual stimuli.