Ideal Observer Analysis
As shown in Fig. 1, the eyelids tend to be more closed in angry faces than in fearful or neutral faces. Hence, the wider cone of gaze observed for angry faces in the current study could reflect poorer visibility of parts of the palpebral fissure (e.g., the iris and sclera) that provide cues to the direction of gaze. To investigate this possibility, we carried out an ideal observer analysis. An ideal observer is a theoretical model that uses the optimal strategy for a given task. The performance of our ideal observer was determined by the amount of variation in pixel luminance between images that was informative for discriminating the direction of gaze (see Appendix 2 for further details). In our task, shifts of gaze were generated by digitally manipulating the position of the iris within the palpebral fissure. Therefore, all low-level information available to perform the task was contained exclusively in the palpebral fissure. The dependent measure of our ideal observer analysis was the 75 % root mean square (RMS) contrast threshold, which represents the minimum stimulus visibility at which the ideal observer was able to achieve 75 % accuracy in discriminating between leftward and rightward gaze. A lower contrast threshold indicates that there is more information available for discriminating the direction of gaze.