This paper aims at classifying a gaze preference decision an operator made taking individual difference into account for purpose of a smooth human-machine interaction. A proposed method, inspired from a visual-psychophysical experiment of gaze preference decision-making when 2 faces are compared, focuses on a likelihood of a chosen face to the subject's gaze shift using an inferential statistical theory. A hypothesis in this psychophysical experiments is well known as the gaze cascade effect, i.e., there is a positive feed back as "more the human look at a face, more they like it" and "more the human like it, more they look at it". A system developed for implementing the proposed method, comprises an eye tracking device, analyzes the operator's eye movement data measured by it, and classifies the decision he/she made using its likelihood curve fit by a logistic model sigmoid function as a criterion. Moreover, the system is designed as changing displayed visual stimuli flexibly based on programming using the measured eye movement data as an image switcher. In order to discuss the proposed method using the likelihood curve, different types of experiments using the image switcher are done. 2 conditions are compared in experiments, i.e., one is when 2 faces are displayed side by side statically, and another is when the face the subject tries to look at disappears dynamically. Thus, the proposed classification method is enhanced by discussing interesting results of the visual-psychophysical experiments to supplement and progress the gaze cascade effect.