A Logic Approach to Pluralistic Ignorance

In this paper, the possibility of modeling the phenomenon “pluralistic ignorance” from social psychology, using epistemic/doxastic logic, is investigated. It is shown that the straightforward formalization of pluralistic ignorance does not capture the phenomenon completely. What is needed in addition is an assumption about the interplay between different agents’ beliefs or an assumption about how agents will change their beliefs about the entire group’s beliefs based on information about a single agent’s beliefs. Pluralistic ignorance is a term from the social and behavioral sciences dating back to the work of Floyd H. Allport and Daniel Katz [5]. Citing Krech and Crutchfield ([6], pp. 388-89) pluralistic ignorance is a situation where “no one believes, but everyone thinks that everyone believes” [2]. Elaborated, pluralistic ignorance is the case in which a group of people share a false belief about the beliefs, norms, actions or thoughts of the other group members, and thus it is an important notion in understanding the social life. Examples of pluralistic ignorance are plenty in the social science literature. One example is the use of alcohol at (American) college campuses, where several studies have shown that many students feel much less comfortable drinking than they believe the average student to feel [8]. Another classical example is the class room example in which, after having presented the students with some difficult material, the teacher asks them whether they have any questions. Even though most students do not understand the material, there may fail to be any questions. Each student interpret the lack of questions from their fellow students as a sign that all the others understand the material and, in order to avoid being publicly displayed as the less intelligent student, they do not dare asking any questions themselves. Misperceiving other people’s norms or beliefs can often occur without it being a case of pluralistic ignorance. Pluralistic ignorance is the case of systematic errors in norm/belief estimation of others. Thus pluralistic ignorance is a genuine social phenomenon and not just some people holding wrong beliefs about other people’s norms or beliefs. Another thing that characterizes most cases of pluralistic ignorance is how fragile it is. Just one public announcement of a private belief or norm will resolve the case of pluralistic ignorance. The two features, being a genuine social phenomenon and being resolvable by a public announcement, will play an important role in the attempt to model pluralistic ignorance using logic in this paper. Pluralistic ignorance has been approached by formal methods before (for instance [2, 4]), but almost none of these methods have been logic. The only exception seems to be Vincent Hendrick’s paper [4] where pluralistic ignorance is modeled using formal learning theory and logic. In this paper the tool will be classical modal logic in the form of doxastic/epistemic logic.