It is well known that human interaction sometimes exhibits various forms of herd behavior, or other seemingly irrational attitudes, at the group level. Interaction can lead to pluralistic ignorance, informational cascades, false consensus effects and belief polarization. Among the many examples of such ``irrational'' collective behavior are market bubbles: everyone buys a bad stock option based simply on the market trend. Similar dynamics, with less dramatic effects, are omnipresent in everyday life; one may just think about a typical situation where every student during a class - wrongly assuming that others understood the lesson - refrains from raising their hand for clarification (pluralistic ignorance), or the situation where people favour a restaurant simply based on the queue outside (informational cascades), or when two different groups reinforce opposite beliefs regarding a certain issue even given the same evidential facts (polarization).
These and similar phenomena being so systemic, they raise the central issue of how rationality on the individual level relates to rationality at the group level. Whether polarization, pluralistic ignorance and informational cascades represent an irrational and unwanted behavior at the group level, or whether there is some rationale for these phenomena, is a matter of debate. Nonetheless, it is central to know if, and how, they can result from rational behavior at the level of the participating individuals (where ``rational'' is to be understood either in the standard decision-theoretic, or game-theoretic, sense). The general purpose of this project is to develop exact multi-agent models to improve the study of these phenomena and our understanding of cognition in a social context. Its novelty consists in employing techniques from dynamic epistemic logic (DEL) endowed with probabilities (its application to this area is unprecedented). Three general issues will be at stake: (1) How can these phenomena emerge - as seems to be the case - in a group of rational individuals, (2) whether and in which measure emergence depends on the individual attitudes about other states of mind, (3) what are the mutual conceptual relations and interplay between the different group phenomena.
The dynamics at stake have been studied at length from an empirical perspective in social science and behavioural economics. In the last decades there have also been serious attempts to devise exact models for them. Although successful in explaining the emergence of such phenomena, these models encounter difficulties in encoding higher order beliefs of individuals (e.g. ``I believe that you believe'' and similar) and thus need refinements to face the issues raised by (2) and (3). DEL has such an encoding power and has already proved fruitful, in other contexts, in explaining the rational core of many processes of interaction between agents.
There are several reasons why it is important to develop exact models in this field of social cognition. First of all, social cognition itself is a fundamental area if we want to understand ourselves as human beings and, in particular, the reflexive nature of human cognition: the fact that much of what we do requires thinking about others' (and our own) mental states. Secondly, exact models of social cognition play a role similar to idealized models in physics and economics; strictly speaking there is neither a perfect vacuum nor a perfect market, yet those idealized concepts have proved to be extremely useful in explaining and predicting real life phenomena. Similarly, exact models of social cognition can be expected to be powerful tools in explaining and predicting social phenomena, even though they abstract from features that are assumed to be of marginal importance. Thirdly, exact models can be seen as models of ideal rationality.
The broad aim of this project is to deepen our understanding of group rationality and its connection with individual rational behaviour. This is done by enriching the theoretical apparatus needed for exploring issues (1), (2) and (3). Depending on how these questions are answered, various practical consequences follow. For instance, if polarization, etc. are basically irrational types of behavior, then we should adjust education, social institutions and policies accordingly. Moreover, if we have a clue as to the triggering causes for them, we can adjust them in a principled way.