Group knowledge and individual introspection

We study distributed knowledge, which is what privately informed agents come to know by communicating freely with one another and sharing everything they know. Knowledge is not necessarily partitional: agents may be boundedly rational and differ in the ability to form higher-order knowledge. We model the inference making process that leads to distributed knowledge, and we do that by introducing revision operators and revision types. Due to the heterogeneity of reasoning abilities, inference making turns out to be order dependent. We show that there are two qualitatively different cases of how distributed knowledge is attained. In the first, distributed knowledge is determined by any group member who can replicate all the inferences that anyone else in the group makes. This finding is in line with the extant literature. In the second case, no member can replicate all the inferences made within the group. As a result, distributed knowledge is determined by any two group members who can jointly replicate what anyone else infers. This case can be interpreted as a form of wisdom of crowd effect and shows that, contrary to what is generally believed, distributed knowledge cannot always be reduced to the reasoning abilities of a single group member.