Discourse on social media platforms is often plagued by acute polarization, with different camps promoting different perspectives on the issue at hand—compare, for example, the differences in the liberal and conservative discourse on the U.S. immigration debate. A large body of research has studied this phenomenon by focusing on the affiliation of groups and individuals. We propose a new finer-grained perspective: studying the impartiality of individual messages. While the notion of message impartiality is quite intuitive, the lack of an objective definition and of a way to measure it directly has largely obstructed scientific examination. In this work we operationalize message impartiality in terms of how discernible the affiliation of its author is, and introduce a methodology for quantifying it automatically. Unlike a supervised machine learning approach, our method can be used in the context of emerging events where impartiality labels are not immediately available. Our framework enables us to study the effects of (im)partiality on social media discussions at scale. We show that this phenomenon is highly consequential, with partial messages being twice more likely to spread than impartial ones, even after controlling for author and topic. By taking this fine-grained approach to polarization, we also provide new insights into the temporal evolution of online discussions centered around major political and sporting events.

This paper presents a semi-automated methodology for generating geometric proof problems of the kind found in a high-school curriculum. We formalize the notion of a geometry proof problem and describe an algorithm for generating such problems over a user-provided figure. Our experimental results indicate that our problem generation algorithm can effectively generate proof problems in elementary geometry. On a corpus of 110 figures taken from popular geometry textbooks, our system generated an average of about 443 problems per figure in an average time of 4.7 seconds per figure.

The way in which social conventions emerge in communities has been of interest to social scientists for decades. Here we report on the emergence of a particular social convention on Twitter—the way to indicate a tweet is being reposted and to attribute the content to its source. Initially, different variations were invented and spread through the Twitter network. The inventors and early adopters were well-connected, active, core members of the Twitter community. The diffusion networks of these conventions were dense and highly clustered, so no single user was critical to the adoption of the conventions. Despite being invented at different times and having different adoption rates, only two variations came to be widely adopted. In this paper we describe this process in detail, highlighting insights and raising questions about how social conventions emerge.