Polarization and Echo Chambers: A Logical Analysis of Balance and Triadic Closure in Social Networks
Mina Young Pedersen

Abstract:
Motivated by the danger of polarization and echo chambers in social networks, we develop several logics to analyze the social phenomena balance, triadic closure and homophily. We first expand on a logical framework known from the literature with several intentions in mind. To explore measures of how far a network is from polarization, we consider and compare a variation of distances between models in relation to balance. We introduce additional modalities to the language of positive and negative relations logic to define previously undefinable frame properties in the original work. We also include dynamic operators in this framework to investigate change in networks with respect to polarization. Then we move away from balance and present tied logic: a hybrid logic of strong and weak ties. We provide an axiomatization, prove soundness and strong completeness and relate our results to analyzing echo chambers. Inspired by work on social group formation we define a subclass of threshold frames in which relations are justified on the basis of features agents in a network share. Lastly, we extend tied logic with epistemic states and dynamic and epistemic modalities to examine the interplay between change and knowledge in networks of strong and weak ties.