Despite much work on social media, analysis of individual influence campaigns, messages, and platforms, we lack the tools and techniques and fundamental research to effectively understand the information flows and their effects on the dynamics of the entire information ecosystem. For example, how information is amplified or dampened as it moves from one online community to another, how information is spinned or framed into narratives that favor or malign viewpoints organically or by foreign actors, how disinformation flows from fringe to mainstream communities, etc. We postulate that the information ecosystem is an attention economy, and that influence-the ability to gather attention towards a particular message or messages- is its currency. As a result, we model the information ecosystem as a complex network of influences flowing between actors, communities and platforms. This paper advocate for the use of information-theoretic entropic methods to model and characterize this complex network of influences over time: Influence Cascades Ecosystem (ICE). We envision leveraging the concept of influence cascades in conjunction with a novel geopolitical news-centric model of the information ecosystem in order to better understand the influence pathways by which various types of information (new articles from trusted, untrusted, fringe or mainstream sources) propagate across the social and traditional hybrid media environment.