The recommendation algorithms on social media platforms are hugely impactful, they shape information flow and human connection on an unprecedented scale. Despite growing criticism of the social impact of these algorithms, they are still opaque and transparency is an ongoing challenge. This paper has three contributions: (1) We introduce the concept of sociotechnical transparency. This can be defined as transparency approaches that consider both the technical system, and how it interacts with users and the environment in which it is deployed. We propose sociotechnical approaches will improve the understanding of social media algorithms for policy-makers and the public. (2) We present an approach to sociotechnical transparency using agent-based modelling, which overcomes a number of challenges with existing approaches. This is a novel application of agent-based modelling to provide transparency into how the recommendation algorithm prioritises different curation signals for a topic. (3) This agent-based model has a novel implementation of a multi-objective recommendation algorithm that is calibrated and empirically validated with data collected from X, previously Twitter. We show that agent-based modelling can provide useful insights into how the recommendation algorithm prioritises different curation signals. We can begin to explore whether the priorities of the recommendation algorithm align with what platforms say it is doing and whether they align with what the public want.