Explainability, interpretability and how much they affect human trust in AI systems are ultimately problems of human cognition as much as machine learning, yet the effectiveness of AI recommendations and the trust afforded by end-users are typically not evaluated quantitatively. We developed and validated a general purpose Human-AI interaction paradigm which quantifies the impact of AI recommendations on human decisions. In our paradigm we confronted human users with quantitative prediction tasks: asking them for a first response, before confronting them with an AI's recommendations (and explanation), and then asking the human user to provide an updated final response. The difference between final and first responses constitutes the shift or sway in the human decision which we use as metric of the AI's recommendation impact on the human, representing the trust they place on the AI. We evaluated this paradigm on hundreds of users through Amazon Mechanical Turk using a multi-branched experiment confronting users with good/poor AI systems that had good, poor or no explainability. Our proof-ofprinciple paradigm allows one to quantitatively compare the rapidly growing set of XAI/IAI approaches in terms of their effect on the end-user and opens up the possibility of (machine) learning trust.