Adaptive Psychological Profiling systems use artificial intelligence algorithms to analyze a person's non-verbal behavior in order to determine a specific mental state such as deception. One such system known as, Silent Talker, combines image processing and artificial neural networks to classify multiple non-verbal signals mainly from the face during a verbal exchange i.e. interview, to produce an accurate and comprehensive time-based profile of a subject's psychological state. Artificial neural networks are typically black-box algorithms; hence, it is difficult to understand how the classification of a person's behaviour is obtained. The new European Data Protection Legislation (GDPR), states that individuals who are automatically profiled, have the right to an explanation of how the "machine" reached its decision and receive meaningful information on the logic involved in how that decision was reached. This is practically difficult from a technical perspective, whereas from a legal point of view, it remains unclear whether this is sufficient to safeguard the data subject's rights. This chapter is an extended version of a previous published paper in IJCCI 2019 [35] which examines the new European Data Protection Legislation and how it impacts on an application of psychological profiling within an Automated Deception Detection System (ADDS) which is one component of a smart border control system known as iBorderCtrl. ADDS detects deception through an avatar border guard interview, during a participants' pre-registration, to demonstrate the challenges faced in trying to obtain explainable decisions from models derived through computational intelligence techniques. The chapter concludes by examining the future of explainable decision making through proposing a new Hierarchy of Explainability and Empowerment that allows information and decision-making complexity to be explained at different levels depending on a person's abilities.