"Dave...I can assure you...that it's going to be all right..." -- A definition, case for, and survey of algorithmic assurances in human-autonomy trust relationships

Those who design, use, and are otherwise affected by advanced, technologies like artificially intelligent, autonomous systems want to know that these systems will perform correctly, understand the reasons behind their actions, and know how to use them appropriately. In short: they want to be able to trust such systems. Consequently, designers have devised various kinds of assurances for assessing trust. Typically, however, these assessments are ad hoc, and have not been formally related to each other or to formal trust models. This paper presents a survey of algorithmic assurances that allow users to calibrate their trust in autonomous artificially intelligent agents and use such autonomous agents more appropriately. To this end algorithmic assurances are first formally defined, and classified, from the perspective of formally modeled trust relationships. The survey is then performed using research from related communities such as machine learning, human-computer interaction, human-robot interaction, e-commerce, and others. The literature for different classes of assurances are identified with seven different levels of integration for artificially intelligent agents; these classes are useful for practitioners and system designers. Recommendations and directions for future work are also presented.