Purpose The purpose of this paper is to report on empirical work conducted to open up algorithmic interpretability and transparency. In recent years, significant concerns have arisen regarding the increasing pervasiveness of algorithms and the impact of automated decision-making in our lives. Particularly problematic is the lack of transparency surrounding the development of these algorithmic systems and their use. It is often suggested that to make algorithms more fair, they should be made more transparent, but exactly how this can be (...) achieved remains unclear. Design/methodology/approach An empirical study was conducted to begin unpacking issues around algorithmic interpretability and transparency. The study involved discussion-based experiments centred around a limited resource allocation scenario which required participants to select their most and least preferred algorithms in a particular context. In addition to collecting quantitative data about preferences, qualitative data captured participants’ expressed reasoning behind their selections. Findings Even when provided with the same information about the scenario, participants made different algorithm preference selections and rationalised their selections differently. The study results revealed diversity in participant responses but consistency in the emphasis they placed on normative concerns and the importance of context when accounting for their selections. The issues raised by participants as important to their selections resonate closely with values that have come to the fore in current debates over algorithm prevalence. Originality/value This work developed a novel empirical approach that demonstrates the value in pursuing algorithmic interpretability and transparency while also highlighting the complexities surrounding their accomplishment. (shrink)