In this thesis, I expand on the concept of algorithmic authority, a concept that I introduced in earlier work to understand the role of algorithms in daily life. Algorithmic authority is the legitimate power of algorithms to direct human action and to impact which information is considered true. In contrast to much other work on algorithms in sociotechnical systems, I argue for more precise use of the word “algorithm”, as well as for the importance of studying algorithmic systems that do consist of “black box algorithms”. Through a study of the users of the cryptocurrency Bitcoin, I explore what it means to trust in algorithmic authority in an open source, decentralized system and contrast it with the authority of centralized and corporate software. My study utilizes data from my survey, interviews, and observation of the broader Bitcoin community. I examine the tensions between members of the Bitcoin community who would prefer to integrate Bitcoin into institutions and those that saw it as a radical use of algorithmic authority. I describe how my participants preferred algorithmic authority to the authority of conventional institutions that they saw as untrustworthy. However, they acknowledged the need for mediating algorithmic authority with human judgment. I examine these tensions between how they would like Bitcoin to be used and how it is being used, and what those tensions can tell us about algorithmic authority. Lastly, I suggest future research directions for examining a wider range of algorithms and better understanding the Bitcoin community.