Firms are racing to introducing algorithms to automate workplaces. Algorithms are replacing with human authorities. Algorithms substitute expert authorities. Using algorithms is better than hiring human experts to predict market share, diagnose cancer and to detect errors. Humans resist. Algorithms replace managerial authorities. Algorithms are your bosses who direct your performances. What makes firms distinct from market is authority, major theorists say. When there is authority, it must be legitimate. Hence, the legitimacy of algorithmic authority is an important question for the coming machine age. If an algorithmic authority is not legitimate, it loses its own foundation. If authority is lost, what makes firms distinct from market is lost. For the last decade, research on organizational research has been aggregated and sophisticated. Regarding the legitimacy of algorithmic authority, many questions abound. What is algorithmic authority? Why is it important for firms? Is that legitimate? Under what circumstances is algorithmic authority perceived legitimate? What aspects of legitimacy (pragmatic, cognitive, moral and relational) is most relevant to algorithmic authority? Is algorithmic authority going to earn legitimacy for the coming machine age? Are firms that use algorithmic authorities going to survive the legitimacy crisis? To be continued.