As governments increasingly adopt algorithms and artificial intelligence (AAI), we still know comparatively little about citizens’ support for algorithmic government. In this paper, we analyze how many and what kind of reasons for government use of AAI citizens support. We use a sample of 17,000 respondents from 16 OECD countries and find that opinions on algorithmic government are divided. A narrow majority of people (55.6%) support a majority of reasons for using algorithmic government, and this is relatively consistent across countries. Results from multilevel models suggest that most of the cross-country variation is explained by individual-level characteristics, including age, education, gender, and income. Older and more educated respondents are more accepting of algorithmic government, while female and low-income respondents are less supportive. Finally, we classify the reasons for using algorithmic government into two types, “fairness” and “efficiency,” and find that support for them varies based on individuals’ political attitudes.