The magnitude and nature of the COVID-19 pandemic prevents public health policies from relying on coercive enforcement. Practicing social distancing, wearing masks and staying at home are voluntary and conditional on the behavior of others. We present the results of a large-scale survey experiment in nine countries with representative samples of the population. We find that both  empirical expectations (what others do) and normative expectations (what others approve of) play a significant role in compliance, beyond the effect of any other individual or group characteristic. Our results are driven by an asymmetric interaction with individuals’ trust in government and science.