A motivation for central bank independence (CBI) is that policy delegation helps politicians manage diverse coalitions. This paper develops a model of coalition formation that predicts when delegation will occur. An analysis of policy preferences survey data and CBI indicators supports the predictions. Case studies, drawn from several countries' recent past and the nineteenth-century United States, provide further support. Finally, the model explains why the expected negative relationship between CBI and inflation is not empirically robust: endogenous selection biases the estimated effect towards zero. The data confirm this.