Why do politicians sometimes pursue policies with uncertain outcomes? We present a model in which politicians are unable to pre-commit to a status quo policy, and where investors and voters face a conflict over the division of output. Politicians may deviate from the status quo and pursue risky policy gambles in order to raise aggregate output to satisfy voters. These policy gambles may have a "populist" and self-fulfilling flavour: they can command electoral support despite being against voters' best interests. We analyse how consensus-building institutions eliminate the gamble equilibrium and enhance voter welfare. We interpret the United Kingdom's decision to leave the European Union through the lens of the model.