Regulating an agent with different beliefs

There is some evidence that people have biased perceptions of risks, such as lethal or environmental risks. Hence their behavior is based on beliefs which may di¤er from the ’objective’ beliefs used by a regulator. The optimal regulation then depends on this di¤erence in beliefs. We set up a general framework and study this policy change. It turns out that, in many situations, the policy change depends on the absolute ’distance’ between beliefs, and not on whether agents over-estimate or under-estimate risks. We characterize the necessary and su¢cient condition for ’more distant’ beliefs to always reduce the regulator’s decision. We apply and extend that condition in several ways.