Regulating an agent with di¤erent beliefs1

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.