Ipsos MORI recently published a report detailing research carried out into the acceptability of governmental interventions, available here.
The poll assessed public perceptions of a hierarchy of policy interventions, from providing information to banning products outright. A majority of participants supported each of the interventions, though it did decrease as they became more severe. However, a substantial number of participants also felt that government should not get involved in individual choices. This 'cognitive polyphasia', a willingness to support specific interventions while also opposing governmental involvement, is seemingly contradictory. The authors suggest that it may point to a desire for government to tackle a particular issue while maintaining a level of suspicion about their involvement. It may also reflect a willingness to support legislation for the bad choices of others, while maintaining a desire to retain your own freedom of choice.
There were differences in support for interventions between countries, with richer countries less likely to support the more severe interventions. In another seeming contradiction, within countries, richer respondents were more likely to endorse the more stringent interventions, perhaps because they do not feel themselves to be the targets of the policies.
Overall, the report suggests that public attitudes towards interventions like incentives, restrictions and bans is quite positive. Those who object to such measures may be in a passionate minority.