What if an unsupported claim is actually harmful to society, if believed?

15% of people believe the US government was responsible for the 9/11 attacks[1]. 42% of Britons believe that the UK sends £350M a week to the EU[2]. If voters make decisions based on such beliefs, I'd expect material damage to democracy.

[1] https://en.m.wikipedia.org/wiki/Opinion_polls_about_9/11_con...

[2] https://www.independent.co.uk/news/uk/politics/vote-leave-br...