Which again is a major point behind statistical data gathering methods and practices. Invalid methods -> invalid results. Regardless of intent.
(Though of course, those intent on deceiving can construct biased samples to drive their agenda.)
Consider as a worse case; there is a political question with a fairly clear reality ("the legislators should legislate the value of exp(1) to be 2.5 to make life easier"). The silent majority ignores the silly poll, and the lunatics who believe this is a good idea all put in a vote because they want to promote their mad cause.
The poll could therefore be biased to be exactly wrong. May as well call it invalid data and save the time thinking about it.
Polling for the value of e is rather like polling for the piloting of a jetliner. You could certainly do it. It would end rather badly in virtually all instances.
I only picked exp() as an example because it can't start a political argument.