[EGreg]

Well, that's the Buridan's ass problem. You simply don't change course unless the majority is large enough. For example unless clearly over 80% of the country votes a certain way, you keep the status quo. If you are unsure, you keep the status quo.

In the Buridan's problem the solution is a timeout: if you haven't made a decision and can clearly see that the timeout has passed, you pick a certain predetermined decision (in this case the status quo).

Polling also prevents sybil attacks, ballot stuffing etc. and is impervious to voter turnouts.