From a technical perspective? Just submit the form on-click to the server via AJAX and store it in combination with the user info in a DB on the server.
From a security perspective? Making a system which only counts one vote from one person once without cheating is nearly impossible and many countries struggle with this kind of problem (because let's be honest, voting from your home computer is very nice!)
What can you do?
What could be done? As a country, e-residency could be implemented, which gives every resident a unique and secure signature they can use to vote. That's just theory, though and hackers will find ways in because of configuration problems and software bugs nevertheless (see Estonia's problems for example).
What can you do? I think, you are out of luck, if you want to have something which has a minimal official character. You could just use facebook or google polls and it would be just as good. The only chance I see is that you verify every user registration with a thorough background-check by inspecting their legal documents.