Unique one-time links are a standard solution, but if the OP's requirements disallow sending the survey credentials to the user, the solution needs to use something that the user already has and the system knows of, and store it in a way that prevents reverse engineering and extracting identifiable information.
This, unfortunately, means that the user has to ...
An online voting system must have at least one of these properties:
Allow unauthorized voting / double voting
Allow to find out who voted for what
Require a party which can be trusted to not falsify or share certain pieces of information
When you have a trusted party, then that party can keep a tally of who voted and a separate tally of votes but ...