Android: How to create a voting/pools app?

I'm thinking of developing an app that will have an up vote/ down vote system (like we have here in stack-overflow). I'm having a hard time building the base - meaning the architecture.

Lets say I have a list with posts, viewed in a ListView and the data comes from a database (Parse.com db). each post will have it's own Int named "votes" containing the amount of up-votes/down-votes it has.

And here is my problem: Absolutely I want every user to be able to up-vote only once to each post. How do I do that? How do I save each user in the database so he could vote only once?

Thanks.