This sounds a lot like bug reporting software, which allows users to upvote issues/bugs. I've seen one that gives each user 10 votes which they can cast however they want, even spending all 10 votes on a single issue. They can change their votes at any time, or automatically get their votes back when the issue is marked as closed, but they can never have more than 10 votes on anything at any given time.
Or alternatively you could use other software development / project management tools, such as Trello, which allow people without edit access to upvote cards or lists.
Though, while these things do allow you to have hundreds or thousands of entries, viewing/browsing/discovering them all is not necessarily handled well in any of the tools I've seen before. I can't imagine trying to scroll through a Trello board that has thousands of cards.