This would be extremely easy to do with just about any database, with no specialty modules needed. Once you have the UI wired up to issue votes, you can have a
cron job (Heroku scheduler, or whatever suites your hosting platform) check the database for all entries with 3 downvotes and then remove them. Of course, you can make the algorithm more complicated by checking for a ratio of downvotes to upvotes, frequency of downvotes, or check for abusive language before deleting downvoted entries. It's all about queries to get the results you're after.
Another solution that's not as smart, but certainly less time consuming, would be to delete all added polls every 24-48 hours and refresh with a standard example set you provide. The assumption here is that you are trying to showcase your work, not give people a serious platform for voting. Aside from saving you a bunch of time, it doesn't provide the reaction that internet trolls crave, so even if someone does create something nasty, there will be nothing to feed their twisted ego and they'll likely just move on. Filters and flags are sometimes seen as challenges rather than boundaries by the more puerile elements of society, so ignoring them can reduce the amount of carnage you have to deal with.