Simply put, IF a user has made less than X posts, then he cannot vote. ELSE he can vote on polls.
If the user cannot vote just show a overlay message like "you need at least x posts to vote" - no need for any admin options etc. Just a quick and dirty plug in
I wanted to use user groups for this originally but ran into issues with rebuilding user caches etc, so I would like to get this done as a add-on.
Please contact me with your quote for this.