Welcome to StackOverflow!
The term you're looking for is badges, and every site has them. While I do agree that in some cases, a desire to earn this badge can make a user a little too cocky with their voting, there's really nothing to worry about. The badges were made to encourage good behavior, not bad, so I'm sure the ones who came up with it had this in mind.
Either way, in my opinion, to vote effectively and appropriately, one needs at least 125 reputation points. This is the threshold for the downvoting privilege on Stack Exchange sites. Users who have the privilege to downvote will likely already or almost understand te voting system completely.
Likewise, users who understand the voting system will be the ones who earn this badge, because by the time you know how the voting system works, you would also have the experience necessary to vote effectively.
And more often than not, a user that throws votes around like garbage will probably be noticed by either some very lonely and attentive user or an automated script that catches odd voting patterns.
So ultimately, you shouldn't worry about it. The people that can get the badge will do so fairly, I think. And, personally, it's harder than it looks. I think most users won't waste the effort. I don't vote too often so it'll be a while before I get that one.