The idea is to award this badge when you get +5 and -5 votes on an answer.
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No, a million times no.
"Controversial" answers are usually bad answers that people who don't know better vote up. Like this one.
Aside from the question as to the usefulness of this badge, your +5 -5 suggestion also has issues. For example, it's the tendency of very highly voted questions to get at least five downvotes. It doesn't make sense for a +200 -5 question to earn a "Controversial" badge.
For example, most of the highest voted questions on RegEx match open tags except XHTML self-contained tags would earn (or come very close to earning) the badge even though it is clearly not warranted.