There's a system in place to detect serial down voting. I'm not positive, but I would suspect it would detect this behavior as well.
It costs 21 rep to downvote an answer. If you're constantly downvoting other answers, I would actually suspect you to lose reputation overall versus leaving other answers alone. Mostly because:
Downvoting someone else's answer doesn't make your answer suck any less. :) The questioner is not likely to be fooled by numbers; they typically accept the solution that works for them regardless of the numbers. In fact, it's not uncommon to see a highly upvoted answer yet a different accepted answer.
And for the most part, frequent users don't see this as a competition. We're here to learn and to teach.