I see how the answer method works here and on all Stack Exchange sites, but, can someone explain to me why those who have answers to a question can downvote other answers. Doesn't this seem a little pointless?! Can someone explain. I'd appreciate it.
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 1 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.
First of all, yes, the system allows you to downvote any post, regardless of whether you're involved answering the same question. But no, this is not a problem. If somebody was really going on a downvote spree we'd be able to detect that.
And here's a very important point: If you're experienced enough in a topic to be able to sufficiently answer a question, you should actually be one of the first to have the privilege to downvote any wrong answers given to the same question.
Let's contrive an example where I answer a question that asks for a Bash script to achieve something. It so happens to be that I know Bash, and somebody else posts a script that isn't working due to some syntax error. Why should I not be able to downvote it? What good behavior would it encourage if I couldn't point out that a post is simply wrong?
Note that quite the opposite is encouraged. The Sportsmanship badge is given to those who upvote competing answers.
Downvotes on main sites usually should mean there's something drastically wrong with the question. We arn't here to punish users who don't toe the line - the downvote/upvote and even the closure system is designed to encourage better questions and answers. I personally like to accompany my downvotes and closures with comments designed to help users work out what went wrong, in order to fix it.
If you DID get a downvote, editing it to fix issues there allows uses to undo said downvote should quality be sufficient to. As such, a downvote isn't a slap on the wrist, its an incentive to do better. We prefer positive reinforcement (upvotes! Badges!), but sometimes a little negative reinforcement would do.
Downvotes arn't the end of the world. Stop worrying and Do Awesome