No, negative reputation the entire point. If you cant give negative reputation it defeats the purpose. I also disagree with your statement that removing the minus option will encourage more constructive posts. Generally if someone spends more than a sentence to elaborate their position, then it will not be rated low.
If someone is receiving a lot of negative reputation, there is a reason, and they should try to change their behavior.
Also, there will always be the few asshats that rate people low for little to no reason, this can not be avoided, but it is also a small minority, which I do not feel would swing anyones ratings one way or another.