I don't think the reason this is not in is because of the number lines of code. You are correct, it would probably be trivial. But, the ability to reverse a vote, unless restricted to a very short period, would encourage group think and certainly wouldn't reduce the signal to noise ratio as you originally claim.
The number of mistaken up votes is probably a very tiny percentage of total votes, and accidental votes from multiple users on the same comment or post are most certainly even more rare. So the odds any given 'noise' comment or post is accidentally upvoted up to a meaningful level are extermely low.
And group think is already a problem on any voting news site. Allowing people to change their vote after they can see how everybody else is voting would certainly not alleviate that problem.
So while allowing a change of vote would help out an individual on their rare case of accidental upvote or downvote, I think the overall community effect would be detrimental.
