People's opinions in real life change all the time so it should be possible to change your opinion on debate.Org
I can see one problem. There could be a whole thread going and then someone changes their opinion. Then is the thread deleted?
What if we preserved old opinions? We could have % yes and % no calculated according to which ever is the most recent choice of the user. Then we could have old opinions accessible by clicking arrows at the top of each opinion. This could show previous opinions which were in the other column. It could also include previous opinions from the same column since a person may still agree with the same column (yes or no) but disagree with this or that aspect of their previous argument and so want to post a new opinion under the same column.
This would be a cool feature. You could look at the evolution of a given person's views and debating skills on debate.Org.