It could be a a day, or three, or seven. I'd set it up as sides are decided after both people have accepted the debate. This would challenge debate skills and expand debater's minds. If they must argue a side they do not agree with, it will help them see the other side.
When one STARTS a debate, he/she would like to see if anyone could argue against his/her opinion. When one ACCEPTS a debate, he/she would like to challenge the challenger's opinions. People should know which side they are taking before accepting to be able to debate properly. If sides are randomly decided, it might only add confusion.