For each reason we should track the number of reasons to agree and disagree with it. This will result in a conclusion at the top of a page, with columns for reasons to agree and reasons to disagree, as shown below:
RTA#1 | RTD#1
For simple math I suggest we just count all the reasons to agree that tree out beneath a belief. However in the future, when we have computers to do our math for us, an argument that is once removed could have 1 point, and an argument that is twice removed could have 1/2 a point and so on.
So what do we do with the scores? How do we know that the ideas with better scores are really better ideas? We don't, but what you don't measure you can't improve. Mankind may never be able to come up with a forum that uses an algorithm to promote better ideas, but I would like to try.
At some level we all know that if we don't promote good arguments and demote bad arguments we will have a less useful website. The problem becomes how do you define a good argument and how do you define bad one. Obviously a good argument uses good data and good logic. At some point if someone uses bad logic, or bad facts, people should post reasons to disagree with their argument. I believe that if we create a forum that allows people to post reasons to disagree and agree with arguments, arguments that are based on sound logic, and good facts will have more reasons to agree with them and fewer reasons to disagree with them.
So what do we do with arguments that have high scores? We move them to the top of the page? Do we delete arguments with low scores? Of course not, we just move them to the bottom of the lists of reasons to agree and disagree. This is like evolution, in that the best arguments get access to better real-estate.