In which I wax mathematical...

I had a thought the other day that may turn into my dissertation topic. I've been mulling over collaborative composition for some time now, but I think I may have finally found the right question. And with any luck, the ultimate answer to my dissertation just might be 42. Wouldn't that be something?

So I might be easiest to explain with an equation, although not a very good one. Let's assume that:

x = value of content produced by an expert.

and

a = value of content produced by an amateur.

Common sense would tell you that most of the time the following statement would be true:

x > a

In other words, the content produced by the expert is going to be more valuable than the content produced by an amateur. Not always, but usually.

The whole point of a wiki is that you have a group of people working on content. So instead of one amateur, you have several. So going back to the math:

x = n(a)

The question this equation poses is what is the value (or range of values) that makes this equation true? Or in other words, how many amateurs would you need working on content to make it as valuable as the content produced by the expert?

In speaking with David Wiley, I can't help but agree that it will likely end as an inverted U. The value of content with just a few amateurs would likely be low. And the value of content where there are hundreds or thousands of amateurs would also be low. But somewhere in there is a 'sweet spot', where the content produced by a number of amateurs is nearly as valuable as the content produced by the experts.

Now, there are a whole slew of problems here. What is valuable? Who is an expert? Who is an amateur? Etc. etc. etc. But I think that somewhere in there is my dissertation topic.