Could someone design a program to solve a large number of simultaneous equations to work out the weighting of each reviewer on metacritic?
Assuming it's a static weighting, yeah. It'd be possible. It'd be a lot of work. You'd have to scrape all the data from a whole bunch of pages, which would be a project by itself. Then you'd have to match the data up with variables. There'd need to be a little bit of leeway to allow things like 94.4 and 94.6. Stuff like that.
Assuming it's a dynamic weighting.
Meta says "the scores are weighted according to the critic's fame, stature, and volume of reviews." Which it might be:
So you could expect that the first review has less weight than the 100th review from the same reviewer. Which might have even less weight than the 1000th review. And you wouldn't want scores to change for older reviews just because the reviewer is worth more now.
This is still mostly doable, but you'd need to keep track of a few more variables. Well the easiest one is how many reviews that the reviewer has had so far with each review. You can probably find a correlation. It's probably still possible to get the exact value, but it'd be a lot of work.
Static weighting is probably a fantastic approximation, but there's a chance that it'll be off.