There are actually a plethora of alternative dispute resolution systems in place in different industry sectors. Many of them are non-governmental in nature (in addition, there are various administrative proceedings that are more lightweight and targeted than civil litigation). The UDRP is not unique (nor are we supposed to be talking about the UDRP this year) -- it's not even unique in the domain world where many ccTLDs have adopted similar DRPs (and some not so similar ). For instance, in the US, false advertising disputes can be brought to the National Advertising Division (NAD) of the Better Business Bureau. Complaints about stockbrokers can go to an SEC administrative proceeding. Etc.
As far as what's being "proved" by the "math": Mark Twain once said, there are three kinds of lies; lies, damned lies, and statistics.
Have a great weekend, all!
Greg