Almost every other UFC event has a fight that goes to the judges that fans think was scored wrong. You can tell the UFC fans that free market judges would at least have to answer to the market/consumer demand vs government judges that don't have to answer to anyone. But the UFC fans will counter with a belief that if the judging was in the hands of the free market (probably the UFC or various third party organizations with excellent reputations), then the fights would start to be fixed.
The counter question would be "Why would the UFC fix fights and risk losing everything they worked so hard to build?"
Or if it was a third party organization providing the judging service, the question would be "Why would that organization risk losing their contract with the UFC, and probably their ability to provide judging services to anyone afterwards?"
Or perhaps "Why do UFC fans have such allegiance to the UFC if they think that the UFC would be corrupt if given the chance?" Or perhaps "Why would incompetent judges be better than corrupt judges?"
The bottom line is, the UFC has to provide customer satisfaction, or they won't make money. The government does not. Who do you think will respond faster to the fans' needs? Who will respond at all?
I posed this very same question to anarcho-capitalists (free market supporters).