There are simple ways to gather lists of likely independent servers. For example, agencies you trust could publish such lists. You could pick three such lists and only trust organizations that appear on two of them.
And if you betray that trust, it will nearly always be easily detectable in an automated way. At that point, everyone will stop trusting you and you'll be back at zero. By contrast, if you accumulate 51% of the mining power, there's no easy way for people to take that away from you and make you start over.
This isn't a procedure, it's a hand-wave. How do the agencies make their lists? And why should I trust them? If I can trust the agencies, why don't I just have them process all the transactions and then dispense with the inefficient global consensus stuff? What happens when courts order the agencies to direct people to processors who seize particular funds or block particular traffic? When the agency servers are hacked?