I think we must be careful about stating how God does things. A general answer is, “The way He wants to.”
And, let’s face it: In the face of a lack of specific instructions, a general answer is required.
The “one man rule” types always fall back on how God always appoints people to be head of this or that. That sounds convincing until you realize it isn’t true. They conveniently ignore how men were sometimes chosen by their peers but God blessed the choice in His subsequent dealings according to His plan.
Jephtha was driven off by his brothers because he was the son of a prostitute. He surrounded himself with scoundrels, so it can be argued that he wasn’t even necessarily a righteous person. Yet, the leaders of Gilead came to him to be their captain in war. There appears to have been no intervention from God until the leaders of Gilead and Jephtha make a vow before the LORD.
Consider how Matthew became the replacement for Judas as the 12th Apostle. We probably are familiar with how they cast lots to choose him, but how was it done? The lots were not cast until they had narrowed the choices down to two individuals: Joseph and Matthew (Ac 1:23). Notice how “they”, not God but “they” – the disciples (v 15), chose these two men. God then, via lots, made His will known between these two men.
Again, notice how the original seven deacons were chosen. Did God point them out to the Church? No. Did the Apostles huddle together and choose them? No. “The Twelve” instructed the Church to “choose seven men” according to some criteria (Ac 6:3, NIV). The Apostles then added their blessing via the laying on of hands, making it official, of the men “they presented… to the apostles” (v 6). The Apostles as leaders gave guidance but did not micromanage the affair. Rather, the Church did the choosing.
So, does this necessarily validate balloting? No, as we are given no real indication of how they, The Twelve, nor how they, the Church, made their wishes known. We are not even told that this is how apostles and deacons must be chosen every time. However, it is apparent that everyone had a chance to give their input one way or the other, so what is the difference?
However, it does blow out of the water the whole notion that a leader must be appointed by another leader or a prophet. It also shows The Twelve operating in cooperation instead of one single leader standing up and demanding it be done his way.
Besides, since HWA is dead and Joseph Tkach disqualified himself, then who would be the one to appoint anyone?
At any rate, I really have to laugh at the notion that somehow having one man in charge will somehow eliminate all politicking and bickering. It happened while HWA was alive! Why did it take him so long to appoint a successor? Because frankly none of the men under him measured up – not one. They were too busy cozying up to HWA trying to get in his good graces before he died. Talk about division and politics!
When will men stop adding to Scripture already? When will men stop giving in to other men simply because they seek power and want to be in charge? Oh, that’s right! They would first have to give up their idolatry and worship of other men!
Bad leadership doesn’t happen because of the form of government. Bad leadership happens because of a lack of Godly virtues on one side or the other (and often both). Corruption can occur in a democracy, a commune or a dictatorship. Strife happens because men give in to their carnal natures.
You can have Godly leadership through one, like King David, or twelve, as in the Apostles. What really matters is whether or not they are truly seeking God first and foremost rather than seeking the glory and worhip of other men.