These verses provide the only description of how the voice of the people worked. There is no indication of ballots, but rather “that the people assembled themselves together throughout all the land, every man according to his mind.” This description makes it appear that groups who felt the same way about a topic gathered together. Next, there was “much dispute and wonderful contentions one with another.” It would appear that they argued back and forth to try to convince others.
We don’t know how they decided who won the voice of the people. We can only tell that they “cast in their voices,” not cast ballots. This would appear to indicate that if someone changed their mind, they might physically move to the group that they agreed with. After some time, it would become obvious which group was larger. How this worked across the whole of the population is not at all clear. It is important for many modern readings concerning the idea of “voice of the people” that we understand that the use of “voice” was not metaphorical, and that it did not represent the modern concept of ballots.