Brant A. Gardner discusses the "voice of the people" in Mosiah 29 and subsequent texts.
Brant A. Gardner, Second Witness: Analytical and Contextual Commentary on the Book of Mormon, 6 vols. (Salt Lake City: Greg Kofford Books, 2007), 3:486-90
Excurses:
The Voice of the People
The book of Mosiah ends with a dramatic rearrangement in Zarahemla’s political landscape. Mosiah not only abdicated his throne; he symbolically destroyed it. He dissolved a monarchy in favor of a government headed by judges. What was this new government? How did it compare to the government by a king?
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One case provides a little more information about how the “voice of the people” might actually function in decision-making
Now this was alarming to the people of the church, and also to all those who had not been drawn away after the persuasions of Amlici; for they knew that according to their law that such things must be established by the voice of the people.
Therefore, if it were possible that Amlici should gain the voice of the people, he, being a wicked man, would deprive them of their rights and privileges of the church; for it was his intent to destroy the church of God.
And it came to pass that the people assembled themselves together throughout all the land, every man according to his mind, whether it were for or against Amlici, in separate bodies, having much dispute and wonderful contentions one with another.
And thus they did assemble themselves together to cast in their voices concerning the matter; and they were laid before the judges.
And it came to pass that the voice of the people came against Almici that he was not made king over the people. (Alma 2:3-7)
This passage describes the people’s assembling in groups, possibly several groups in several locations, and presumably at the village/town/hamlet level along kin-compound lines. The population was already too large to allow for a single assembly split into two. At each location, the two opposing bodies had “much dispute and wonderful contentions.” While this division may possibly have been figurative and the debates individual rather than communal, I argue that we should read this verse literally and as collective and organized (though not necessarily orderly) debates. The “voice of the people” appears to quite literally be a group function, not a synonym for ballot-casting, I propose that these groups, probably of men only, created vocal and “wonderful” shouting matches from two points of a public space, then men moving from one group to another as they were persuaded by the arguments. As one group attained the majority, the collective “voice” would be manifest in their increasing numbers, while the opponents’ numbers decreased. Therefore, the “vote” was determined for that village/town/hamlet.
Of course, this reconstruction is speculative, but the proposed entails fit the descriptions. In some cases, contention may not have been a factor at all, as, for example, in confirming a seated king who already had the weight of lineage behind his selection. Mosiah’s succession from Benjamin would be such an example. The process of how the voice of the people functioned, however, is best seen in contested cases. In all cases, it appears to be very different from modern voting.