Political: The voice of the people was not normative in and of itself.
If the Nephite "voice of the people" were a democratic vote, then the majority would carry the day, and there would be no need to bring the "voice of the people" before the judges. Thus the voice of the people functions as an indicator of the public opinion which the judges might perhaps ignore, but would do so knowing that they were contrary to the statistical will of the people.
It is also probable that some part of their continued reign as a judge was related to the support of the people, if we remember that kings such as Benjamin declared that he ruled at the sufferance of the people. Thus while the voice of the people was not normative, it would be influential.
Alma 2:7
7 And it came to pass that the voice of the people came against Amlici, that he was not made king over the people.
Here we have the reverse of the sustainings of Zeniff, Benjamin, etc. Amlici could not achieve the voice of the people, therefore he could not be king - even had he been appointed one.
This still appears to argue against the democratic notion, as kings do not rule by election of people, but selection of the gods. It does fit, however, with the notion of Benjamin ruling at the sufferance of the people, and the polling of the voice of the people for the choice of the son to be successor to Mosiah.