Dilemma, How Bees Argue is too concise as is but too long to post in its entirety, so I will try to paraphrase all but a paragraph or two but recommend you actually read the article at the link because my paraphrase won't do it justice.
Late Spring, early Summer when a colony of honey bees becomes overcrowded, a third stay put and rear a new queen, two thirds, perhaps 10,000, leave with the old queen to start a new colony. Initially, they travel only 100 feet or so and gather in a beard-like cluster.
From there several hundred scouts, the oldest, most experienced, some 30 miles for a potential new homesite. Some dozen of these make the initial scout, each inspecting the cavity of the potential site and returning to the cluster to do waggle dances that encode direction and distance to the site they inspected.
Most scouts are recruited to tout a site by the dances. Each dance is seen by only a few other bees who seem to pick dances at random. The recruited scouts then visit the danced site and return to do their own recruitment dance. Recruits will re-inspect and re-dance but after 1 to 6 trips, the recruit just stops.
The decline in touting sites is accelerated by conflict. Bees that tout one site will sometimes head-butt and beep at bees touting other sites. After about 10 head-butts a scout quits.
While inspecting a potential site, scouts touch other scouts and when they see 20 to 30 other scouts, implying a majority, they return to the cluster and make a special sound to declare the search over.
"...Site quality depends on cavity size, entrance size and height, cavity orientation relative to entrance, and wall health. How do they do pick the best site?
"Each scout who inspects a site estimates its quality, and encodes that estimate in its dance about that site. These quality estimates are error-prone; there’s only an 80% chance that a scout will rate a much better site as better. The key that enables swarms to pick better sites is this: between their visits to a site, scouts do a lot more dances for sites they estimate to be higher quality. A scout does a total of 30 dances for a lousy site, but 90 dances for great site."
When all the scouts have returned, then all the bees fly off to the selected site.
And that's how bees argue about picking a new site.
The author concludes: Now that I know all this, it isn’t clear how relevant it is for human disagreement. But it does seem a nice simple example to keep in mind. With bees, a community typically goes from wide disagreement to apparent strong agreement, without requiring particular individuals to ever giving up their strongly held opinions.