It's my understanding that by 'fairly egalitarian' it is meant that democratic practices were common at most times, but there was usually some hierarchy of authority in place too. So that if say another community invades, or there's a sudden decrease in resources, there's somebody for the community to look to for direction.

Sometimes those were elder councils, sometimes one person, like a war chief or shaman... But it would understandably vary on occasion and over time, as early and primitive societies weren't bound by unchangeable rules.

Perhaps for many years the elders of a tribe are very inclusive of others in decision making, but then several die from illness and one psychopath rises to power as a warchief and bullies the few remaining into following their lead, until they and many males die in battle and the community falls back into a more egalitarian state led mostly by the remaining elder women.

There are countless variations of these themes that could play out over time within the millions of primitive communities that have existed over the history of the human race.

But from what I've encountered, while studying these things as a personal curiosity, is that when these societies were at their healthiest, as judged by peace and sustainability of resources, they tended to be pretty damn egalitarian. And most didn't exactly have a name for that, it's just the way things were, they saw and thought of themselves as one unit. You are me, I am you, we are equals--respecting and caring for you is respecting and caring for myself.

Individuals who didn't exhibit this kind of inclination would be understandably seen as broken, dysfunctional, and dangerous--a threat to the community.