I have noticed that the tribal organization was very similar to modern democratic system, but on a much smaller scale.

So, when there was something to decide, there was usually some sort of leader, who would say what to do. But, in community-wide matters, such as flooding, burnt village, lack of food, etc. - in such matters, they often organize some sort of voting. Either council meeting (parliament), or open voting (referendum).

The leader is also involved in cross-tribe relationships - basically, a president. The main difference is that tribal communities lack the clear definition of executive, legislative and judicial branches. That is because it is a remnant of feudalism, which was introduced later on. In tribal societies, the law is formally made by the word of the leader, but the leader still uses others' help in making them. There are also traditions that enforce democracy to some point. And, if the leader is not following traditions, then it's a straight path to rebellion. With as much social security, as Hunter Gatherer tribes had, rebellion basically equals change of leader.

On the other hand, the penalty system is highly controlled by the tight community, which makes no need for judicial system.

So, even if there are no periodic elections, it still works as today's communities. You need to have influence, and you need to impress your people, in order to become a leader.