In aboriginal or other primitive societies is the largest & strongest man usually the chief or not?

How are chiefs actually chosen in primitive societies? Best hunter, lover, dancer tale teller … what?

Is it usually the biggest, strongest, best fighter, best hunter type alpha male or are there more complex leadership criteria primitive peoples use?

A chief implies a social stratification of the classes and the chief is likely a hereditary position. A chief is going to have formal duties, obligations and powers. Egalitarian societies have what’s know as a “big man.” The big man doesn’t typically have any formal powers but people pay attention to him because he seems to know what’s going on, dispenses good advice and people like/respect him.

My anthropology professor in undergrad did ethnographies of and lived among several stone age cultures, and apart from systems that gave hereditary leadership positions, he descibed the “Big Men” of the group as ruling though general recognition of their intelligence and the force if their personality. Some of them he described as easily among the most intelligent men he’d ever met.

Normally it is one the the smartest who also is pretty strong. It tends to be a balance of parents, strength and wisdom.

It should also be recognized that the tribe may have several distinct leaders with different functions. The war leader may not be the same as the leader sought for his wisdom in peacetime. The shaman may have great authority in the spiritual realm.

As opposed to modern western democratic society, where the tallest man generally wins the election?

This.

Also generally, the “leader” in the HG society I know best (Kalahari Bushmen) is kind of an ad hoc thing - generally there’s no day-to-day management of group function, lots of stuff happens by group consensus after debate, and as such, it’s the best “politicians”, the well-liked people with the history of good ideas, who tend to get the group to do what they want. Not necessarily men, either. But for e.g. negotiating with the authorities or the like, it’s usually an older man, so I’d say a combination of experience and intelligence, not brawn, is what works for a leader. But mostly experience. This also goes for roles like hunt leader, the younger, stronger men definitely take their lead from the older guys.

I know you didn’t necessarily ask them, but amongst our primate cousins, it is usually the most socially intelligent who holds onto power the longest. Those with strength due to have an advantage, but if they don’t have the support of others, they won’t last long. Amongst the capuchins I studied, the biggest, toughest males tended to be the second in command. In some cases, the biggest ones would also be the alpha, but they were socially astute rather than just being brutes.