Richard Wrangham: "The Goodness Paradox: How Evolution Made Us Both More and Less Violent":

The key fact about humans is that within our social communities we have a rather low propensity to fight: compared to most wild (social) mammals we are very tolerant.

Wrangham's main line of argument goes like this:
Homo sapiens' body and behavior show many traits of domestication (the author describes in great detail the process of domestication on the basis of the well-known text-book example of Belyaev's silver foxes); but given that no one else was there to domesticate us, humans must be a case of self-domestication.
How did this happen?

Wrangham distinguishes two types of aggression: We are low on the scale of one type (reactive aggression), and high on the other (proactive aggression). Reactive aggression is the “hot” type, such as losing one’s temper and lashing out. Proactive aggression is “cold,” planned
and deliberate (murder, war, capital punishment). He believes that Homo sapiens became amore tame, domesticaed species because our ancestors (starting around 300,000 years ago) killed the most aggressive males of their groups, thereby crearing a powerful selection force. Just like Belyaev allowed only the least aggressive silver foxes to reproduce, men and women during the stone age plotted to kill the bullies and would-be dictators, exluding the genes for reactive aggression from the human gene pool.

Is this a plausible scenario?
We know that hunter-gatherers are fiercely egalitarian, they resent being dominated by anti-social persons, bullies - mostly men. Wrangham bases his argumentation on the work and research of Christopher Boehm, who has shown in books like "Hierarchy in the forest" and "Moral origins" how groups deal with such would-be tyrants. Boehm describes a whole gamut of so-called "levelling mecanisms", from ridicule and ostracism to murder. But Boehm makes it clear that execution is only the ultima ratio when all other means fail to control a male bully.

That is one of the weak points of Wrangham's analysis: that he does not show that murder of aggressive males has been common enough to be a strong selective force that has been able to cause domestication of the whole species. He just makes the claim, but does not offer any empirical evidence or mathematical model to support his theory (unlike for example Bowles and Gintis in their excellent book "A cooperative species", a book full of evidence and modelling).

Another weak point of his theory is the place of cooperation in his picture. Wrangham acknowledges the importance of cooperation as an important ability, but claims that
cooperation depends on a very low propensity for reactive aggression.
I do not think that this is true. Wolves or hyenas show a high level of (reactive) aggression, but they are also highly cooperative (when they hunt). But wolves or hyenas are not domesticated.

Another inconsistency is that Wrangham treats cooperation as a prerequisite for execution of male bullies because the weaker members of the group have to plot and coordinate their forces to kill such an aggressive man. He writes: "Shunning would be insufficient to affect an individual who is able to intimidate or defeat all others in a fight. Subordinates’ resentment could be translated to effective resistance only by coalitionary force. Cooperation among the weaker individuals is needed."

I think that Wrangham stresses an important aspect of human social life, but his theory is somewhat simplistic when he tries to present capital punishment as the central mechanism of the evolution of human sociality. I think that he fails to explain human morality, which IMO is more than just self-defense. People follow moral rules not only because they are afraid of punishment; they act morally because they identify with moral rules.

What Wrangham and his execution theory does not explain is human ultrasociality (see Peter Turchin's excellent book). The key element of humans' social nature is "collective intentionality" (Michael Tomasello), a concept Wrangham mentions once, but without discussing it or grasping its importance. That is another weak point of the book that the author does not bother to discuss different theories of the evolution of morality. He mentions briefly van Schaik, Gintis, Tomasello, but dismisses their argument in a few words.
In my opinion, Tomasello's "A natural history of human morality" offers a more profound and convincing picture than Wrangham rather simplistic account.

To sum up: Homo sapiens is a strange species with unique features, and one of them is the stark contrast of peaceful behavior within group and often violent behavior against out-groups or traitors or deviants or bullies within the own in-group. But Wrangham's execution theory gives only one aspect of the big picture, it describes just one mechanism of social control, but the author does not convince me that execution of aggressive males has been the most important driving force in the evolution of Homo sapiens' social life.