Let me save you a huge amount of condescension and repetition:
Mr Pinker is a sort of neo-Hobbesian whose entire argument hinges on 2 concepts:
1) Per-capita/percentage (he frequently alternates between percentage and percapita) death is markedly less under a 'leviathan' model where a centralized State controls the absolute authority to mete out punishments.
2) Any exceptions to this rule are to be elaborately explained away, but essentially comes down to claiming individuals or groups involved are somehow 'stateless'.

I happen to largely agree with point 1, yet still can't stand the methods and tap-dancing he uses to arrive at it.

Onto the book itself:
Steven Pinker wanders from point to point like a drunken squirrel. He believes that the plural of 'anecdote' is 'data', and that using wildly inaccurate statistical samples and methods is perfectly fine as long as they support his underlying world view. He cherry-picks quotes, data, and models, and fails to apply basic scientific methods to the data. Instead, he applies confirmation bias to it.
The writing is condescending, dull, full of wandering and side-tracking and virtually guaranteed to offend as many people as possible - even people like me who actually agree with most of his point.

Hiding casual ethnocentrism like his claim that England is the source of all modern civilization behind vague anecdotes and stories (then excusing away the Scottish, Irish, and Welsh, British Imperialism, and anything that might inconveniently disprove his assertion) all the while ignoring entirely the Scandinavians, all of Asia, and even the Middle East is just plain foolish.

I find it amusing at best that he uses the bible as his source for 'ancient barbarism', somehow deciding that works of fiction are a reliable source for a society. By that same yardstick, Greeks and Romans would have engaged in massive amounts of incest (since their mythology has so much of it), and modern Westerners would be the most violent vigilante culture in history (since our videogames, books, and films revolve largely around one or two people killing scores in some form of 'against the system' narrative)

Just avoid this pile of pulp. He may claim to be a 'Cognitive Scientist', but he seems to have long since fallen into the trap of soft science - "if you can't dazzle them with data, baffle them with bullshit".