Pinker doesn't have any strong answers as to why violence has declined
Violence has not declined, but has increased hugely and horrifyingly during the democratic era - world wars instead of national wars, a gigantic increase in the rate of homicide and assault, an even more gigantic increase in the rate of imprisonment. http://www.parliament.uk/documents/commons/lib/research/rp99/rp99-111.pdf
In Britain, everything has been criminalized, except crime, which has been decriminalized.
In 1874 2 people were arrainged for homicide in NYC. 1 was held for trial. This rose substantially in 1875. Six people were held for trial.
Until the red terror of the French Revolution it used to be that the Spanish inquisition, which typically murdered a few dozen per year, was the example of horrifying state repression.
Today Egyptians murder a lot more than a dozen Christians per year, and everyone is impressed by how wonderfully democratic they are.
Queen Bloody Mary murdered 200 people, resulting in eight hundred refugees, and went down in British history as a horrifying bloody handed tyrant.
About two million Hindus were massacred for religious reasons in the partition of India, and hardly anyone remembers, that being fairly routine for the twentieth century.
During the twentieth century Sihanouk murdered twelve thousand, and gets written up as a saint. Tito a few hundred thousand, and is viewed as the exemplar of tolerant and peaceable communism.
During more than fifty years of what the Icelanders themselves perceived as intolerably violent civil war, leading to the collapse of the traditional system, the average number of people killed or executed each year appears, on a per capita basis, to be roughly equal to the current rate of murder and nonnegligent manslaughter in the United States.
Decolonization was a gigantic crime, that has killed almost as many people as communism.