I tend towards liberalism on a personal scale, that is, I believe that individuals can transcend, or control, there violent nature...however, so far, we have not seen it demonstrated to any real degree that it can happen on a societal basis. (although I wish it would).
Pinker's point is that it can and has. People used to attend public hangings as a form of amusement; now they don't. People used to abuse those who were put in stocks for fun; we've abolished the stocks and would find the abuse appalling. Queen Elizabeth I had someone hung, drawn and quartered following the old method, which involves hanging them and disemboweling them without killing them, then pulling them to pieces while still alive. A hundred years earlier it was standard treatment for traitors; the reaction in her day was so negative she made sure the executioner killed the next traitor outright by hanging before performing the rest of the treatment.
Society has changed. People have changed. Attitudes have changed. In the west first, but it's spreading along with McDonald's and rock & roll.
Not speaking to you particularly, I've got to laugh at how Steven Pinker has been turned into yet another partisan issue. Since when has levels of violence been a marker of partisan identification? The guy's an academic. Agree with his work or not, you're not going to disprove it by calling it "liberal."