Pinker makes his case that men are morally better than they were before by getting out the charts and graphs and adding up the numbers--showing we do fewer bad things and more good things now than we used to. There are a lot of questions here, such as how comparable modern statistics are to those collected in prior times--as well as how we will ever know exactly how many murders their were in past societies that didn't have our penchant for adding everything up.
And Pinker addresses this issue like he addresses every other issue: quantitatively. But, of course, that's never the whole story. Here is Dostoevsky's underground man, addressing this issue qualitatively, giving a whole different--and less sanguine--picture of man's moral state (and saying not very nice things about the sophisters and calculators like Pinker):
Why, to maintain this theory of the regeneration of mankind by means of the pursuit of his own advantage is to my mind almost the same thing ... as to affirm, for instance, following Buckle, that through civilisation mankind becomes softer, and consequently less bloodthirsty and less fitted for warfare. Logically it does seem to follow from his arguments. But man has such a predilection for systems and abstract deductions that he is ready to distort the truth intentionally, he is ready to deny the evidence of his senses only to justify his logic. I take this example because it is the most glaring instance of it. Only look about you: blood is being spilt in streams, and in the merriest way, as though it were champagne. Take the whole of the nineteenth century in which Buckle lived. Take Napoleon -- the Great and also the present one. Take North America -- the eternal union. Take the farce of Schleswig-Holstein... . And what is it that civilisation softens in us? The only gain of civilisation for mankind is the greater capacity for variety of sensations -- and absolutely nothing more. And through the development of this many-sidedness man may come to finding enjoyment in bloodshed. In fact, this has already happened to him. Have you noticed that it is the most civilised gentlemen who have been the subtlest slaughterers, to whom the Attilas and Stenka Razins could not hold a candle, and if they are not so conspicuous as the Attilas and Stenka Razins it is simply because they are so often met with, are so ordinary and have become so familiar to us. In any case civilisation has made mankind if not more blood-thirsty, at least more vilely, more loathsomely bloodthirsty. In old days he saw justice in bloodshed and with his conscience at peace exterminated those he thought proper. Now we do think bloodshed abominable and yet we engage in this abomination, and with more energy than ever. Which is worse? Decide that for yourselves. They say that Cleopatra (excuse an instance from Roman history) was fond of sticking gold pins into her slave-girls' breasts and derived gratification from their screams and writhings. You will say that that was in the comparatively barbarous times; that these are barbarous times too, because also, comparatively speaking, pins are stuck in even now; that though man has now learned to see more clearly than in barbarous ages, he is still far from having learnt to act as reason and science would dictate. But yet you are fully convinced that he will be sure to learn when he gets rid of certain old bad habits, and when common sense and science have completely re-educated human nature and turned it in a normal direction. You are confident that then man will cease from intentional error and will, so to say, be compelled not to want to set his will against his normal interests.Read the rest here.
...What is bad (this is my comment again) is that I dare say people will be thankful for the gold pins then. Man is stupid, you know, phenomenally stupid; or rather he is not at all stupid, but he is so ungrateful that you could not find another like him in all creation. I, for instance, would not be in the least surprised if all of a sudden, àpropos of nothing, in the midst of general prosperity a gentleman with an ignoble, or rather with a reactionary and ironical, countenance were to arise and, putting his arms akimbo, say to us all: "I say, gentleman, hadn't we better kick over the whole show and scatter rationalism to the winds, simply to send these logarithms to the devil, and to enable us to live once more at our own sweet foolish will!" That again would not matter, but what is annoying is that he would be sure to find followers -- such is the nature of man.