Among voters, the picture is more complex. In 1972, for example, 29% of Democrats called themselves liberal or very liberal, a figure that rose by 18 points to 47% by 2012. During those four decades, the share of Republicans regarding themselves as conservative or very conservative rose by fully 30 points, to 76% from 46%. The average Democratic voter moved about half a point to the left on the standard seven-point ideological scale; the average Republican voter moved about three-quarters of a point to the right. Republicans are now a predominantly conservative party, while Democrats remain a coalition of liberals and moderates.

On the role of government, Republicans have moved much further right than Democrats have to the left. It is hard to overstate the intensity of Republican sentiment on this issue. Between 1972 and 2012, the share of Republicans who regard themselves as very conservative on taxes and using government to promote jobs and social services soared to 38% from 9%, and the share of economic conservatives overall rose to 80% from 48%.

But on social and cultural issues, the picture looks different. In 2012, according to Mr. Abramowitz, “Democratic voters were somewhat farther to the left of center than Republican voters were to the right of center.”