Far from suggesting a major retreat, all four sources show the global proportion of democracies at or near an all-time high.

For instance, Polity’s measure — which combines assessments of political competition, constraints on the executive, and openness of executive recruitment — put the proportion of democracies in 2016 at 59 percent, up from 50 percent in 2000. Each of the other three was within 4 percent of its all-time peak.

One gauge of democratic quality — the proportion of countries earning Freedom House’s top political rights score — has dropped from 32 percent in 2005 to 28 percent in 2016. But it only fell to its level in the 1990s, a time when Western commentators were declaring the triumph of liberal democracy.