Mr. Mounk and Mr. Foa developed a three-factor formula to answer that question. Mr. Mounk thinks of it as an early-warning system, and it works something like a medical test: a way to detect that a democracy is ill before it develops full-blown symptoms.

The first factor was public support: How important do citizens think it is for their country to remain democratic? The second was public openness to nondemocratic forms of government, such as military rule. And the third factor was whether “antisystem parties and movements” — political parties and other major players whose core message is that the current system is illegitimate — were gaining support.

If support for democracy was falling while the other two measures were rising, the researchers marked that country “deconsolidating.” And they found that deconsolidation was the political equivalent of a low-grade fever that arrives the day before a full-blown case of the flu.

Venezuela, for instance, enjoyed the highest possible scores on Freedom House’s measures of political rights and democracy in the 1980s. But those democratic practices were not deeply rooted. During that apparent period of stability, Venezuela already scored as deconsolidating on the Mounk-Foa test.

Image Yascha Mounk, a Harvard lecturer.

Since then, Venezuelan democracy has declined significantly. In 1992, a faction of the Venezuelan military loyal to Hugo Chávez attempted a coup against the democratically elected government. Mr. Chávez was elected president in 1998 on a wave of populist support, and he immediately passed a new constitution that consolidated his power. His government cracked down on dissent, imprisoned political opponents and shredded the country’s economy with a series of ill-planned economic overhauls.

Likewise, when Poland joined the European Union in 2004, it was hailed as an especially strong example of a post-Communist country making the transition to consolidated democracy. But Mr. Mounk and Mr. Foa found strong signs of deconsolidation during that period: As early as 2005, nearly 16 percent of Poles said they believed democracy was a “bad” or “fairly bad” way of running the country. By 2012, 22 percent of respondents said that they supported army rule. And in the mid-2000s, a series of antisystem parties began to gain traction in Polish politics, including Law and Justice, Self-Defense of the Republic of Poland, and the League of Polish Families.