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Pollsters try to measure it. Politicians compete for it. Protesters clamor for it. Journalists try to track it.

This illusive “it” is legitimacy, or the public’s support of leaders who best express a people’s values and principles. And perhaps nowhere has legitimacy shifted so swiftly in a country than in Venezuela over the past year. In recent days, signs of this change have been on view for the world to witness, offering lessons in how a nation struggles to renew its social contract and its popular sovereignty.

The clearest sign is a plan by the coalition of Venezuela’s opposition parties to set up a “parallel government” to the ruling regime of President Nicolás Maduro. The president’s popularity has sunk so low that the opposition, called the Democratic Unity alliance, feels assured of public backing. And Mr. Maduro is so worried by the prospect of an alternative state that he threw two opposition figures, Leopoldo López and Antonio Ledezma, into military prison this week.

Another sign is that the opposition-run legislature, which has been sidelined by Maduro, went ahead and appointed new judges to the supreme court (which Maduro has co-opted). He then had three of the judges arrested.

On July 16, the opposition was so confident of its legitimacy that it held a nationwide referendum on Maduro’s plan to change the Constitution and give himself near-dictatorial powers. Voter turnout was more than 7 million of the 20 million voters. By comparison, the turnout on July 30 for Maduro’s referendum on the constitutional change was only 3.6 million, according to pollster Innovarium.

Maduro’s slipping legitimacy can also be measured by his coddling of the military in order to keep their guns on his side. Venezuela now has more active generals than all of NATO. The president is also accused of allowing many officers to engage in illegal businesses.

When a leader’s legitimacy dips, he often misjudges the ultimate source of power. It is not out of the barrel of a gun. It rests on the highest aspirations of the people, reflected in their hopes for freedom, individual rights, peace, and prosperity. Under Maduro, the basic qualities of governance have eroded, caused by his misrule as well as a drop in world oil prices since 2014.

Venezuela is home to the world’s largest petroleum reserves. But you wouldn’t know it by the scarcity of goods, the level of crime, and the flow of people fleeing the country.

The opposition coalition, however, must be careful in how it claims a right to rule. It must work within the 1999 Constitution. It must not let its most radical members instigate violence during peaceful protests, which have now lasted since April. It must keep a door open to officials in the regime who may want to join it in creating a government of national unity.

Most of all, it must reach out to the rural poor who are the base of Maduro’s support. These Venezuelans feel left out from the privileged lives of the rich and middle class. Maduro has bought their loyalty through a system of patronage enforced by armed militias. As historian Bernard Fall once wrote, when a country is near civil war, the group that can “out-administer” the other in delivering goods and safety will win.

Legitimacy in Venezuela also rests to a degree on the views of other countries. Most big nations in Latin America now side with the opposition. But the region’s attempts to mediate a solution have so far failed.

A government’s legitimacy to rule is based not on brute force or free handouts. It relies on a leader’s relationship to the people’s noblest ideals. Those are often gauged by elections, polls, or protests. But they lie in the hearts of individual citizens, who are free to direct them to the most legitimate leaders.