In a New York Times essay on Sept. 23, Sasha Vasilyuk wrote about her aunt and uncle in Donetsk, one of the Russian-occupied regions of Ukraine where a staged referendum on annexation was about to begin. Knowing the vote would be a sham, Vasilyuk’s relatives told her they had no intention of taking part. “I don’t know anyone who is planning to vote,” said her aunt, “unless they come to our houses and force us at gunpoint.” In the event, forcing Ukrainians to vote at gunpoint was precisely what the Russians did. Soldiers armed with Kalashnikov rifles, accompanied by someone with a portable ballot box, went door to door to ensure that residents cast a ballot.

In the Russian-controlled city of Kherson, the referendum was conducted “under the muzzle of an automatic rifle,” one resident told The Washington Post. “They ring the doorbell of apartments, knock down the doors of those who don’t open them, and demand that people come out and put a mark that they agree to join the Russian Federation.” In some places, residents had to vote in the open and place their ballots in see-through containers.

The official outcome, announced Tuesday by Russia’s state media, was a foregone conclusion: a landslide for annexation. In two of the four Russian-controlled regions, Donetsk and Luhansk, more than 98 percent of the ballots were in favor of joining Russia. In Zaporizhzhia, the vote in favor was 93 percent. In Kherson, 87 percent.

Sham elections are par for the course in Russia. Widespread fraud and ballot stuffing ensured a lopsided victory for Vladimir Putin’s ruling party in last year’s parliamentary vote, for example. And when Moscow has sought to enlarge its empire by force, the phony voting has long been accompanied by very real violence. In 2014, when a “referendum” on annexation was held in Russian-occupied Crimea, journalists witnessed dissenters getting beaten and threatened by pro-Kremlin thugs.

The images of Ukrainians being forced to vote under the gaze of masked gunmen brought to mind a vivid description I heard as a college student from one of my instructors, an immigrant from Latvia. She described the vote organized by Moscow in 1940 to endorse her country’s absorption into the Soviet Union, which had invaded Latvia a few weeks earlier. As professor Miller recounted it, the ballot, which was not secret, offered two options — a big circle to mark Yes and a tiny one for No. Everyone understood what was expected of them. When one or two brave souls nevertheless voted No, they were dragged off and beaten. Time magazine reported at the time that Russia considered anyone failing to vote in the election a traitor who “may be shot in the back of the head.” TASS, the Soviet news agency, reported that the vote in favor of annexation was 97.5 percent. The results were inadvertently announced in Moscow 12 hours before the ballots in Latvia were counted.

Putin’s flunkies didn’t make the mistake of announcing the Ukraine results in advance, but it would have made no difference if they had. The outcome — overwhelming support for Russian rule — was prearranged, just as it had been in Crimea in 2014.

What is the point of holding such obviously bogus elections? Apart from a few Russian client states, the world never recognized Putin’s seizure of Crimea and will reject the latest referenda in eastern Ukraine. Secretary of State Antony Blinken expressed scorn for Putin’s “diabolical scheme” to steal parts of Ukraine and said the United States would impose still more sanctions on Russia and its top officials. NATO’s Secretary General Jens Stoltenberg, calling “the sham referenda” organized by Russia “a blatant violation of international law,” declared firmly: “These lands are Ukraine.”

The most popular explanation for Putin’s fake votes is that they are meant to supply a veneer of legality to Moscow’s occupation. In declaring the territories to now be part of Russia proper, Putin can claim that any attempt by Ukrainian forces to recapture them is an attack on Russia itself. He is likely to again play the nuclear card, perhaps with the goal of pressuring Ukraine and the West to end the fighting with a cease-fire that leaves the “annexed” regions in Moscow’s hands.

Still, why go through the charade of holding an election that no one considers legitimate? Why bother with a pretense that everyone sees through?

I suggest two answers.

One is that even the mere form of an election — even the most superficial “democracy theater” — conveys a patina of legitimacy that autocrats and dictators crave. However spurious the vote, however outrageous the conditions under which it is held, going through the motions of holding an election and casting ballots creates the illusion, or at least produces a whiff, of democracy. Over time, that illusion sticks. Landslide results, though utterly false, get reported as news by the media. The free world stoutly maintains that it will under no circumstances acknowledge such undemocratic maneuvers as lawful. Yet over time, despite itself, it does. The United States never formally recognized the Soviet annexation of Latvia and the other Baltic nations in 1940. But when those countries moved to reclaim their independence in 1990, Washington reacted at first not with full-throated encouragement but with a chilly aversion to disrupting the status quo.

A second reason dictators continue to stage fake elections is that, counterintuitive as it may seem, they make autocratic regimes stronger. Political scientists Carl Henrik Knutsen, Håvard Mokleiv Nygård, and Tore Wig have found that even sham elections enable dictatorships to “co-opt members of the opposition, for instance, or learn more about the strength of the opposition,” as they wrote in 2017. “Elections also help dictators build a strong organizational apparatus and signal their strength to intimidate potential opponents.”

There may be no easy way to quell Putin’s brutal aggression and cynical ruthlessness. For the United States and its allies, the wisest approach is to support Ukraine with steadfastness and fortitude. Western leaders should make a point of repeating at every opportunity that fraudulent elections will have no effect whatsoever and that all occupied Ukrainian land, Crimea included, must be disgorged by Moscow. In a “60 Minutes” interview recently, President Biden was asked how long American diplomatic and military support for Ukraine would continue. “As long as it takes,” Biden said. Exactly right.