For months now, it has been evident that the problem with coronavirus vaccine hesitancy is twofold: Not only do the unvaccinated question the safety of the vaccines, but about as importantly, they often doubt the vaccines’ effectiveness in very inaccurate ways. It’s one thing to be convinced to take a vaccine if you worry about side effects; it’s quite another if you also don’t think there’s any benefit.

Now a new poll from Gallup lays bare just how badly misinformed the unvaccinated are on that latter count. And that misinformation overwhelmingly lies on one side: the GOP.

Gallup asked people two questions: First, “what percentage of unvaccinated people have been hospitalized due to the coronavirus?” And second, “what percentage of fully vaccinated people have been hospitalized due to the coronavirus?”

Americans as a whole are actually reasonably well-informed about this. The median American — that is, the person exactly at the midpoint of all views — estimates the vaccines’ efficacy in preventing hospitalization is 80 percent. A study released this month showed the number is actually about 86 percent.

Gallup’s number derives from some wildly varying estimates of the hospitalization rates for vaccinated and unvaccinated people. For example, Democrats tend to oversell the danger to unvaccinated people, with a plurality wrongly believing at least half require hospital care. (This is why Gallup uses medians rather than averages.) But on balance, when you look at the relative numbers, the median American gets the benefit of vaccines about right.

But then we get to the subgroups. And that’s where we get a sense for just how warped the perceptions of the vaccines are, particularly among unvaccinated Republicans.

Among Democrats, the median view of the vaccines’ efficacy is about right for both vaccinated and unvaccinated people. The median vaccinated Democrat says the vaccines are about 88 percent effective at reducing hospitalizations, while the median unvaccinated Democrats pegs the number at 80 percent. The median vaccinated Republican is less sold on the efficacy of the vaccines even than the median unvaccinated Democrat, estimating a 73 percent reduction in hospitalization from the vaccines they’ve taken. But again, that’s in the ballpark.

Which brings us to unvaccinated Republicans. The median unvaccinated Republican believes that the percentage of unvaccinated people like themselves requiring hospitalization is 5 percent. How does that compare to how they believe the vaccinated fare? It’s exactly the same. They believe the hospitalization rate for vaccinated people is also 5 percent. So the median unvaccinated Republican essentially says the vaccines have net-zero efficacy — i.e. there is no benefit to getting vaccinated when it comes to landing in the hospital.

This, it bears reemphasizing, is not even close to accurate. A recent Centers for Disease Control and Prevention study found that unvaccinated people in Los Angeles County were 29.2 times more likely to require hospitalization. This was because they were about five times more likely to get infected, and then, once infected, significantly more likely to wind up in the hospital.

If anything, the most telling gap in this poll is between unvaccinated Democrats and unvaccinated Republicans. Both haven’t seen fit to get the shot; one group, though, is significantly more likely to correctively perceive a benefit if they do, while the other sees little-to-no benefit.

The dilemma from there is figuring out how that happens and what can be done about it. How is a class of people so badly misinformed about the efficacy of vaccines? Gallup surmises that it’s about the news they are consuming.

“Given previous studies on the effects of the media and information during COVID, one possible reason is that Democrats are more consistently exposed to information that favorably portrays vaccine efficacy,” Jonathan Rothwell and Dan Witters write.

Another way to say that would be that they are more consistently exposed to information that actually portrays vaccine efficacy accurately. Unvaccinated Republicans are getting their information from right-wing media and social media that dwells significantly more upon — and often hyperbolizes and misconstrues — the supposed negative aspects of the vaccines.

But while it’s been established how much that media and social media ecosystem oversells the side effects of the vaccines, less well established is how much it’s also feeding false perceptions of how well the vaccines work, even apart from those side effects. That might be as much because it ignores studies like the one in Los Angeles County as that it spins them in a negative light. It’s also possible that people who have decided not to get vaccinated are expressing doubt about vaccine efficacy to justify that decision.

But the effect is the same. And it makes persuasion of the remaining unvaccinated — and especially unvaccinated Republicans — doubly difficult.

Clarification: Some have noted that the median efficacy numbers used by Gallup in the chart above don’t line up with the median estimates for hospitalization risk next to them.

Gallup has clarified that the efficacy rates derive not from those median numbers listed, but from the median of all the estimates of the vaccines’ efficacy. “There are three median values shown, all of which are based on individual data,” it said. “1) the median of the unvaccinated risk distribution, 2) the median of the vaccinated risk distribution, 3) the median of the efficacy estimate. The median of the efficacy estimate of all individuals does not equal the ratio of the medians, because not every individual has the same efficacy estimate.”