There is not much of a partisan gap here, nor is there that much of a difference between partisans and independents. Substantial minorities in both parties and a majority of independents believe something about the state of U.S. military power relative to the rest of the world that is just breathtakingly wrong. It is startling that 47% of Americans don’t know that the U.S. is far and away the world’s leading military power, especially when the U.S. military has been engaged in so many wars during the last twelve years and national politicians refer to U.S. military predominance all the time. One might simply bemoan the degree of public ignorance that this poll result reflects, but that isn’t sufficient. In this case, a faulty, exaggerated view of other states’ military power probably accounts for most to the respondents’ error.
Golan-Vilella notes that the error keeps cropping up each time Gallup asks this question:
After all, as Gallup has asked that question over the past twenty years, at least 34 percent in every survey have denied that America has the world’s strongest military. The number may have increased over the past three years, but the misperception it represents is not a new one.
Indeed, looking at Gallup’s results over the last twenty years, it is not immediately obvious why the respondents’ error changes one way or the other:
I agree that threat inflation  must have some role in giving Americans the wrong idea that there are other states equal to to the United States in military power, since it’s doubtful that nearly half the population could come to such a seriously mistaken conclusion without some significant help from alarmist hawks. But hyping and inflating threats from other states can’t be the whole story. The last time that so many Americans misjudged the extent of American military power this badly was in 1999, which followed six years of fairly frequent, uncontested uses of U.S. military power in various parts of the world. By that point, the U.S. was already being criticized by French Foreign Minister Vedrine as a “hyperpower,” so it’s odd that there are any Americans that would be under the impression that other states were military equals with the U.S. By comparison, the belief that the “U.S. is number one” rose throughout the Bush years (the period when hawkish threat inflation was arguably the worst it has ever been since the Cold War) and reached its highest point halfway through Obama’s first term. It then dropped quite quickly over the last few years.
This suggests two possible additional explanations. When the U.S. fights major foreign wars, the well-publicized exercise of U.S. military power–no matter how unnecessary or self-defeating–drives the public perception that the “U.S. is number one” up and drives the other result down. When the U.S. concludes these wars or is perceived to be in the process of bringing them to a conclusion, we seem to see the reverse. A related explanation is that concluding wars, withdrawing forces from other countries, and considering the possibility of reduced military spending provoke hawkish warnings of American “decline.” That leads to a different sort of alarmism about the dangers to the world that could result from this so-called “decline.” Hegemonists don’t seem mind encouraging the public to believe that other states are near parity with the U.S. in military strength so long as it achieves the goal of frightening them into support for all-time post-WWII high levels of military spending, which is why we sometimes hear nonsensical hegemonist warnings about the dangers of Russia or China taking America’s place as hegemon.