Welcome to Poll Watch, our weekly look at polling data and survey research on the candidates, voters and issues that will shape the 2020 election.The trips this week to Kenosha, Wis., by President Trump and Joseph R. Biden Jr. laid bare the political bets both presidential candidates are making about how voters will respond to the scenes of unrest playing out in some American cities.Mr. Trump has focused on his support for law enforcement while criticizing rioters as “anti-American,” hoping to stir fear among swing voters about unruly demonstrations.Mr. Biden, for his part, has hit back hard, insisting that right-wing vigilantes are also a big part of the problem — and that systemic racism must be rooted out of law enforcement to help heal the country. At the same time, he has sought to turn attention back to the coronavirus pandemic, saying the president has failed to address both crises.The question on most political observers’ minds is simple, but impossible to answer in a simple way: Which narrative will win?For pollsters, who use straightforward questions to take a read on the national mood, this moment presents a challenge. How can they ask questions that drive to the heart of the debate, when neither side can even agree on its terms?In recent weeks the standard wordings have felt insufficient, and polling firms have adjusted the questions they’re asking. They’re seeking to determine which candidate’s approach resonates more — not only whether voters are truly worried that the flare-ups of urban violence will reach their homes, but also whom they blame for them and how they think they should be quelled.“What we want is good measurement, and if past measurements are out of whack with the current situation, then we have to revise them and try to test other approaches,” said Gary Langer, whose polling firm conducts research on behalf of ABC News, The Washington Post and other news outlets.Take “race relations,” for instance. He said that “may be a term or a phrase that has durability in some circumstances, but is not particularly apt in current circumstances.”In polls released on Thursday by Quinnipiac University from the battleground states of Pennsylvania and Florida, researchers asked voters who they thought would do a better job guiding the country through a crisis — language that intentionally wasn’t specific to the pandemic or the protests.In both cases, voters were slightly more likely to choose Mr. Trump than they were when asked about the coronavirus crisis specifically. (Since the start of the summer, he has consistently earned low marks on the pandemic.)In Pennsylvania, a slim majority still preferred Mr. Biden to command the country during a crisis, but in Florida, it was about an even split: 49 percent Mr. Biden, 47 percent Mr. Trump.This partly helps explain why Mr. Trump has sought so hard to replace conversations about racial justice and the coronavirus with a focus on what he has called “mob violence.” In Pennsylvania, just 31 percent of independent voters said they preferred Mr. Trump on handling racial inequality — but that ticked up to 40 percent when asked who would better handle a crisis.Still, the fact that most independents did not choose Mr. Trump even on this question underscores his difficulties with this crucial group, which narrowly broke for him in 2016, according to exit polls, but now consistently expresses misgivings about re-electing him.The president’s attempts to highlight the clashes in cities have clearly had an impact: In its polls of Pennsylvania and Florida, Quinnipiac gave voters a choice of eight top issues and asked them to identify their No. 1 concern. In Pennsylvania, where Mr. Biden led by eight percentage points among likely voters, “law and order” was roughly tied for second place, along with race relations and the coronavirus. Only the economy was cited more often.In Florida, nearly one in five voters cited law and order as the main concern — again, second only to the economy.In both cases, conservatives — following Mr. Trump’s lead — were far more likely than others to name law and order as their biggest concern, but 12 to 15 percent of moderates chose it too.An ABC News/Washington Post poll of the country conducted just before the party conventions asked voters whether they thought they would be safer or less safe from crime under a Biden administration. The most popular answer, chosen by four in 10, was that things would probably be about the same either way. But among those who picked a side, there was a seven-percentage-point tilt toward those who thought they would be less safe under Mr. Biden, not Mr. Trump.White suburbanites — a group being targeted by both campaigns — were 20 points more likely to say Mr. Biden would make them less safe than to say Mr. Trump would.Still, it’s not clear that most voters see the protests as a dire threat, as Mr. Trump is encouraging them to do. According to a USA Today/Suffolk University poll of the nation released this week, Americans said by a 21-point margin that even though some protests had resulted in violence, peaceful demonstrations should not stop. That poll was conducted before news emerged that a Black man had died in Rochester, N.Y., in March after police officers placed a mesh hood over his head, adding fresh fuel to the fire of protesters’ frustration.Fox News released three polls on Wednesday from battleground states: Arizona, North Carolina and Wisconsin.Those polls asked voters whom they trusted more to handle criminal justice and policing, a more specific query than “race relations” but perhaps not as threatening as “crime.” In Arizona and Wisconsin, voters leaned toward Mr. Biden by five points, but in North Carolina they were basically split even.In all three states, the preference for Mr. Biden on policing and criminal justice lagged slightly behind his advantage over Mr. Trump in the horse race. And it was significantly less than his usual lead when people were asked whom they trusted more to handle race relations.Although the economy is still the most often-cited concern for voters in many battlegrounds, it’s not guaranteed that Mr. Biden would altogether benefit from pushing the debate onto economic matters. Polls continue to show that he has failed to reverse voters’ slight preference for Mr. Trump as a steward of the economy.But on the coronavirus, Mr. Biden clearly has the advantage. Multiple national polls this week showed Mr. Biden with a double-digit lead on whom Americans preferred to handle the pandemic; independents chose Mr. Biden by roughly 20 points.