Will a potential Republican presidential candidate give a speech about the crisis in Ferguson, Missouri? It would be a political opportunity, a chance to prove that he is precisely the type of leader the likely 2016 candidates will claim to be.

In the GOP jockeying for position, every public flashpoint provides a chance for a candidate to distinguish himself in a crowded field. The men thinking about a run are usually not shy about speaking up. In the crassest political terms, a dedicated speech would allow a candidate to use the public attention surrounding the grand jury verdict and its aftermath to gather some attention for himself. Afterward, he could make fundraising calls and quote from the favorable press coverage. If the speech is good enough, perhaps a friendly columnist would say that he looked “presidential in addressing the complex issues of the day.” Meanwhile, loyal aides could call reporters and say the speech demonstrated that the candidate had shown he was the unique figure to expand the Republican Party’s appeal, something beyond being a party that ex-Republicans described as “narrow minded,” “out of touch,” and full of “stuffy old men,” words used in the post-2012 autopsy commissioned by the Republican National Committee.

Perhaps that’s not enough political benefit to entice a GOP candidate into giving a risky speech on a topic GOP primary voters don’t have at the top of their list. As voters, we should hope several of them give such speeches, though, because they would give us insight into whether the candidates have a few of the attributes that might be useful if they were ever elevated to the top job.

The first thing we’d learn is if a candidate can speak across the divide. Almost all GOP candidates are claiming that they could solve Washington’s political mess by bringing people together. A central attribute required for that—whether its uniting the religious and secular, poor and wealthy, or conservatives and liberals—is being able to speak to two different constituencies, demonstrating that you understand the frustrations of each side and using that understanding to build a tentative path to progress. Here’s a chance to show some of those skills. The bar is low and achievable. No one expects a candidate to have the solutions, he simply needs to show he is sensitive to the challenge.

For some candidates—particularly the governors—such remarks would be a special opportunity to show what they’ve learned in office about race relations. Govs. Scott Walker, John Kasich, and Chris Christie, and former Gov. Jeb Bush, have governed states with large black populations in some cities. Surely they can draw on that experience. Walker was Milwaukee County executive in a county with a 26 percent black population. Christie was a federal prosecutor, which gives him special insight.

Perhaps most important, we’d get a window into a candidate’s worldview as he framed the issues. “Ferguson is a manifestation of the racial division as we see it right now,” Ben Carson, who is thinking about running in 2016, said on Meet the Press. “There are a lot of people around this nation who feel things are unfair for them, who feel disenfranchised. And it makes them ripe for a tinderbox situation like this to occur.”

True, but what is that division about? Is it, as President Obama says, about a “simmering distrust that exists between too many police departments and too many communities of color”? Or is the larger issue about poverty and the legacy of racism, early-childhood education, drug laws, and family structure? These are issues that affect people of color but also white Americans. Every presidential candidate of both parties should have a take on how to frame and address these questions.

The least substantive thing we’d learn is whether a candidate has rhetorical power. But speechmaking does matter in campaigns, and a bad speech can muddle the benefit of political gambits. Sen. Rand Paul’s speech at Howard University in April of last year was somewhat risky, but it was a bland speech, which gave us insight into the way interesting ideas can die at the edge of the podium.

A possible model is Barack Obama’s keynote address at the “Call to Renewal” in June 2006, in which he tried to bridge the gap between the religious and secular in politics. All of the tough problems of poverty and the environmental stewardship that both parties wanted to address would remain unsolved, said the first-term senator, “unless we tackle head-on the mutual suspicion that sometimes exists between religious America and secular America.”

The speech was a political gambit. Obama wanted to show that he was a different kind of Democrat, one who believed in Jesus and had been transformed by his message—something that would also make him a more appealing candidate to a broader group of voters. Obama was trying to show that he could be a bridge—a leading voice in a secular party speaking for the values of the other party by chastising himself for too easily dismissing their faith-inspired views on issues like abortion. When he was a Senate candidate, Obama’s campaign had characterized anti-abortion-rights politicians as “right-wing ideologues who want to take away a woman’s right to choose,” and a doctor had written him to say that he had been offended by the implicit denigration of his faith. “I felt a pang of shame,” recalled Obama. “It is people like him who are looking for a deeper, fuller conversation about religion in this country.”

Future Republican presidential candidates aren’t likely to borrow from the man in office they think has been so ineffective, but he was a rather successful politician in 2008 in part because of speeches like this, which appealed to voters’ desire for greater national unity. As my colleague Jamelle Bouie pointed out on the Slate Political Gabfest, the most effective speech any politician could give in the wake of the Ferguson verdict might be one given by a Southern Republican. If a Republican, whose party benefits from the overwhelming support of white voters, could serve as a witness, at some level, to the feelings of distrust and anger within the black community, it might contribute to the conversation so many people say we should be having. It would not require abandoning values or offending their core constituency. Such a speech could even eclipse whatever President Obama says on a visit to Ferguson, given that he is hemmed in by the responsibilities of his office and the political crust of the past six years.

Of course, a potential GOP presidential candidate might choose an entirely different path. Instead of offering an example of bridge building, he might decide that the requirement after Ferguson is to defend the police force against a media that has convicted an officer trying to do his job in a brutal environment and speak up for the 61 percent of Republicans who in August thought race was getting more attention than it deserved, according to a Pew poll. Whichever route a candidate takes, such a speech would certainly distinguish him, and almost every future candidate wants that right now.