In the case of inappropriate touching, 29 percent said that they would be less inclined to support the apologizing candidate; 25 percent said that they would be more inclined; 46 percent said neither.

In a diverse set of contexts, then, an apology tended to decrease rather than to increase overall support for those who said or did things that many people consider offensive. These findings are in line with earlier work by Richard Hanania, a research fellow at Columbia University, who found that apologies by public figures do not help and can even backfire.

Why is that? It’s hard to say for sure, but one reason may be that an apology is like a confession. It makes wrongdoing more salient. It can lead people to think: “We thought he was a jerk; now we know he is. He admits it!”

That’s why an apology can increase the antipathy of those who are inclined to dislike a public figure. And for those who are inclined to like him or her, an admission of wrongdoing is not likely to be a big plus, either. It may even look like a sign of weakness. President Trump, for one, is loath to apologize — for anything — and his supporters seem to love him for it.

To be sure, this research should be taken as preliminary. The surveys I have described are relatively small, and despite the demographic diversity of the various groups, they are not nationally representative. They also leave open questions. Perhaps the real impact of apologies occurs over weeks or months. The content and context of the apology surely matter. In some cases, a heartfelt statement of contrition can be essential if the goal is to make storm clouds pass.

Whatever their effects, apologies might be morally mandatory. As in ordinary life, so in politics: They might be a way of showing respect to those who have been offended or hurt, and of recognizing their fundamental dignity.

But the basic point remains. As a matter of simple strategy, apologies may not be a great idea. It is sometimes smarter for public figures to remain silent — or to change the subject.