A new survey finds that a substantial majority of voters believe Hunter Biden profited off his father’s vice presidency, though many respondents said they thought it common for children of politicians to trade on their parents’ names. This suggests many Americans are getting mixed messages on the investigations into President Biden’s son.

For nearly three years, the younger Mr. Biden has been a key part of Republican messaging against the president, with congressional Republicans claiming that the president’s son engaged in influence peddling and made corrupt business deals involving his father, among other things.

The new survey from the Economist and YouGov finds that, while most Americans believe that the younger Mr. Biden profited based on his father’s position in government, they don’t necessarily see children of politicians profiting on their parents’ names as unusual, and they have devoted a limited amount of attention to the issue.

According to yesterday’s poll, 72 percent of Americans believe that the younger Mr. Biden made a profit from his father’s position in government. Another 6 percent believe he did not, and 22 percent said they were not sure.

Broken down by party, 53 percent of Democrats, 72 percent of independents, and 92 percent of Republicans reported believing that Mr. Biden had profited from his father’s position.

As a baseline, the survey also asked, “How often do adult children of U.S. presidents personally profit from their parents’ positions in government?”

In response to this question, 41 percent said that a president’s child “always” profits from a parent’s position, and 44 percent said that they “sometimes” do. Another 4 percent said a president’s child “rarely” profits from a parent’s position, and 1 percent said that they “never” do.

In terms of the Department of Justice’s investigation into the younger Mr. Biden, a topic that has become a recent source of complaints for critics of the president’s son, respondents appeared to have mixed feelings.

The survey found that 38 percent thought the investigation had been “fair,” 22 percent said it had been “unfair,” and another 40 percent weren’t sure whether it was fair.

Even some Republican respondents appear to have lost track of the tangled investigation into the younger Mr. Biden and the various claims made about the justice department investigation by Republican officials over the past three years.

Among Republican respondents, 32 percent reported feeling that the investigation has been fair, 37 percent reported feeling that it has been unfair, and 39 percent reported not being sure.

In terms of which voters are paying attention to the investigations into the younger Mr. Biden, the poll found that Republican voters are the most likely to be interested in news related to the president’s son.

Among Democrats, 35 percent said they had heard a lot about the investigations, 53 percent said they had heard a little, and 12 percent said they had heard nothing at all.

Among Republicans, 49 percent said they had heard a lot, 43 percent said they had heard a little, and 9 percent said they had heard nothing at all about the investigations.

Among independents, 29 percent said they had heard a lot about the investigations into the younger Mr. Biden. Another 46 percent said they had heard a little, and 25 percent said they had heard nothing at all.

The poll of 1,500 adults had a margin of error of plus or minus 3.2 points.