(AP Photo/Charlie Neibergall)

Current Secretary of State Hillary Rodham Clinton waves at the crowd at the 2008 Democratic National Convention.

Shortly before the Democratic National Convention opens in Charlotte, North Carolina, next September 3, Barack Obama should announce that he has asked Secretary of State Hillary Clinton to join him on the ticket as the vice-presidential candidate, and Vice President Joe Biden to become secretary of state in his second term—and that both of them have agreed.

A Clinton-Biden switch can improve the odds of a Democratic victory at a time when economic conditions would make re-election difficult for any president. As secretary of state, Clinton has been associated with the part of the Obama administration that enjoys the highest approval. Just as important, she has not been associated with economic policy and could now provide the ticket with a fresh voice and sense of renewal on economic issues.

According to polls, Clinton has been the most admired woman in America for the past seven years. Much of the old hostility toward her has faded away, and what remains is a wide respect for her steadiness, perseverance, and intelligence. Recent surveys put her approval ratings in the high 60s, considerably higher than Biden or Obama himself. In fact, a Gallup poll earlier this year found that 45 percent of those who disapprove of Obama’s performance viewed Clinton favorably. As was true in 2008, she continues to have more appeal than Obama among older, white voters, a group that turned sharply toward the Republicans in 2010.

The main value of bringing Clinton forward as vice president, however, would be to raise enthusiasm and voter turnout in the core constituencies of the Democratic Party. Clinton’s strength among women, Latinos, and Jews could be of particular value in 2012.

One recent poll suggests that Hillary Clinton’s bases of support could help Obama in a crucial state. According to a survey of voters in Florida by Suffolk University, Republicans would win the state with Marco Rubio as their vice-presidential nominee, but Obama would prevail by adding Clinton.

Of course, Clinton has said that she intends to step down from the State Department at the end of Obama’s term and that she has no further intention of running for president. “I have made my contribution,” she told NBC’s Today show in October. “I’m very grateful I’ve had a chance to serve, but I think it’s time for others to step up.”

Referring to her 2008 primary race against Obama, she continued: “We had had a hard-fought election, and I wanted to beat him, and he ended up beating me. But he asked me to serve our country and him in his administration. Why? Because we both love our country. So I said yes.” If Obama now asked her to join him as vice president, she might also say “yes,” with much the same explanation.

The appeal of switching Biden’s and Clinton’s roles is that it would also show no disrespect to Biden, who chaired the Senate Foreign Relations Committee before becoming vice president. By all accounts, Biden has done a capable job, but he does not have anything approaching Clinton’s electoral appeal.

Some may object that, despite the attractions of a switch, the choice of vice-presidential candidates doesn’t affect the outcome of presidential elections. But that’s not what the political-science literature on the subject suggests. In a 2010 study in Presidential Studies Quarterly, Bernard Grofman and Reuben Kline find that the choice of the vice president has limited but, as they say, “non-trivial effects” on voters’ choices. At most, they detect a shift of only about 1 percent of the vote (though their model cannot capture voter-turnout effects). Still, several recent presidential elections have been decided by close margins. If Obama wins in 2012, it seems unlikely that he will win in a landslide. An extra 1 percent of the vote—tipping a state like Florida—could be decisive. Ask Al Gore.

There is also a longer-term consideration for the Democratic Party. If an Obama-Clinton ticket succeeds, it would position Clinton unambiguously to run for president in 2016. That may not just be in Clinton’s interest. Because of losses in gubernatorial and congressional elections in 2010, the Democrats today do not have a deep bench of potential presidential candidates with ready-made appeal. The party’s best shot in 2016 may well be with Clinton.

If Obama were to ask Clinton to run as vice president, they would need to work out her portfolio of responsibilities. Beginning with Gore, recent vice presidents have exercised far more influence than most of their predecessors, and Clinton would reasonably expect a significant role. There’s no reason to think she couldn’t resolve that with Obama; from all appearances, they’ve been able to work effectively together while she’s been secretary of state.

But why should Clinton risk her reputation in what may seem like a chancy race in 2012? After all, if she just steps down from the State Department, she will not only have a respite from public demands but also the opportunity to position herself as the front-runner for 2016 regardless of what happens in 2012.

Unless Obama can prevail on her to join him on the ticket, Clinton may well decide that her best course is to return to private life. Anyone who has traveled as many miles as she has as secretary of state has a right to rest. But that is also a reason why her decision to run with Obama would be so well received among Democrats. Clinton doesn’t need to do it, but if she does, she could make all the difference.