It would be a mistake for Hillary Clinton to ask Sen. Elizabeth Warren of Massachusetts to be her running mate on this fall’s Democratic ticket. And Clinton is too savvy to do so, despite a recent poll in which more than a third of Democrats surveyed favored Warren’s selection.

There are obvious reasons for rejecting Warren, not the least of which is Clinton might then find herself in competition with her vice presidential choice. Warren has a strong following with the far left of the party and apparently is being promoted for the job by Clinton’s primary nemesis, Sen. Bernie Sanders, who technically still is in the race for the nomination despite Clinton’s status as the presumptive nominee.

Warren has been an all-out supporter of Sanders, and the thinking, apparently, goes that Clinton might need her to heal wounds in the wing she represents. While those who supported Sanders, many of them quite young, wouldn’t be expected to vote for Donald Trump, they might lose their enthusiasm for voting in general. So why not give them second best with Warren?

Clinton already is far ahead in the women’s vote. What she really needs is to crack the wall of distrust in the white male electorate. Another woman on the ticket would hardly do that. In fact, it might drive away votes.

The elephant — make that a donkey — in the room clearly is the question of whether voters would be comfortable with two women at the very top of the political food chain. After all, Clinton will presumably be the very first female major party nominee. Should she share it with another woman, especially one not closely compatible with her thinking? Probably not any more than Barack Obama should have chosen a fellow African-American as his running mate.

Warren is a charismatic figure with a proclivity for upstaging and might be difficult to manage. Her approach to government would hardly be in sync with that of Clinton, who is much closer to the center in her political philosophy.

Warren also represents one of the bluer states in the union, and Clinton should be able to carry it without her help. In truth, she and Clinton aren’t all that friendly. The Washington Post recently described their relationship as “frosty,” citing Warren’s book, “The Two Income Trap: Why Middle -Class Mothers and Fathers Are Going Broke,” as accusing Clinton, then a U.S. senator from New York, as being owned by Wall Street.

While a dozen names have been circulated as potential Clinton running mates, the early betting has focused on two: Sen. Tim Kaine of Virginia and Julian Castro, the secretary of Housing and Urban Development, both of whom strongly appeal to Latino voters, which, considering recent Republican-generated moves against Obama’s immigration policy, seems hardly necessary. Kaine, however, would give the ticket balance in a swing state.

Others being considered include Sen. Sherrod Brown of Ohio and Sen. Cory Booker of New Jersey. Brown is also from a highly important swing state, and Booker, as a former mayor of Newark, brings strong understanding of urban problems. Their party prominence and national name recognition, like Kaine’s, however, seem lacking.

In a recent poll for Bloomberg Politics, only 5 percent favored Kaine and 6 percent Brown as the possible vice president choices. Castro drew 12 percent, and Booker 17 percent. Democratic Party leaders are concerned that picking either Brown or Booker would damage the party’s ability to recapture the Senate because the act of replacing them would be left to Republican governors.

So where did Warren stand in the Bloomberg survey? She drew a strong 35 percent of the Democrats polled, a result that seemingly emphasizes the problems she might bring to Clinton during the campaign; Warren’s just a bit too popular, if one accepts the validity of the Franklin Roosevelt model for selecting a running mate.

Harry who? Much of the nation had never heard of Harry S. Truman when the obscure Missouri senator was picked as Roosevelt’s running mate in 1944. In four terms, the Depression-era and wartime president never chose a vice president he felt might compete with his own popularity. Obama wisely chose loyal and voter-friendly Joe Biden as his running mate.

Clinton is likely to follow those leads.

Dan Thomasson is an op-ed columnist for Tribune News Service and a former vice president of Scripps Howard Newspapers.