DOVER, N.H.—Benjamin Bolger, an educational consultant from Hanover, N.H., left Elizabeth Warren’s rally no more certain about his vote than when he arrived.

Four years ago, Mr. Bolger, 44 years old, supported Hillary Clinton hoping his daughter might grow up with the first female American president. But while Mr. Bolger said he was strongly considering Ms. Warren in the 2020 race, he was also drawn to former Vice President Joe Biden and former South Bend, Ind., Mayor Pete Buttigieg.

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