And in a conflict heavily focused on which candidate is telling the truth, Ms. Warren faces a real risk: Several studies have shown that voters punish women more harshly than men for real or perceived dishonesty.

Depictions of female candidates as calculating or conniving are political mainstays. As long ago as 1984, opponents launched “authenticity” attacks against Geraldine Ferraro, the first woman to appear on a major party’s presidential ticket. This pattern endures regardless of who is telling the truth, these studies conclude, and regardless of either candidate’s intentions. If voters conclude that Ms. Warren is lying, it is most likely to hurt her more than it will hurt Mr. Sanders if voters conclude that he is lying.

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