We included a question in our surveys that allows us to estimate which candidate undecided respondents actually supported: “If you HAD to choose, which presidential candidate do you find to be more truthful: Donald Trump or Hillary Clinton?” For “decided” voters, this question accurately predicted their vote intention 98 percent of the time in the GfK survey and 94 percent in the SRI survey.

For undecided voters, the emphasis on truthfulness and the way the question required a choice (“if you HAD to choose”) should have helped alleviate respondents’ concerns about being judged for their response. Indeed, nearly every survey respondent answered it. We believe that undecided voters’ answers revealed their fundamental partisan leaning.

And once they did so, Clinton’s lead shrank in both surveys. For example, in the GfK survey, the standard question showed that 42 percent supported Clinton, 34 percent supported Trump, 11 percent supported some other candidate, 12 percent did not plan to vote and 1 percent did not answer. So Clinton led by eight points.

But when asked the question about truthfulness, Clinton’s lead shrank by half — to four points. In other words, already in early October, pushing people to reveal their preferences by asking about truthfulness helped Trump.