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Because this is a good use of time on Saturday night, I want to just pull out this 2016 post-mortem from the pollsters' professional org (full disclosure, I'm a member), which examines in depth the possibility for a shy Trump vote.
Short version: tests “yielded no evidence.”
Short version: tests “yielded no evidence.”
1. If "shy Trump" voters were a major factor, support for Trump should have been greater in polls that didn't use live interviewers.
"[I]nterviewer administered polls did not under-estimate Trump’s support more than self-administered IVR and online surveys"
"[I]nterviewer administered polls did not under-estimate Trump’s support more than self-administered IVR and online surveys"
2. You also might expect to see "shy Trump voters" be uniquely likely to say they were undecided or refuse to answer.
"[T]here is no evidence that higher rates of undecided or refusals to answer (that is, nondisclosure) is associated with level of Trump support"
"[T]here is no evidence that higher rates of undecided or refusals to answer (that is, nondisclosure) is associated with level of Trump support"
3. A few pollsters actually directly tested the live-interview/non-live interviewer experiment directly, by dividing respondents into two groups. From Pew: "There was no significant difference by mode of interview on any of four questions asking directly about Trump"
4. If voters were uniquely reticent to say they supported Trump, you'd expect him to outperform the polls more than other GOP candidates did.
Trump outperformed live-caller poll estimates by an average 1.4 points, compared to 1.3 points for GOP senate candidates
Trump outperformed live-caller poll estimates by an average 1.4 points, compared to 1.3 points for GOP senate candidates
5. "Shy Trump voters" might have been less inclined to divulge their support to female/non-white interviewers. No evidence of this, which "is not conclusive evidence against the Shy Trump hypothesis. However, the result is inconsistent with expectations of the Shy Trump theory"
6. Trump supporters might have been less likely to answer polls all together. This is one of the more alarming versions. A subsequent Pew study on non-response found "D-leaning adults were not more inclined to take the survey than R-leaning ones." https://www.pewresearch.org/methods/2018/10/09/the-rbs-poll-comports-well-with-data-from-the-full-voter-file-about-the-partisanship-of-registered-voters/
Anyway, you can't prove a negative, but there's simply not a whole lot of evidence to suggest that "shy Trump voters" are a major factor with what went wrong in 2016, including in places you'd expect to find that evidence.
The report is worth reading if you're interested in that sort of thing!
Here's also a more in-depth piece I wrote on the post-mortem:
https://www.huffpost.com/entry/polls-wrong-2016_n_590b9e9de4b0104c734d6132
And a piece from 2018 on what pollsters have changed since: https://www.huffpost.com/entry/how-polling-has-changed-since-2016_n_5bde07b4e4b04367a87d14ab
Here's also a more in-depth piece I wrote on the post-mortem:
https://www.huffpost.com/entry/polls-wrong-2016_n_590b9e9de4b0104c734d6132
And a piece from 2018 on what pollsters have changed since: https://www.huffpost.com/entry/how-polling-has-changed-since-2016_n_5bde07b4e4b04367a87d14ab
To lift from that first piece -- what happened in 2016 was "a perfect storm of small but compounding problems." Some, e.g. weighting issues, are fixable. Others, e.g. late deciders breaking hard one way, are just a part of the uncertainty inherent in even good polls.
Election polls aren't useless. They're also not a guaranteed forecast of what's going to happen in the future, nor a pinpoint-precise measurement of what people think now. In general, they're a pretty good gauge for the basic state of an election at the time they're taken.
For sake of balance, contrarian take: https://www.washingtonpost.com/news/monkey-cage/wp/2016/12/13/why-the-polls-missed-in-2016-was-it-shy-trump-supporters-after-all/
