For much of my grad student career, I was part of "a convenient study population" — University of Illinois graduate students, or just grad students in English — and I definitely got invitations to be studied. With exquisitely bad timing, I finally rebelled and counseled rebellion in 1969 or 1970, when it turned out the researcher was the wife of another grad student in English at the U of IL, who (the husband) was both a well-liked colleague and a paraplegic, to add to the apparent nastiness of what could be interpreted as an attack on this nice couple.
I didn't intend to attack them. It's just that by 1970 I was tired of people's being quite so generous with my time and tired of people prying into my opinions, attitudes, and various feelings. As an undergraduate, my fraternity chapter had at least gotten free stuff for marketing tests — I recall Tiparillos as one horrible product we tried — and I was coming to the conclusion that if someone wanted my time, they could bloody-well pay for it.
And a few years later, I was offered a pittance to participate in surveys: primarily about batteries for some reason.
Anyway, by 1970 I'd had it with being surveyed, and I've gotten downright churlish about it lately, when I'm asked repeatedly to be "kind enough to take a short survey" to help construct The Grand Taylorite Panopticon to monitor employees and (more positively) independent folk selling books and films and other products.
So I understand how people far more dissatisfied with America in 2016 than I am would refuse to respond to political pollsters and how this could skew polls enough to get them wrong, Wrong, WRONG on the final outcome of votes such as that for BrExit and the 45th President of the United States.
Nowadays, all sorts of people are on-line and potentially in "convenient study populations" and are getting studied up the whazoo. Adding this to all the other generous donations of our time — starting with phone menus — it is no wonder that increasing numbers opt out.
So, Attention, Pollsters! (of all sorts): You're going to have to find indirect ways of measuring opinions. People who respond to your queries may become increasingly atypical, and maybe annoyed enough to get very creative with their responses.