Assuming there is a PC choice and an PI choice in a vote is there a known tendency of voters to tell pollsters that they are going to make the PC choice when in fact they are actually going to make the PI choice?
The pollsters (and the betters) obviously thought the “remain” option would get at least 50% of the vote and it wasn’t really that close (although doubtless they will tell us it was within their margin of error). And Trump has generally done considerably better than anyone predicted. And maybe will do better in November than anyone predicts.
There’s the well-known “Bradley effect” where white voters tell pollsters they support an African-American candidate but then vote for the white opponent.
It’s not reliable though, because studies also show that even solidly conservative white voters will vote for an African-American candidate because of economic or other reasons. Take a look at Barack Obama’s perfromance when he ran for Senate in 2004.
Social desirability bias.
It’s not limited to politically correct vs incorrect choices, either. It refers to any time the respondent minimizes or under-reports negative information (things that are shameful, undesirable, or embarrassing). It can also refer to people over-reporting or over-emphasizing positive information. This can include telling the pollster what you think they want to hear or saying whatever will make yourself look good.
Where did you hear that the pollsters had remain above 50%? I don’t think many polls in recent weeks had either side above 50, and several had leave over remain.
Watch the latest episode of Wrecked on TBS. In short, their plane crashes on a desert island. The survivors find a DVD player with enough battery power to play only one DVD, and a search of the luggage yields only two DVDs: Dumb and Dumber To, along with the MLK Jr. epic Selma. Thinking this might be the last DVD they ever get to see, they should of course choose Selma. No one is quite brave enough to say anything else, at least while everyone else is watching, but privately they all choose the Dumb movie. I thought it a nice representative of what the OP is asking.