This frightens me because it sounds like the setup for a preference cascade, where everybody realizes that they aren't alone, that everybody else thinks as they do. Suddenly the familiar order inverts almost overnight.
To some extent, you see the real preferences when it comes to single-issue referendums (since the vote is secret, and there are no secondary "tactical voting" considerations there that might skew the preference). Some examples:
https://ballotpedia.org/Washington_Referendum_88,_Vote_on_I-...
https://ballotpedia.org/California_Proposition_16,_Repeal_Pr...