I do believe I have a very plausible hypothesis, though, and I find it sufficiently plausible that I'm going to reserve judgement on the true beliefs of people until we see that anonymous poll.
Which is exactly why we not only allow, but actually enforce it in elections. If your vote could have a strong impact on e.g. your future employment, you wouldn't be free to vote for what you think is best, you'd be compelled to vote for what you think is perceived best.
I'd also point out that secret ballot is not universal in the US. Certainly the votes of elected officials are not secret. But neither are open votes at, say, a town hall meeting.
I'm not suggesting they'd have to do that, I'm saying that there's a very good reason why we usually do that. As organizations become more and more political, I expect that to hit harder and for more of them to adopt secret voting.
> Certainly the votes of elected officials are not secret.
And I find that reasonable. You want to know whether the person you voted for actually does what they said. In Germany, parliament votes are public, but important votes are secret.
For the less important votes, they'll just ask for raised hands and note who won, but not who voted in what way (we now have TV channels film the votes and then use interns to determine who voted what).
For important votes, they're done secretly: you can tell who voted, but not what they voted for. There's no way to hold them accountable, the system is working as intended.
If you want to know what people really think without the possibile influence of preference falsification, it needs to be an anonymous poll.