What sense did you mean to describe Democrats/libertarians/etc. choice about a singleton? Actual informed choice? Does this choice disagree with what you think they should choose (in the sense of what they would choose if they were smarter and more informed than they can ever actually be, but with the same values, which are not necessarily equal to yours)?

An uninformed choice would be a random choice.

Nothing is random in this sense. A choice made with limited ability to reason, even if "informed", still involves a fair amount of noise. Not being reliably informed of what the question actually means is but a grade of the same problem. Thus, I meant "uniformed choice" in the sense of not being reliably the correct choice, for one reason or another.