This entails the ability to change one's mind as in "previously, I would have done this but given the new evidence now I favor that" - something often seen as weakness in politicians.
"So why were you wrong in your estimate?" or even worse, now your estimates gets discounted next time. And the same holds true if it happens the other way round.
It can be useful to explicitly state error bars. "Delivery will take three to seven days" communicates uncertainty much more clearly than "delivery will take about five days".
It sadly means unwashed masses, including your administration and your bosses, are hostile to rationality, and to their own peril. But we all know that.
