Before reading your answer: Human beings are bad at estimating volumes, as opposed to lengths. I would form my estimate by observing the apparent density of jellybean in the jar (e.g. by examining a square centimeter cross-section), observing the dimensions, and multiplying. Then, on the second stage, I would discard estimates which are radically different from mine (cutoff to be chosen based on observed distribution), and take the mean of the remaining. I would allow myself to be influenced in my choice of data to include by those whose data I was already inclined to include in my average.

After reading your answer: Should I notice an apparent and popular upweighting of certain responses such as you suggest, I would increase the weight of those in my average.