wnoise comments on Navigating disagreement: How to keep your eye on the evidence - Less Wrong
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Re: problem 1: Jelly bean number estimates are just like thermometer readings, except that the reading is in someone’s head, rather than their hand. So the obvious answer is to average everyone’s initial, solitary impressions, absent reason to expect one individual or another is an above-average (or below-average) estimator.
If your friends use lopsided weighting schemes in their second answers, should you re-update? This depends a lot on your friends.
I would look for response clusters. Each participant could have a different counting method rendering different results (e.g. - estimate volumes/ count radius & height/ estimate there's an empty cone at the top which you don't see), and some methods could be common pitfalls. Therefore, some results - those obtained by a wrong way of counting, should be discarded, otherwise the median result would lead away from the right result. In order to decide which is the right response cluster, trying to figure out each method/mistake and determining the correct one would be useful. Of course, your method is not necessarily the right one, just because it's yours.