[Question] Wisdom of the crowds?

According to an aggregate of forecasts on metaculus, the probability of bitcoin going above 100k within the next 5 years is 60%.

Under which conditions is it rational to have my probability for some event match the (i) median of a large group of estimates (e.g. from metaculus)
or (ii) the average of their estimates? Or, (iii) is it merely rational to set (i) or (ii) as my prior?

If yes, to any of these possibilities, why? What is the justification? Could someone point me towards the literature on this question?

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