I am quite unsure as to the veracity of the claim that "the average will converge [upon] the truth". I recall cases being made (as asides) for the opposite conclusion. Intuitively even, this idea of equating truth with convergance towards the average opinion appears contradictory, counterfactual, and ahistorical. Excuse my being brass, but a "wisdom of crowds" seems to me oxymoronic on its face. I'd love to be persuaded otherwise though; mainly due to my perception of a lack of credence towards your view. Perhaps I have misunderstood your qualifier: "As long as there isn't a strong truth bias to people's estimate . . . "? Off the top of my head, I can't imagine any scenario in which a mixed population of laypeople and academics/experts would converge towards the same (vote average) findings as a sample of a handful of experts/academics. For example, would The Average converge towards correct mathematics or physics answers? Besides trivial, non-technical questions that do not require complex analysis, I think not. (See: False Memory: Mandela Effect. [0] [note])
[0]: https://en.m.wikipedia.org/wiki/False_memory#Mandela_effect
[1]: https://en.m.wikipedia.org/wiki/Information_cascade
[Note]: My point is that groups' thinking is liable to be compromised. (After all, what has been more important to a human — evolutionarily: the truth or social access?) Also see: Information Cascade. [1]
{Post-Scriptum: My position is that if averages for answers to questions were taken, from the 'crowd' of the whole Earth, then these would diverge significantly and routinely from The Truth. If there are cases in which you feel this to not be the case I would inquisitively consider such scenarios waveBidder.}
<Edit: Deletion: " . . . ~difficulty in lending~ . . . ">