OK. If the 2nd proposition holds, why do you think the agreement in the 1st proposition is correct? If they do think they are not qualified to decide as a group

OK. If the 2nd proposition holds, why do you think the agreement in the 1st proposition is correct? If they do think they are not qualified to decide as a group, why do they think they are qualified to correctly select the leader? But that aside, as I already explained, this is pretty easy to do with voting. All that's needed is that everybody (including the leader) voices their opinion. The people who feel that they are not qualified to make the decision can just vote for what the leader would vote for. Maybe what you mean is that there is a person A who thinks that person B should get no vote, because they are not qualified enough (or perhaps that some other person C should get more votes, it's a similar deal). But this is already reflected in the "objective" probability of B making the correct decision. So either A's opinion agrees with the probability (through his own probability to make good judgement), in which case it doesn't matter. Or, it disagrees with the probability, and then following A's opinion can only make the result worse.