A call for solutions and a tease of mine

Downvoted for the tease aspect - don't do that. Instead, make a post describing the assumptions and premises in concrete terms that lays the foundation for your proposal. Or put the whole thing in an open thread and see what responses you get and what you'd need to expand on before making a top-level post.

not downvoted for the problems I suspect you'll hit. I very much hope you can address them, though:

You say: opinions, the judgment, of the group members, not their personal preferences, but there aren't many individuals who can clearly distinguish among these things. If your mechanism depends on rational participants, it won't work too well for humans.

More importantly, you say that a well-defined group charter is a given. But there is no group with such a thing. Groups tend to have natural-language charters, and members routinely ignore even those.

The obvious answer from this crowd is some kind of prediction market, with the "group charter" being turned into a measurable utility function with which to make the judgments about the success or failure of a policy. If people are restricted to using only money from an equal "allowance", plus whatever they have earned from predictions, over time those who have made more accurate predictions gain the most influence on the outcomes of the decisions.

It seems likely that the optimal solution would, perhaps strongly, depend on details that are not given in your post. The composition and size of the group spring to mind, but there are other factors as well.
Is there any specific type of group that you're thinking of, or do you think that there is a one size fits all solution? The latter seems unlikely unless you are thinking of a meta-strategy for choosing between decision making processes rather than a decision making process.

Different members have different opinions, because they're not perfect reasoners and because their interests don't reliably align with those of the group.

I'm going to channel Margaret Thatcher: there is no such thing as society. That is, there is no such thing as "the group's interests" and attempting to compare the solution you have to the "group's interests" is the wrong question. The real question is, how do you aggregate the opinions of those members?

It seems almost impossible to me that there will be a "universally correct" solution, especially if where to draw group boundaries is part of the problem. If the optimal economic organization is hierachical groups existing in a non-hierarchical ecosystem, then it seems wrong to claim hierarchy is universally correct (when it is terrible applied globally) or that non-hierarchical is universally correct (when it can be terrible applied locally).

I think the "tease" element here might be better suited for the Discussion section, though the topic itself certainly seems interesting enough to merit a top-level post.

I think that lots of people are ignoring the whole 'could be implemented' part.

Given a group objective function so well defined that only measurement errors and uncertain expectations make choosing the optimum nontrivial, there remains the difficulty of obtaining group members' honest estimation of the outcome distribution of the plans under consideration. Further, you want to do better than just averaging estimates; you want to combine information without double-counting.

When (as in reality) people's actual preference for the group decision isn't exactly the stated group objective, I'm daunted by the difficulty of soliciting their reasons+evidence in such a way that they can't dishonestly push the decision toward their desired outcome.

As historical examples you give forms of democracy and hierarchy, which are ways for a group to choose which action to take out of several options. But then you say that you don't want answers like IRV. I can't tell how to interpret your proposed distinction between "opinions" and "preferences".

Obviously, if we're talking about voting methods, then Arrow's Impossibility Theorem and some other related theorems may be of interest. Loosely speaking, they say that no deterministic way of structuring a group can simultaneously meet certain basic standards of fairness and consistency.

If all you want to do is solicit opinions but not vote on them, then I propose that the most straightforward way is best: ask for opinions. Let them be submitted anonymously to avoid going to Abilene.

Prediction markets?

Brainstorm a bunch of actions and outcomes. Each member privately assigns an utility to each possible outcome, how likely they think each action is to lead to each outcome, how trustworthy they think each other member is on the question, etc. etc. Then you feed all of this into a black box AI algorithm and it outputs what action should be taken, which everyone simply has to take on faith until they have enough examples to take it on induction.

So my answer is the meta one of "I don't know, but whatever it is it'll be a complex or even downright inelegant, found through testing and interaction with the real world and/or simulations rather than armchair theorising or mathematical derivation from first principles, probably involve large datasets and some kind of machine learning algorithms, and not possible to implement well on a human brain".

What was that line in Fight Club?

Narrator: When people think you're dying, they really, really listen to you, instead of just... Marla Singer: - instead of just waiting for their turn to speak?

No matter what anyone says here, I get the feeling you're just waiting for your turn to speak. Why don't you just do it?

A post like this belongs in Discussion.

Well I came up with an interesting idea a few weeks ago for this very problem.

You get a hypothetical bayesian judge to take each person's opinion as evidence.

I don't know the details, but you might make people do some calibration tests to adjust for overconfidence, stupidity, etc.