What? Evidence is almost never a probability.
I... don't think we're using the same Bayesianism, or we're having serious communication problems.
Suppose my spam filter sees the word "movie." It thinks P("movie"|legit)=.005, and P("movie"|spam)=.001. That gives a likelihood ratio of 5 that the email is legitimate because it saw the word "movie". That likelihood ratio isn't a probability- but it's a ratio of probabilities.
The problem in question, though, isn't analogous to determining whether emails are spam or legit (logistic regression). It's the problem of how to write emails. And so if one person wants to end the email with "Sincerely," another with "Warmly," and a third with "Yours," how do you turn that into input for your Bayesian judge? I suppose you could elicit the probabilities that the person emailed will buy from you (how much do they buy?) given the word chosen, but it's not obvious that would be helpful, especially when you're doing this for everything at once rather than targeted A/B testing. (Also, what do you do when it's clear a fourth word should have been considered?)
The word "movie" is not a probability itself, the same way the opinions people express are events and not probabilities.
With people's opinions of what to do, there's no reason you have to constrain what they say to things like "I, Bob, assign 50% probability that plan A is the best". Even if you did that, you still have to consider that as evidence, it's not like you can use another agent's probability estimate directly in some way that you can't use other types of statements, because it's not your estimate. Bob might not even know prob...
So here's the problem: Given a well-defined group charter, how should groups make decisions? You have an issue, you've talked it over, and now it's time for the group to take action. Different members have different opinions, because they're not perfect reasoners and because their interests don't reliably align with those of the group. What do you do? Historical solutions include direct democracy, representative democracy, various hierarchies, dictatorships, oligarchies, consensus...But what's the shoes-with-toes solution? How do they do it in Weirdtopia? What is the universally correct method that could be implemented by organizations, corporations, and governments alike?
This Tuesday, I posted an idea. I came up with it about ten, maybe fifteen years ago, decided it was awesome and revolutionary, and spent a few years doing some extremely ineffectual advocacy for it. I've pushed for it in various contexts on and off since then, but I'd basically shelved it until I had a better platform to talk about it. And recently I realized, belatedly, that Less Wrong is probably the perfect audience. You're going to be open to it, and you'll be able to competently critique it. And maybe some of you will use it.
I posted this tease first because the idea is a solution to a problem you may not have thought for five minutes about. I want to give you the opportunity to come up with other solutions, or discuss how to rigorously evaluate ideas. Also, I'm really curious to see whether anybody independently reinvents mine. Over the years, I've had the experience several times of reading someone else's work and thinking they're about to start pitching my idea. But they never do. It all gives me complicated feelings.
Please discuss in the comments. Remember, we're aggregating the opinions, the judgment, of the group members, not their personal preferences. So answers like “iterated runoff voting,” “bargaining theory X,” or “coherent extrapolated volition” are not in themselves what I'm looking for. If you happen to know what my idea is, or manage to find it by google-stalking me, please don't give it away yet.