From Julian Sanchez, a brilliant idea unlikely to be implemented:
American politics sometimes seems like a contest to see which group of partisans can take greater umbrage at the most recent outrageous remark from a member of the opposing tribe. As a mild countermeasure, I offer a modest proposal for American universities. All freshmen should be required to take a course called “Offense 101,” where the readings will consist of arguments from across the political and philosophical spectrum that some substantial proportion of the student body is likely to find offensive. Selections from The Bell Curve. Essays from one of the New Atheists and one of their opponents, and from hardcore pro-lifers and pro-choicers. Ward Churchill’s “little Eichmanns” monograph. Defenses of eugenics, torture, violent revolution, authoritarianism, aggressive censorship, and absolute free speech. Positive reviews of the Star Wars prequels. Assemble your own curriculum—there’s no shortage of material.
For each reading, students will have to make a good faith, unironic effort to reconstruct the offensive argument in its most persuasive form, marshaling additional supporting evidence and amending weak arguments to better support the author’s conclusion. Points deducted if an observer can tell the student doesn’t really agree with the position they’re defending.
Only after this phase is complete will students be allowed to begin rebutting the arguments. Anyone who thinks it’s relevant to point out that the argument is offensive (or bigoted, sexist, unpatriotic, fascistic, communistic, whatever) will receive a patronizing look from the professor that says: “Yes, obviously, did you not read the course title? Let’s move on.” Insofar as these labels are shorthand for an argument that certain categories of views are wrong and can be rejected as a class, the actual argument will have to be presented.
I don't think you're looking at the right quantity. You're right that if what matters is how close you are to truth, but you have no clue what the truth is, then you should stick to the center of mass.
But I think that having a population distribution that's closer to the probability distribution of the truth is more useful than individual beliefs. If 99% of people believe C, then positions L and R are not going to get any traction even if they are true. However, if 33% of people believe each of L, C, and R, then at least the true position has lots of supporters, whatever it is, and so arguments for the truth are more likely to be discovered.