I'm interested in how people form valuations of the opinions of others. One domain to study is art. We have a long historic record of how the elite arbiters of taste have decided what artists and what artworks were great.
This is more relevant to 21st century American thought than many of you probably think. The defaults we assume, the stories that are told on television and in our movies, the things taught in our colleges, were partly determined by assertions made by continental philosophers and psychologists of the 18th through 20th centuries, most of which they just made up. 
The process by which philosophers eventually get their views accepted into the Western canon looks the same to me as the process by which musicians or painters are accepted into or cast out of the Western canon. Neither has much to do with the quality of the product.
For centuries, artists have been judged not so much by the quality of their work as by its novelty, and by its ability to raise questions while resisting any definitive answers. As one art critic wrote, "Probably more people have thought Hamlet a work of art because they found it interesting, than have found it interesting because it is a work of art. It is the Mona Lisa of literature."
Ironically, that was T. S. Eliot, just a few years before writing "The Love Song of J. Alfred Prufrock" and writing rave reviews of James Joyce's Ulysses.
I think novelty was the main criterion for artistic greatness by the middle of the 19th century. It was almost the only criterion, in all of the fine arts, by 1925.
But there is one artist who sticks out among the desperate attention-seeking artistes like an ordinary thumb: Brahms. Brahms accomplished something that, AFAIK, no one else had in any fine art, in all of European history going back to the Middle Ages. He made art in a style that had gone out of fashion before he was born, not ironically, not nostalgically, but because he liked it. As I understand it, Brahms was still writing symphonies in the style of Beethoven after Chopin and Liszt were dead. And his work became both popular, and accepted by the elite arbiters of taste into the canon, not for introducing any new style, but simply for being enjoyable. Or, as an unsophisticated ignoramus might say, good.
That would be analogous to a philosopher's ideas being accepted just for being correct!
Is that a fair representation? If so, why was he accepted into the canon, when anyone else who tried to just make good stuff would, I imagine, be laughed at or ignored? 
 Analytic philosophers were more rigorous, so nobody liked listening to them. There seems to be a Gresham's Law effect: The presence of bad philosophers who claim to have reached exciting conclusions without any nasty logic or math, makes it impossible for more rigorous work to get a hearing within society and the arts.
 I'm open to the idea that Robert Frost may be another exception, though I'm not aware of poems written in 1870 that could be mistaken for Robert Frost poems. I'll also note that people tried to stamp out appreciation for his poems because he wouldn't get with the Modernist program.