If you go to the Google Sites page Nereffid supplemental, you can see the results of several months' worth of polls I conducted on TalkClassical last year and this.
TC users (some of them, at any rate) like to produce "recommended lists" that rank favourite works; just recently I hosted the Pre-1700 Works list. But the way these are done requires that participants have to choose which work to favour over another, and there's often going to be a clash between what you personally prefer and what you think should be on a list (for example, there's the desire to spread things round, and not let one composer dominate). When the Post-1950 Works list started, I was somewhat troubled - first because the voting system was terrible and second because some participants stated clearly that post-1950 music of a certain sort was not welcome (ie, Shostakovich). Round about this time I also started to become more interested in the notion of the classical "canon" and how one might go about quantifying it.
So I hit on the notion of a basic poll, where the voter is faced with a list of works and must simply pick the ones they like; putting all the results together would effectively produce a "recommended list" but without the complication of any individual having to rank anything. One interesting aspect of this is that a work that gets plenty of votes is not only well-liked but also well-known. There would no doubt be many works that might be seen as canonical by a handful of people but to the wider listening public they would be unfamiliar - and post-1950 works are a prime example. My original notion was that the polls would each focus on a particular year, so that bit-by-bit I could produce a list to reveal which post-1950 works people really liked. After a couple of dozen polls I got the feeling that some voters just didn't bother participating if it was an era they had no interest in (it's a curious thing; I added the "I don't know any of these works" option to overcome this, but it doesn't seem to encourage everyone), so I switched to themed polls and then, not wishing to put so much intellectual effort in if it wasn't going to pay off, just randomized lists of works. I got past 200 polls but they appeared to be running out of steam so I called a halt; but that was over 2,600 works, with at least 30 people (usually quite a few more) offering an opinion on each one.
There are the inevitable quirks you get when the polling population is different for each poll, and certainly the TC population overall has a few quirks too, but the collated results are largely what one might expect. Back in February, when I passed 2,000 works, I started a discussion thread on the topic.
It turns out that, yes, Shostakovich does seem to dominate post-1950 music!
One of the most fascinating discoveries was that - bearing in mind that TalkClassical's active members are by definition people who are enthusiastic about classical music - only 20% of the works were liked by at least half of the voters. Bear in mind too that the polls covered practically all of the "canonical" works (I didn't get all Beethoven's piano sonatas in, for instance, but that's the highest level of omission I'm talking about). And only 5% of the works (130 of them) were liked by at least two-thirds of voters. And of those 130, 43 are by Beethoven and Mozart! So what on earth is the canon? Surely, for instance, La Traviata and Parsifal are part of it? Well, they were liked by about 42% of voters in the A la carte polls, putting them well below Mendelssohn's 1st string quartet, Prokofiev's Scythian Suite, Chopin's op.41 Mazurkas, Bach's Toccata in C minor BWV 911... Clearly, the canon can't be defined by votes alone, and there are numerous other factors involved (vocal works generally are less popular than orchestral music in the polls; and some composers are so popular that even when I invented a fake Bach cantata it got enough votes to put it in the top three-quarters of the overall rankings!). But still, the undeniable implication of the poll results is that a work that is considered canon may well be unliked or unknown by a majority of self-professed classical music enthusiasts.
This post has gone on for a bit; if I remain in a posting mood there'll be plenty more analysis and vague thoughts to come...