We’ve had a series of threads like this one in which Octarine is asking for favorite Beatles songs from each album. Supposedly, when all albums are tabulated, the best one from each will be compared, and the one with the highest number will be the winner.
Now I’m not a statistician, but it doesn’t seem right to me. One album may not have any really great songs, while another may have several. Comparing the best of each would mean excluding some favorite songs and including some not-so-great.
Again, I’m not a statistician. It seems to me that a better method would be to ask for 3 favorites from each album, then list them and have everyone pick their 3 favorites.
I think the #1 winner would be the same, but the runners-up may be very skewed.
I think you’ve identified a problem with the voting structure. It divides the candidates into groups, and assumes the groups are all of the same quality. It similar to the problem of selecting sports teams for the playoffs by picking the winner of each division - the divisions aren’t necessarily equal.
Picking three favorites from each album would be similar to the wild card system in sports, where some second-place teams also make the playoffs.
It turns out that when you have three of more choices, there is no voting system that is guaranteed to pick the one that is preferred by the largest number of people. This was proved mathematically in Arrow’s Impossibility Theorem. (I’m actually oversimplifying the theorem, but I don’t want to go into a treatise here.) There are voting systems that are less likely to produce sub-optimal results, but no voting system is perfect.
If I wanted to know which were the most popular Beatles songs, I’d do an iTunes search and sort the results by popularity, which are (presumably) based on vast numbers of actual sales:
1 - Here Comes the Sun
2 - Let it Be
3 - Hey Jude
4 - Come Together
5 - Blackbird
6 - In My Life
7 - Twist and Shout
8 - Revolution
9 - While My Guitar Gently Weeps
10 - Yesterday
I doubt that Octarine is looking for the most popular Beatles song amongst the general public. As you said, it’s pretty easy to find that information. I think he’s looking for the Beatles song that Dopers think is the best (or, at least, those Dopers who participate in the poll).
When I look up The Beatles on iTunes, “Hello Goodbye” is #14. “Yesterday” does show up again at #40, but it’s from a different album than the one at #10. Still, I’d imagine if you counted the actual number of downloads of “Yesterday” from the (at least) 5 different albums available there that contain it, its ranking would probably go up.
Yeah, I’m actually a little surprised by some of those numbers. I would not have guessed the #1 in ten guesses and I would have expected “Yesterday” to be top five, if not number one.