The Jellybean Mystery is the first religious rite of the New Church of Hope. It's just a classic jellybean jar guessing contest. Everyone writes their name and a guess for how many jellybeans are in the jar.
Mathematically, it [almost] always turns out the same: the average of the guesses (none of which are right) is closer to the right number than the best individual guess. It isn't even very hard to see why, if we take a simplified case with just three guesses.
Say we have beans in the jar, and three people make a guess. One of them will be closest. The other two will, by definition, not be closer. It is more likely that one will be higher (than the right answer) and one of them will be lower, so as long as they aren't completely random numbers but somehow relate (by estimating or guess) to the actual number of beans, they are likely to balance out.
The best guess logically 'clears' an area near the right number, because no other guess is closer, regardless of whether the best guess or the other guess is high or low. The distance from the right number is cardinal, independent of the direction. So we've almost mathematically guaranteed that, averaged along with the best guess, the other two guesses will move the average slightly closer to the right number, even if all three guesses were completely uneducated (but not entirely random).
It doesn't matter if you can 'logically' explain it, though, the Jellybean Mystery is still pretty thrilling to experience. It's been known to change people's lives. Certainly mine and CJs.
How it relates to the Philosophy Of Reason and the New Church of Hope is most easily understood by reading some of the Wiki. This blog isn't to argue the truth of the reasoning, but to publish my personal experience, trying to change the world by re-inventing religion entirely, and calling it reason, because that's what that word means.