In 1907, Francis Galton famously found that when a crowd were asked to guess the weight of an ox, the average value of their responses was surprisingly accurate. Galton’s experiment found the average was within 1 percent of the ox’s true weight. By canceling errors across individuals, the mean response often proves more accurate than individual estimates.
This only works if all individuals are allowed to guess independently. If people hear an estimate, it becomes their mental basepoint, and answers then range around that first estimate.