I’m developing software which needs some math which is outside of my wheelhouse.
I have a series of numbers, each single number in the series is submitted by a user. I want to determine the probability that the mode number in the series is the correct number. We’ll assume that we have no prior knowledge and so any number could be correct, but the most common number is most likely correct.
For instance, we have the series [3, 3, 5, 3], what are the odds (expressed as a %) that the true number is 3? (We must assume that the mode number is the "true number" otherwise this problem becomes impossible I believe.)
Bonus: if we assign a reputation to each user (expressed as the percentage of their submissions that are not the mode value for a given sequence), we can determine that some users are less “trustworthy” and we could factor that into the original confidence %.