Problem Statement

The   wisdom of the crowd   is the collective opinion of a group of individuals rather than that of a single expert. Wisdom-of-the-crowds research routinely attributes the superiority of crowd averages over individual judgments to the elimination of individual noise,   an explanation that assumes independence of the individual judgments from each other. Thus the crowd tends to make its best decisions if it is made up of diverse opinions and ideologies.

Scott E. Page introduced the diversity prediction theorem:

Therefore,   when the diversity in a group is large,   the error of the crowd is small.

For a given   true   value and a number of number of estimates (from a crowd),   show   (here on this page):

Use   (at least)   these two examples:

Let's start with the solution:

diversityStats <- function(trueValue, estimates)
{
  collectivePrediction <- mean(estimates)
  data.frame("True Value" = trueValue,
             as.list(setNames(estimates, paste("Guess", seq_along(estimates)))), #Guesses, each with a title and column.
             "Average Error" = mean((trueValue - estimates)^2),
             "Crowd Error" = (trueValue - collectivePrediction)^2,
             "Prediction Diversity" = mean((estimates - collectivePrediction)^2))
}
diversityStats(49, c(48, 47, 51))
diversityStats(49, c(48, 47, 51, 42))