knowledge_gap {metaggR}

Calculate the Knowledge Gap

Description

This function computes the knowledge gap described in Palley & Satopää (2021): Boosting the Wisdom of Crowds Within a Single Judgment Problem: Weighted Averaging Based on Peer Predictions. The current version of the paper is available at https://papers.ssrn.com/sol3/Papers.cfm?abstract_id=3504286

Usage

knowledge_gap(E, P, alpha)

Arguments

E

Vector of J \ge 5 estimates of the outcome.

P

Vector of J \ge 5 predictions of others. The values must be in the same order as the estimates in E. Specifically, for all j = 1, ..., J, E[j] and P[j] give the jth judge's estimate and prediction of others, respectively.

alpha

Vector of J \ge 5 weights. The alpha[j] element is the weight assigned to E[j]. The weights can be any values in the real line as long as they sum to 1.

Value

A singular value representing the knowledge gap. This represents the expected distance between the weighted combination of the judges' estimates, where the weights have been given by alpha, and the optimal aggregate estimate called the Global Posterior Expectation (GPE).

Examples

# Illustration on the Three Gorges Dam Example in Palley & Satopää (2021):

# Judges' estimates:
E = c(50, 134, 206, 290, 326, 374)
# Judges' predictions of others
P = c(26, 92, 116, 218, 218, 206)

# First find the knowledge-weights that minimize the knowledge gap:
alpha = knowledge_weights(E,P)
knowledge_gap(E,P, alpha)

# Small perturbations increase the knowledge gap:
alpha_per = alpha 
alpha_per[1] = alpha_per[1] + 0.001
alpha_per[2] = alpha_per[2] - 0.001
knowledge_gap(E,P, alpha_per)