knowledge_weights {metaggR}

Calculate the Weights that Minimize the Knowledge Gap

Description

This function computes the weighted used in the knowledge-weighted estimate of 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_weights(E, P)

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.

Value

Jx1 vector of weights that minimizes the knowledge gap and lead to the knowledge-weighted estimate.

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)

# Weights used in the knowledge-weighted estimate:
alpha = knowledge_weights(E,P)

# Knowledge-weighted estimate is 329.3266
t(alpha) %*% E

# Alternatively, the knowledge-weighted estimate can be calculated using 
# the knowledge_weighted_estimate() function. This returns 329.305, which
# is slightly different from the above result. The difference arises because
# knowledge_weighted_estimate() improves stability by standardizing the 
# judges' responses before aggregating them.
knowledge_weighted_estimate(E,P)