Coin_Flips: Data: Coin Flips

Description

Palley and Soll (2019) recruited individuals on Amazon Mechanical Turk and asked them to estimate the proportion of heads in 100 flips of a biased two-sided coin. The probability of heads was unknown to the participants, who were told that it could be anywhere between 1% and 99%. Before responding, each judge was shown a sample of flips that all judges saw (shared information) and another sample of flips that was only seen by that individual or by a subset of judges (private information). Three information structures were considered:

Symmetric: All judges saw their own unique sample of flips. There are a total of 72 judgment tasks under this condition.
Nested: Some judges saw only the shared sample while others saw an additional common sample. There are a total of 24 judgment tasks under this condition.
Nested-Symmetric: Some judges saw only the shared sample while others saw their own additional sample of flips. There are a total of 24 judgment tasks under this condition.

Usage

E_COINS_SYMMETRIC
E_COINS_NESTED
E_COINS_NESTED_SYMMETRIC
P_COINS_SYMMETRIC
P_COINS_NESTED
P_COINS_NESTED_SYMMETRIC
THETA_COINS_SYMMETRIC
THETA_COINS_NESTED
THETA_COINS_NESTED_SYMMETRIC
ID_COINS_SYMMETRIC
ID_COINS_NESTED
ID_COINS_NESTED_SYMMETRIC

Arguments

Format

E_COINS_SYMMETRIC: is a list of the judges' estimates of the proportion of heads in 100 flips of a biased two-sided coin under the Symmetric condition. Specifically, the \(j\)th element is a vector of the judges' estimated proportions in the \(j\)th task.

E_COINS_NESTED: is a list of the judges' estimates of the proportion of heads in 100 flips of a biased two-sided coin under the Nested condition. Specifically, the \(j\)th element is a vector of the judges' estimated proportions in the \(j\)th task.

E_COINS_NESTED_SYMMETRIC: is a list of the judges' estimates of the proportion of heads in 100 flips of a biased two-sided coin under the Nested-Symmetric condition. Specifically, the \(j\)th element is a vector of the judges' estimated proportions in the \(j\)th task.

P_COINS_SYMMETRIC: is a list of the judges' predictions of other judges' average estimate of the proportion of heads in 100 flips of a biased two-sided coin under the Symmetric condition. Specifically, the \(j\)th element is a vector of the judges' predictions of others in the \(j\)th task.

P_COINS_NESTED: is a list of the judges' predictions of other judges' average estimate of the proportion of heads in 100 flips of a biased two-sided coin under the Nested condition. Specifically, the \(j\)th element is a vector of the judges' predictions of others in the \(j\)th task.

P_COINS_NESTED_SYMMETRIC: is a list of the judges' predictions of other judges' average estimate of the proportion of heads in 100 flips of a biased two-sided coin under the Nested-Symmetric condition. Specifically, the \(j\)th element is a vector of the judges' predictions of others in the \(j\)th task.

THETA_COINS_SYMMETRIC: is a vector of the actual proportions of heads under the Symmetric condition. Specifically, the \(j\)th element is the actual proportion of heads in the \(j\)th task.

THETA_COINS_NESTED: is a vector of the actual proportions of heads under the Nested condition. Specifically, the \(j\)th element is the actual proportion of heads in the \(j\)th task.

THETA_COINS_NESTED_SYMMETRIC: is a vector of the actual proportions of heads under the Nested-Symmetric condition. Specifically, the \(j\)th element is the actual proportion of heads in the \(j\)th task.

ID_COINS_SYMMETRIC: is a list of the judges' identification numbers in the judgment tasks under the Symmetric condition. Specifically, the \(j\)th element is a vector of identification numbers of judges' who participated in estimating the proportion of heads in the \(j\)th task. These values make it possible to track a judge across judgment tasks.

ID_COINS_NESTED: is a list of the judges' identification numbers in the judgment tasks under the Nested condition. Specifically, the \(j\)th element is a vector of identification numbers of judges' who participated in estimating the proportion of heads in the \(j\)th task. These values make it possible to track a judge across judgment tasks.

ID_COINS_NESTED_SYMMETRIC: is a list of the judges' identification numbers in the judgment tasks under the Nested-Symmetric condition. Specifically, the \(j\)th element is a vector of identification numbers of judges' who participated in estimating the proportion of heads in the \(j\)th task. These values make it possible to track a judge across judgment tasks.
Remark.: The elements of each list correspond to the same meal. For instance, the \(j\)th elements of THETA_COINS_SYMMETRIC, E_COINS_SYMMETRIC, P_COINS_SYMMETRIC, and ID_COINS_SYMMETRIC represent the true proportion, estimates, the predictions of others, and identification numbers associated with the \(j\)th task under the Symmetric condition.