Prelec Probability Weighting Gamma Estimator
One parameter Prelecw(p)=exp[−(−lnp)^γ]inverse at actual independently elicitedw, pinterior fractions, p≠exp(−1); not fit multiple parameters. Actual independently qualified instrument/cohort/matching units; no diagnosis, causal outcome, validated personal prediction or universal clinical cutoff.
Description
The one-parameter Prelec model relates objective probability to a decision weight.
The one-parameter Prelec model relates objective probability to a decision weight.1
Inverting one elicited point requires interior probabilities and an identifiable objective probability. The calculation and input requirements are explained below.
When to use Prelec Probability Weighting Gamma Estimator
Enter decision weight and objective probability strictly between 0 and 1.
How to use Prelec Probability Weighting Gamma Estimator and how it works
- Prepare the measurements or independently established model inputs described below, with matching units and observation scope.
- Enter the required fields and run Prelec Probability Weighting Gamma Estimator.
- Read the result fields using the formula, output units, signs and ordering explained below.
- Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| actualDecisionWeight | Actual Decision Weight. Use the units and matching context stated in the calculation below. | number | Required; fraction from 0 to 1; finite; other constraints below |
| actualObjectiveProbability | Actual Objective Probability. Use the units and matching context stated in the calculation below. | number | Required; fraction from 0 to 1; finite; other constraints below |
Enter decision weight and objective probability strictly between 0 and 1. Reject objective probabilities for which abs(ln(-ln(p))) is below 1e-12. Divide ln(-ln(weight)) by ln(-ln(probability)). Signed finite exponents are accepted; multi-point or constrained behavioral calibration is not performed.
gamma=ln(-ln(weight))/ln(-ln(probability)) Apply the input ordering, units and branch conditions stated above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the calculated or selected fields below. | object |
| result.value | Numeric result under the formula and output units explained above. | number |
{
"input": {
"actualDecisionWeight": 0.5,
"actualObjectiveProbability": 0.5
},
"output": {
"result": {
"value": 1
}
}
}Limitations and assumptions
The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.
All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.
Alternative or Complementary methods
Use Thurstone Case V Scale Value Calculator for a complementary operation: Thurstone Case V scaling converts pairwise preference probabilities to normal deviates.
Use Prospect Value Function Alpha/Beta Estimator for a complementary operation: A power-value model becomes a straight line after logarithmic transformation.
References
Similar or alternative tools
- Thurstone Case V Scale Value Calculator
Thurstone Case V scaling converts pairwise preference probabilities to normal deviates.
- Prospect Value Function Alpha/Beta Estimator
A power-value model becomes a straight line after logarithmic transformation.