Description
Return one probability-weighting function value.
Decision models distinguish monetary payoffs, probabilities, model values and subjective equivalents. Discounting, probability weighting and reference-dependent utility terms depend on supplied parameters and cannot by themselves establish actual preferences or an appropriate allocation.
Return one probability-weighting function value.
When to use this tool
Use Probability Weighting One Branch Term when evaluating the stated decision-model, lottery or discount contribution.
How to use the tool and how it works
- Enter probability, gamma. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read weight. Use the output convention below.
Return one probability-weighting function value. Require probability in [0,1] and gamma > 0; endpoints return themselves, interior weight = p^gamma/(p^gamma+(1-p)^gamma)^(1/gamma).1
Prospect models distinguish reference-dependent outcome value from probability weighting. A single supplied value or weighting branch is not a complete cumulative-prospect evaluation or an empirical preference estimate.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| probability | Probability | Required. Finite number; minimum 0; maximum 1. |
| gamma | Gamma | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| weight | One nonlinear probability weight; need not be a complete normalized decision distribution. | Required. Finite number. |
{
"input": {
"probability": 0.5,
"gamma": 1
},
"output": {
"weight": 0.5
}
}Limitations and assumptions
- This is one weighting branch rather than a complete cumulative prospect model; gamma is not estimated or recommended.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Fit and validate an appropriate complete decision model against relevant observations; distinguish model scores from money and assess actual financial choices separately.
References
-
Calculation and input contract: behavioral-economics/probability-weighting-one-branch-term — tool.io
-
Advances in prospect theory: cumulative representation of uncertainty — Amos Tversky and Daniel Kahneman
Similar or alternative tools
- Prospect Loss Aversion Value Gap
Return a reference-dependent piecewise prospect value.
- Lottery Branch Weighted Utility Term
Multiply an explicit lottery branch probability by caller-supplied signed utility without choosing a utility function.