Description
Return surplus and weight times its natural logarithm.
Cooperative-game calculations compare coalition values, allocated payoffs or voting weights. A single coalition term or party share can be useful in a larger calculation without establishing a complete power index, core allocation or bargaining solution.
Return surplus and weight times its natural logarithm.
When to use this tool
Use Bargaining Weighted Logsurplus One Party Term when you need one explicit coalition, voting or bargaining term.
How to use the tool and how it works
- Enter allocation, disagreement, weight. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read surplus, logObjectiveContribution. Use the output convention below.
Require allocation strictly above disagreement and nonnegative weight. Return surplus and weight times its natural logarithm.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| allocation | Allocation | Required. Finite number. |
| disagreement | Disagreement | Required. Finite number. |
| weight | Weight | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| surplus | Surplus | Required. Finite number. |
| logObjectiveContribution | Weight times natural logarithm of surplus on the declared numeric scale. | Required. Finite number. |
{
"input": {
"allocation": 12,
"disagreement": 2,
"weight": 0.5
},
"output": {
"surplus": 10,
"logObjectiveContribution": 1.151292546497023
}
}Limitations and assumptions
- This is one party's objective term, not an optimized bargaining solution. A common surplus scale is assumed and even zero weight does not permit nonpositive surplus.
- 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
Evaluate all required coalitions and allocation constraints for the chosen solution concept. Keep payoff units, quota conventions, feasibility and normalization explicit.
References
Similar or alternative tools
- Bargaining Disagreement Coordinate Gap
Return disagreementCoordinate minus referenceCoordinate as gap.
- Need Weighted Allocation One Share
Return budget×needWeight/totalWeight.