Description
Remove that player's weight; flag veto only when the grand coalition wins and all others together fail.
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.
Remove that player's weight; flag veto only when the grand coalition wins and all others together fail.
When to use this tool
Use Coalition Veto Player Budget when you need one explicit coalition, voting or bargaining term.
How to use the tool and how it works
- Enter allWeights, playerIndex, quota. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read withoutPlayer, isVeto, winningGrandCoalition. Inspect isVeto, winningGrandCoalition before interpreting the associated values.
Require nonempty nonnegative weights, positive quota and an in-range player index. Remove that player's weight; flag veto only when the grand coalition wins and all others together fail.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| allWeights | All Weights | Required. Array of finite number; maximum items 256. |
| playerIndex | Player Index | Required. Safe integer; minimum 0. |
| quota | Quota | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| withoutPlayer | Without Player | Required. Finite number. |
| isVeto | Is Veto | Required. Boolean. |
| winningGrandCoalition | Winning Grand Coalition | Required. Boolean. |
{
"input": {
"allWeights": [
6,
3,
1
],
"playerIndex": 0,
"quota": 7
},
"output": {
"withoutPlayer": 4,
"isVeto": true,
"winningGrandCoalition": true
}
}Limitations and assumptions
- Equality with quota wins. These are supplied weighted-voting rules, not legal voting rights, and losing grand coalitions have no veto flag under this definition.
- 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
- Banzhaf One Swing Indicator Term
Compare coalition weight before and after adding the player, and flag swing only for a losing-to-winning change.
- Core Coalition Excess One Subset
Sum it, subtract the sum from coalitionValue for excess, and flag blocked for strictly positive excess.