Description
Compare coalition weight before and after adding the player, and flag swing only for a losing-to-winning change.
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.
Compare coalition weight before and after adding the player, and flag swing only for a losing-to-winning change.
When to use this tool
Use Banzhaf One Swing Indicator Term when you need one explicit coalition, voting or bargaining term.
How to use the tool and how it works
- Enter coalitionWeight, playerWeight, quota. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read withoutWins, withWins, swing. Inspect withoutWins, withWins, swing before interpreting the associated values.
Require nonnegative coalition/player weights and positive quota. Compare coalition weight before and after adding the player, and flag swing only for a losing-to-winning change.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coalitionWeight | Coalition Weight | Required. Finite number; minimum 0. |
| playerWeight | Player Weight | Required. Finite number; minimum 0. |
| quota | Quota | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| withoutWins | Without Wins | Required. Boolean. |
| withWins | With Wins | Required. Boolean. |
| swing | Swing | Required. Boolean. |
{
"input": {
"coalitionWeight": 4,
"playerWeight": 3,
"quota": 6
},
"output": {
"withoutWins": false,
"withWins": true,
"swing": true
}
}Limitations and assumptions
- Quota equality counts as winning. This is one coalition's swing indicator, not a normalized Banzhaf power index or a legal voting judgment.
- 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
- Coalition Veto Player Budget
Remove that player's weight; flag veto only when the grand coalition wins and all others together fail.
- Shapley One Coalition Marginal Term
Return withValue minus withoutValue and weight 1/[players × binomial(players-1, coalitionSize)], then their product.