Description
A minimum winning coalition here means inclusion-minimal: removing any included party loses the supplied majority.
Election and representation indicators depend on the selected vote, seat, population, or eligibility denominator. A threshold also needs an explicit equality and rounding rule. A single quotient, balance, or share can support a larger counting workflow without implementing the full electoral procedure.
A minimum winning coalition here means inclusion-minimal: removing any included party loses the supplied majority.
When to use this tool
Use Coalition Minimum Winning Removal Test when you need this particular counting term under an explicit vote, seat, threshold, or reporting-base rule.
How to use the tool and how it works
- Enter seats, threshold. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read total, winning, minimal, removalTotals. Inspect winning, minimal before interpreting the associated values.
For nonnegative integer seats and a positive integer threshold return total, each removalTotal=total-seats[i], winning=(total>=threshold), and minimal when winning and every removalTotal is below threshold.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| seats | Seats | Required. Array of safe integer; maximum items 256. |
| threshold | Threshold | Required. Safe integer; minimum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| total | Total | Required. Safe integer. |
| winning | Winning | Required. Boolean. |
| minimal | Winning coalition with every one-member removal below threshold. | Required. Boolean. |
| removalTotals | Removal Totals | Required. Array of safe integer; maximum items 256. |
{
"input": {
"seats": [
30,
25
],
"threshold": 51
},
"output": {
"total": 55,
"winning": true,
"minimal": true,
"removalTotals": [
25,
30
]
}
}Limitations and assumptions
- Minimal means inclusion-minimal under this threshold, not fewest parties or fewest seats. An empty coalition is not winning; zero-seat members can prevent minimality.
- 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. Signed zero is exported as zero.
Alternative or Complementary methods
Compare the supplied counting rule with the authoritative procedure for the relevant election or chamber. Complete allocations need additional eligibility, ranking, transfer, tie, and reporting rules beyond one arithmetic term.
References
Similar or alternative tools
- Coalition Surplus Member Removal
For nonempty nonnegative weights, positive majority, and a valid removedIndex return total=sum(weights), afterRemoval=total-weights[removedIndex], and removable=(afterRemoval>=majority).
- Party Switch Seat Balance Update
Return nextFirst, nextSecond, and netFirst=switchSecondToFirst-switchFirstToSecond.