Description
Find candidates with no strict pairwise loss, including tied or unobserved comparisons.
A ballot record is an explicit selection or ordered list of literal candidate IDs. A tally depends on its rule: first choice, approval, positional scores and pairwise comparisons use different evidence. Partial rankings do not by themselves define a preference for or against omitted candidates. Counts and weights describe supplied records, not certified voters.
Find candidates with no strict pairwise loss, including tied or unobserved comparisons.
When to use this tool
Use the weak unbeaten set to retain candidates with no observed strict pairwise defeat.
How to use the tool and how it works
- Enter candidates, ballotsJson using the definitions below. Serialize JSON text fields in the decoded shape shown below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.candidates, using the stated boundary, ordering, sign and absence conventions.
Build counts using only ballots that list both compared candidates. Retain candidates whose count is at least the reverse count against every other candidate.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| candidates | Distinct literal candidate IDs in the output row/column order. | Dense list of at most 128 literal strings, each at most 8,192 UTF-16 units. |
| ballotsJson | JSON array of ballot arrays of literal candidate IDs. Each row is a selection or partial ranking according to this operation; empty ballots are allowed. | Text, at most 8,192 UTF-16 code units; narrower grammar/range rules also apply. |
These decoded structures show the examples inside JSON text fields. Supply their serialized JSON strings as input.
{
"ballotsJson": [
[
"a",
"b"
],
[
"b",
"a"
],
[]
]
}| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.candidates | Candidates with no strict pairwise loss, in declared bank order. |
{
"input": {
"candidates": [
"a",
"b",
"c"
],
"ballotsJson": "[[\"a\",\"b\"],[\"b\",\"a\"],[]]"
},
"output": {
"result": {
"candidates": [
"a",
"b",
"c"
]
}
}
}Limitations and assumptions
- Tied and wholly unobserved comparisons satisfy this weak condition, so even a never-listed candidate may be unbeaten. This differs from a strict pairwise winner.
- Candidate banks use distinct exact string IDs. Unless an audit explicitly accepts them for reporting, unknown IDs and repeated IDs within a ballot are rejected. Rankings may be partial. These operations do not authenticate records, infer voter intent or apply jurisdiction-specific election rules.
- Every declared outer field is required and unknown outer fields are rejected. Strings and JSON text have size limits, lists are bounded to 128 entries, and JSON nesting/node counts are bounded. Tighter operation-specific bounds stated above take precedence.
- Numeric outputs must remain finite and within safe-integer magnitude. Original record indexes and cell coordinates are zero-based; stated half-open ranges exclude their end.
Alternative or Complementary methods
Choose a tally rule before comparing outcomes. Audit candidate identity and repeated entries first, retain the treatment of empty and partial ballots, and apply any election-specific eligibility or tie-breaking procedure separately.
References
Similar or alternative tools
- Strict Pairwise Ballot Winner Check
Find candidates with a strict observed pairwise win against every other declared candidate.
- Ranked Ballot Pairwise Margin Table
Calculate signed pairwise preference margins in candidate-bank row and column order.