Description
Calculate signed pairwise preference margins in candidate-bank row and column order.
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.
Calculate signed pairwise preference margins in candidate-bank row and column order.
When to use this tool
Use signed margins to compare the two directions of each observed pairwise preference.
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.margins, using the stated boundary, ordering, sign and absence conventions.
Build the pairwise preference table from jointly listed candidates. Return table[j][k]-table[k][j] for every candidate pair.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.margins | Signed pairwise margins, row preference count minus reverse count, in candidate-bank order. |
{
"input": {
"candidates": [
"a",
"b",
"c"
],
"ballotsJson": "[[\"a\",\"b\"],[\"b\",\"a\"],[]]"
},
"output": {
"result": {
"margins": [
[
0,
0,
0
],
[
0,
0,
0
],
[
0,
0,
0
]
]
}
}
}Limitations and assumptions
- Positive entries favor the row candidate over the column candidate. Margins are antisymmetric and the diagonal is zero; partial rankings leave unobserved pairs at zero.
- 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
- Ranked Ballot Pairwise Preference Table
Count pairwise preferences only when both candidates appear in a supplied partial ranking.
- Strict Pairwise Ballot Winner Check
Find candidates with a strict observed pairwise win against every other declared candidate.