Borda count over ranking ballots: positional scoring (top of m gets m-1).

Condorcet-inconsistent and clone-sensitive — useful as a contrast rule. Truncated ballots give unranked candidates the average of the remaining points (never a silent zero). Errors if any ballot is not a ranking.

Copeland over ranking ballots: +1 per pairwise win, +0.5 per pairwise tie.

Condorcet-consistent: a candidate that beats all others pairwise wins. Errors if any ballot is not a ranking.

Condorcet winner over ranking ballots: beats every other candidate pairwise.

If the majority relation cycles (e.g. a>b>c>a) there is NO Condorcet winner: winners is empty, winner is null, and note says so. Errors if any ballot is not a ranking.

Approval voting: each candidate scores the total weight approving it.

Consumes approval ballots ({kind: "approval", approved: [...]}). An empty approval set is valid and adds nothing. Errors if any ballot is not approval.

Single-winner STV / instant-runoff over ranking ballots.

Rounds: count top active preferences; a strict majority wins, else eliminate the fewest-voted (ties broken by eliminating the lexicographically largest) and transfer. Ballots with no remaining preference are exhausted. Clone-resistant. Errors if any ballot is not a ranking.

Linear opinion pool over probability-distribution ballots.

Returns the weight-averaged distribution in scores (it PRESERVES confidence rather than collapsing to an argmax vote); winner is the argmax for convenience. Ballots are {kind: "distribution", distribution: {cand: p, ...}} summing to 1. Errors if any ballot is not a distribution.

Plurality baseline over ranking ballots: most first-choice votes wins.

Strict-majority rule over ranking ballots.

A candidate wins only with > 50% of first-choice weight; otherwise there is NO winner (winners empty, note explains). Distinct from plurality.

Apply any rule by name (enum rule) — a single dispatch entrypoint.

Equivalent to the per-rule tools. rule is one of: borda, copeland, condorcet, approval, stv, opinion_pool, plurality, majority.