Glossary — voting methods & criteria

One-line definitions for the keywords used across these lessons — STAR and every method it's compared against. Grouped from beginner vocabulary to advanced theory. Most entries end with → quick jumps to the demo election's page (ballots + results) and/or the interview episode that show the term in action.

Why one glossary? Most of the vocabulary below — monotonicity, Condorcet, summability, center squeeze, vote-splitting, the Equal Vote criterion — is the shared language used to compare methods, so it doesn't belong to any single method. Method-specific terms are grouped by method (STAR mechanics; Other methods) with stable anchors, so a method page can deep-link to just its slice.

Per-method glossaries

Method-specific terms also live next to each method, cross-referencing the shared vocabulary here:

• STAR — scoring round, finalists, automatic runoff, Equal Support, runoff reversal, Bloc / Proportional STAR
• Approval — the approval line, double-bubble, SPAV/PAV
• Range / Score — total-score win, exaggeration strategy, scale granularity
• Ranked Robin & Condorcet — Copeland, cycles, Ranked Pairs / Schulze / Minimax
• RCV-IRV — IRV, exhausted ballots, center squeeze, STV, Hare

The shared criteria (monotonicity, Condorcet, summability, center squeeze, the Equal Vote criterion, spoiler / vote-splitting…) stay below — they're the language for comparing methods, so they belong to no single one.

Core vocabulary

• STAR — Score Then Automatic Runoff: score every candidate 0–5; the two highest totals advance to an automatic head-to-head runoff. → main page STAR — start here; the two rounds: Scoring Round + Automatic Runoff
• Score / star rating — a 0–5 value expressing how much you support a candidate (like a five-star review). → The Score Ballot
• Expressiveness — how much of a voter's real opinion the ballot can carry. A ranked ballot captures order only ("A over B"); a score ballot captures order and strength ("A a lot, B a little") — and lets you rate two candidates equally. More expressiveness means the electorate's true preferences survive the count instead of being flattened at the ballot. It's the core virtue STAR advocates lead with. (One precise caveat: a 0–5 ballot's six levels can strictly order at most six candidates; with 7+, a ranked ballot can encode a strict order the score ballot can't — see the scale note. But "more expressive" is the wrong axis past that point: the two ballots then express disjoint sets of orderings, neither a subset of the other, and the 0–5 ballot still records far more distinct opinions — 279,936 against 5,040 at seven candidates. Counted here.) → scores vs. ranks (the distinction); one voter, three ballots (what each ballot captures and throws away); the fidelity ladder; the 301 deep dive, what the ballot can and cannot say — expressiveness, measured, and its worked election, one electorate, nine candidates, five papers.
• Scoring round — STAR's first round: add up each candidate's scores; the top two become finalists. → demo equal_support_runoff_demo
• Finalists — the two highest-scoring candidates, who advance to the runoff. → the round that chooses them, The Scoring Round; the round they compete in, The Automatic Runoff.
• Automatic runoff — STAR's second round: each ballot counts as a full vote for whichever finalist it scored higher; the preferred finalist wins. (Deep-dive deck: Automatic Runoff — see LINKS — source-of-truth registry.) → demo equal_support_runoff_demo; episode "Aren't Equal-Score Votes Just Discounted?"
• Head-to-head / pairwise — a direct comparison of two candidates: which one more ballots scored higher.
• Equal Support — the house term for scoring the two runoff finalists the same. Your scores are still counted in full (they helped choose the finalists); in the runoff you simply don't tip the margin between two candidates you rated equally. It covers two honest cases:
  • loved both (e.g. 5/5) — genuine equal support;
  • disliked both (e.g. 0/0) — sometimes called Equal Opposition (equal non-support), the precise label for this half.
• Aka Equal Preference / No Preference — the terms some tools and critics use. We lead with "Equal Support" on purpose, and this is the one place the akas are documented (don't reintroduce them as lead terms elsewhere). Why the choice:
  • "No Preference" sounds like an empty or discarded ballot — the exact "you discounted my vote" criticism. "Equal Support" says the opposite: the ballot was counted and expressed real support.
  • It's scoped to the two finalists, not the whole ballot. A voter with "Equal Support" here may have had a strong favorite who didn't reach the runoff — they're not opinion-less.
  • Honest caveat: "Equal Support" slightly overstates the disliked-both (0/0) case — which is exactly why Equal Opposition exists as the exact term for it.
• Not an abstention — the ballot participated fully. Contrast RCV-IRV, which exhausts (discards) a ballot that ranks neither finalist. → mechanics The Automatic Runoff Round; objection "Aren't Equal-Score Votes Just Discounted?"; demo equal_support_runoff_demo
• Scored (cardinal) ballot — rates each candidate independently 0–5; equal ratings allowed. The ballot behind the scored family (Approval → Range → STAR). → concept Scores vs. Ranks — Don't Confuse Ranks and Ratings; the score↔rank conversion is the The Fidelity Ladder — converting between scores and ranks
• Ranked (ordinal) ballot — orders candidates 1st, 2nd, 3rd; conveys order but not degree of support. One ballot, several tabulations — RCV-IRV, Ranked Robin (Condorcet), STV — so it's shared ballot-family vocabulary, kept here rather than folded into any one method. Whether equal ranks are allowed distinguishes strict vs weak ranks: Strict vs. Weak Ranks — Not All Ranked Ballots Are the Same. → concept Scores vs. Ranks — Don't Confuse Ranks and Ratings; per-method Glossary — RCV-IRV (and ranked-ballot terms) and Glossary — Ranked Robin & the Condorcet family
• Preference profile / profile — the collection noun: one ballot (one voter's preferences) per voter — an election's entire input. Every ballots: block in this repo is a profile; so are the ≻₁ … ≻ₙ columns of a theory paper. Group identical ballots with counts — this repo's collapse_ballots view — and you have a textbook's preference schedule (aka preference table): the same object, grouped presentation. ("Voter profile" occasionally means the same thing in casual theory writing, but don't lead with it — in campaign practice a "voter profile" is a demographic dossier on a person, not a set of ballots.) Watch the silent default: unqualified, social-choice writing uses "preference profile" for strict, complete rankings (linear orders — no ties, no truncation, order only). That's the field's modeling convenience, not the meaning of "preference" — so when the ballot type matters, qualify what the profile carries: a ranked profile, strict or with ties (weak orders); a score profile (0–5: order + ties + strength; theory akas utility / grade profile); an approval profile (0/1). The distinction is live in our own tooling: pref_voting loads linear orders as Profile but needs ProfileWithTies once ballots tie or truncate — and its own election-data overview is a textbook sighting of the silent default: item 1 defines a Profile as "an election where each voter submits a linear order," with truncation/ties (ProfileWithTies) and grades/scores (GradeProfile) listed as separate classes further down rather than under an umbrella "ballots come in kinds" framing. → house rules: TIPS — Terminology; what only scores carry: Preference vs. Support; score↔rank conversion: The Fidelity Ladder

The problem STAR addresses

• Choose-One / Plurality / First-Past-The-Post — vote for exactly one candidate; most votes wins. Accurate only with two candidates. → episode Our Voting System Is Broken — The Problem with Plurality
• Two-party dominance — a party system with two viable parties. Genuinely contested (governability/accountability vs. limited choice/underrepresentation), so treated even-handedly: the spoiler-enforced part is method-caused and fixable with better single-winner voting; the deeper single-member-district tendency is structural. → Two-Party Dominance — pros, cons, and what changes it
• Duverger's law — single-member plurality tends toward two parties; proportional representation toward many. The reason better single-winner methods don't by themselves end two-party dominance — only proportional (multi-winner) methods reliably do. → Two-Party Dominance
• Two-party-preferred (2PP) — the standard Australian metric reporting the final Labor-vs-Coalition split after preferences flow; a symptom of two-party dominance persisting under the Alternative Vote. → The Alternative Vote in Australia
• Vote splitting — similar candidates divide their shared supporters, letting a less-preferred candidate win. → demos split_voting/; episode Our Voting System Is Broken — The Problem with Plurality
• Spoiler effect — a candidate who cannot win still changes who does, by splitting another's support. → concept The spoiler effect; demo 04_star_wars_vote_split; episode What's So Good About STAR Voting? (Seg 1)
• Favorite betrayal — being pressured to score/rank a front-runner above your true favorite. → episode Favorite Betrayal — Does Only RCV Avoid It?
• Lesser-evil voting — backing a tolerable front-runner instead of your favorite to block a worse outcome. → episode Our Voting System Is Broken — The Problem with Plurality
• Wasted vote — a vote with no effect on the result. An overloaded term with four distinct senses — plurality loser/surplus votes, IRV ballot exhaustion, the spoiler "throwing your vote away" pressure, and the "no wasted votes" method claim — pinned down (with the honest read of the STAR claim) in Wasted Votes.
• Two-round system — separate primary + general/runoff elections; STAR does both jobs on one ballot. → The Automatic Runoff (how STAR folds the second round into the first ballot); why a separate runoff buys less than it looks: misrepresentation
• Plurality / minority winner — a winner with the most votes but less than majority support. → episode Our Voting System Is Broken — The Problem with Plurality. Weak on its own: with three or more real candidates a sub-majority winner is close to arithmetically automatic, so the bare percentage describes the size of the field as much as the winner — watch it fall 34% → 25% → 11% on one unchanged electorate in the pineapple progression. The indictment that lands is the absolute loser or Condorcet loser fact instead. → Majority & minority candidates sorts the five senses of "majority candidate"
• "Relative majority" (a false friend — it means plurality) — European sources (translating German relative Mehrheit, French majorité relative) call plurality a "relative majority." In English this is actively misleading: a relative-majority winner routinely has far less than half the vote, so it is not a majority at all. Decoder for the family:
• Relative majority = plurality — most votes; may be well under 50%. (US: "first-past-the-post".)
• Absolute majority = more than half of the votes — strictly ⌊n/2⌋ + 1, not "50% + 1" (with 99 votes cast, more than half is 50, not 51). Always state half of what: votes cast, valid votes, or total membership — they differ, and the choice can flip a result.
• Simple majority — ambiguous, so avoid it: in most parliamentary usage it means more of one option than the other among those voting (abstentions excluded); some writers use it for plurality. Say which you mean.
• Qualified / supermajority — a raised bar (⅔, ⅗, or a fixed count), typical for constitutional changes.

House usage: say plurality for most-votes-wins and majority only for over-half. → Plurality · Majority Criterion

Mechanics

• On-screen report (older docs may call it the "echo") — the report the LH engine prints on screen as it tabulates a file. The engine's built-in defaults decide how much of it shows; a file's options: block can override them, and the --full flag puts everything on screen — none of that ever changes the result. Contrast the _tabulated.txt mirror, which ignores options: and always renders full detail. → LH reporting options
• Equal scores allowed — you may give two candidates the same score; you're never forced to invent a preference. → demo 03a_c3_b3_style-bullet-vote
• Exhausted ballot — (an RCV-IRV term; IRV-specific, not all ranked methods — Ranked Robin / Condorcet counts read every rank) a ballot set aside mid-count because all its ranked candidates were eliminated. FairVote's single word covers several very different cases (voter-side vs method-caused); STAR's runoff never eliminates anyone, so it doesn't discard ballots this way. → episode "Exhausted Ballots" — What FairVote's Word Actually Hides
• Voluntary exhaustion (self-truncation) — the voter-side case: you ranked fewer candidates than allowed, so the ballot exhausts as the direct result of your own choice. Not a method flaw. → Forced vs. Voluntary Exhaustion
• Forced exhaustion — (house term; standard: involuntary truncation) the method-caused case: you ranked every candidate you were permitted to, yet the ballot still dropped out — because a ranking cap (NYC 5, Minneapolis 3) wouldn't let you rank the rest. A fully-ranked ballot can't exhaust in single-winner IRV, so this is a property of the ballot design, not the voter — and it vanishes if the cap is lifted. → Forced vs. Voluntary Exhaustion
• Tiebreaker — a rule that resolves ties (for the finalists or the runoff); here, candidate priority / lot order. The full ladder (pairwise → five-star → lot, in both rounds), plus what BetterVoting JSON carries and what you may set in a hand-written YAML, is in STAR Tie-Breaking — The Full Chain.
• Dead rung — the tiebreak ladder's five-star step (which counts votes of score 5, the scale max) when no tied candidate scored a 5, so it reads 0–0 and the tie falls through to the lot. The rung counts only 5s — it never steps down to 4s, so piling up 4s can't break the tie. Equal non-zero five-star counts fall through the same way. Mnemonics: "no fives, no rung — drop to the lot", "it counts fives, not fours." akas: broken / missing / empty / phantom rung. → cases The "dead rung" — when STAR's five-star tiebreaker can't fire
• Undervote / abstention — a ballot that scores no one (blank or ~); counts as turnout but supports no candidate. It stays in the quorum numerator (still participated) but drops out of the runoff percentage (no preference). → Quorum — did enough of the electorate show up?
• NOTA (None of the Above) — a ballot option to reject every listed candidate. Usually non-binding: Nevada's "None of these Candidates" (the only US jurisdiction with it) has topped the poll more than once, yet the highest-polling candidate still takes office. Binding versions do exist — UK student unions' RON ("Re-open Nominations") genuinely reopens nominations, and Colombia's voto en blanco forces a fresh election with new candidates if it wins a majority — so "NOTA is symbolic" is a fact about implementation, not about NOTA. Distinct from a spoiled ballot (?), which is often accidental. Note an expressive ballot blunts the need for it: scoring everyone 0 registers the same dissatisfaction while still letting you rank the options you're stuck with. → NOTA on a STAR ballot · abstention vs zero vs NOTA
• Roll-off (partial abstention) — voting in some contests on a ballot but skipping others, typically the down-ballot ones; the most common form of abstention in any multi-race election, and the one the usual "active vs passive abstention" split has no room for (the voter neither stayed home nor cast a blank ballot). Distinguish the three cleanly, since they mean different things and are reported separately: blank (-, nothing marked — a deliberate "none of these" signal), spoiled/invalid (?, marked unusably — often accidental, so don't read it as intent), and race abstention (~, this contest skipped on purpose). → multi-race elections
• Quorum — a turnout threshold (separate from who wins): enough of the eligible electorate must participate or no winner is declared. Opt-in via eligible_voters + quorum; default is a majority (>50%) of eligible voters; participation includes abstentions. → page Quorum — did enough of the electorate show up?; demo quorum_demo_c3_b6

Properties & criteria

• Majority finish — STAR's runoff guarantees the winner beats the runner-up among voters who expressed a preference between them. → demo 06b_c9_runoff-overturns-leader (runoff overturns the score leader); full walkthrough When the top-scoring candidate isn't the winner (why the top-scoring candidate isn't always the winner, as a 3→9-candidate progression)
• Runoff Reversal — the STAR outcome where the Scoring-Round leader loses the Automatic Runoff to the finalist more voters prefer (the score winner ≠ the STAR winner). Not a malfunction — the runoff elects the finalist preferred by the majority (of voters with a preference); the engine's report flags the event with a [Runoff Reversal] block. The plain-language house term is "the runoff overturns the score leader." → walkthrough When the top-scoring candidate isn't the winner
• Three notions of "winner" — Condorcet (beats all head-to-head), Score (most total stars), and Runoff (majority pick between finalists) can name three different candidates in one election; STAR targets the runoff winner by design. → page Three Notions of "Winner" — Condorcet, Score, and Runoff; demo three_winners_cw_score_runoff
• Condorcet winner — the candidate who beats every other head-to-head; STAR usually (not always) elects them. Aka Condorcet candidate, pairwise champion, beats-all winner — four names, one definition, and none of them names a method: Ranked Robin, Ranked Pairs, Schulze and Minimax all elect this candidate whenever one exists. With a general audience prefer beats-all winner, the only one that explains itself. (It stays a pairwise-majority fact either way — a ranked ballot carries order, not intensity, so none of the four says anyone was enthusiastic: preference vs. support.) Three further aliases are in circulation and are not safe swaps — Wikipedia and reform sources also gloss this candidate as a majority-preferred candidate (scope-ambiguous: over every rival is this candidate, over one rival is a single pairwise result — which is all STAR's runoff delivers, and what "the majority-preferred finalist" means throughout this library), a majority winner (collides with over-half; a beats-all winner may hold no absolute majority at all, and one who does is the majority criterion's subject instead), or a tournament winner (collides with tournament solutions, which read the C1 graph and usually return a set). Two of the three trade a precise pairwise fact for the word majority. → the full table, with what to say instead: the naming decoder → demo equal_support_runoff_demo
• Condorcet efficiency — how often a method elects the Condorcet winner, counted only over elections where one exists (cycles are excluded — no winner to elect). Not a single number for any method: it swings with the electorate model and the size of the field, by more than the gap between methods. Measured here across six methods, STAR runs 74–99% and Ranked Robin is 100% by construction. → page Condorcet efficiency, measured; hub Condorcet efficiency
• Condorcet loser — the candidate who loses every head-to-head. → catalog The Condorcet loser paradox (a method electing them anyway); live case bv1525_condorcet_loser_bloc
• Weak Condorcet winner / weak Condorcet loser — the ties-allowed versions. A weak Condorcet winner beats or ties every other candidate head-to-head (equivalently: loses to none); a weak Condorcet loser loses or ties to every other. Unlike the strict versions, neither is necessarily unique — several candidates can be jointly unbeaten. Worth knowing because the engine prints it: when no strict Condorcet winner exists, the report says either weak Condorcet winner: X (exactly one unbeaten candidate) or names the several unbeaten ones — and that second case is indifference, not a cycle, which is the distinction the line exists to draw. Weak winners are common wherever ballots allow equal ranks or equal scores, since ties in a pairwise matchup are then possible at all. → worked across five methods: The weak Condorcet loser — the candidate who beats nobody
• Condorcet compliance — always electing the Condorcet winner; STAR is not compliant (a deliberate tradeoff). Aka the Condorcet winner criterion (the usual academic and Wikipedia name), Condorcet consistency, or being a Condorcet extension. Mind the type: the criterion is a property of a method; the winner is a candidate. The shared words make "does STAR elect the Condorcet winner?" (sometimes) and "does STAR satisfy the Condorcet winner criterion?" (no) look like one question — they are two, and only the second is a guarantee. → hub Condorcet efficiency; the aliases sorted out in the naming decoder
• Smith set (top cycle) / Smith criterion — the generalized Condorcet winner: the smallest non-empty group of candidates who each beat every candidate outside the group head-to-head. When a Condorcet winner exists the set is just them; in a cycle it's the whole top clump (and a Condorcet loser is never in it). A method is Smith-efficient if its winner always comes from the set — a strictly stronger promise than Condorcet compliance: Ranked Robin/Copeland, Ranked Pairs, and Schulze keep it; Minimax, RCV-IRV, and STAR don't. → concept page The Smith set — the smallest club that beats everyone outside it; demo 04_smith_set_c4_b7
• Center squeeze — a broadly-liked moderate eliminated early for lacking first-choice support; an RCV-IRV failure STAR avoids. (aka "core collapse" — one author's (elsim) label for the extreme case where successive elimination returns the next-worst candidate; noted by Nanson, 1882. Non-standard coinage — a vivid name for worst-case center squeeze, not a separate phenomenon.) → page Center Squeeze; demos: RCV-IRV squeeze / STAR fix
• Clone independence (clone-proofness) — adding a near-identical candidate (a "clone") should never change who wins in a way that helps whoever ran the clone. Two attacks: crowding — cloning a rival to split their support (this is the vote-splitting / spoiler mechanism; Choose-One is maximally vulnerable and RCV-IRV inherits it via center squeeze, while scored methods and Ranked Robin resist it because they don't count first-choices) — and teaming — cloning yourself to field a crowd (the narrower, rarer failure). STAR strongly reduces both (scoring a doomed favorite 5 doesn't drain a compromise you also score, so it never fully eliminates every variant but sharply limits them); Ranked Robin passes crowding outright and fails teaming only in a Condorcet cycle — and even then only under some tiebreaks. → worked example Ranked Robin and clone independence; the vote-splitting face the split-voting set; concept The spoiler effect and clones & the subset choice condition; exercise Recruit a spoiler
• Later-no-harm — adding a lower preference never hurts your top choice; RCV-IRV has it, STAR intentionally does not. → episode Favorite Betrayal — Does Only RCV Avoid It?; exercise Later-no-harm, both readings
• Equal Vote Criterion / Equally Weighted Vote — every ballot must have an equal-and-opposite ballot that cancels it (the Test of Balance, Mark Frohnmayer). STAR, Score, and Approval pass; Choose-One and RCV-IRV fail — the structural root of vote-splitting. → pages The Equally Weighted Vote (STAR passes) / RCV-IRV Fails the Equal Vote (Equality) Criterion (RCV-IRV fails, stated fairly)
• Vote unitarity — the equal vote's multi-winner extension (Keith Edmonds): every voter holds the same budget of influence, and it is spent only in exchange for representation gained — electing a candidate you scored 0 costs you nothing, so your full budget carries into later rounds. The design principle behind Sequentially Spent Score. → demo the two bullet voters (two zero-spend ballots keep 5 stars each and decide the second seat); method page Sequentially Spent Score
• Monotonicity — raising a candidate on your ballot never causes them to lose (and vice versa). → page IRV Non-Monotonicity — When More Support Makes You Lose; demos: RCV-IRV before/after (X loses), STAR before/after (X holds)
• Participation criterion — voting honestly never yields a worse result than not voting; its failure is the no-show paradox. Pure point-summing methods (Score, Approval, Choose-One) are immune by arithmetic; a runoff, elimination, or pairwise stage forfeits the guarantee (STAR, RCV-IRV, Condorcet methods) — STAR far more rarely than IRV. → hub Participation; catalog the No-Show paradox; live pair participation_no_show; the STAR-side failure as an exercise The tenth ballot
• Favorite-betrayal criterion — you never gain by scoring someone above your favorite. → episode Favorite Betrayal — Does Only RCV Avoid It?
• Consistency (join-consistency / reinforcement) — if every part of a split electorate separately elects X, the combined electorate must elect X. Point-summing rules pass by arithmetic — a district sweep is mathematically binding for Score/Approval (essentially only scoring rules pass, a classical result of H. P. Young); a runoff, elimination, or pairwise stage forfeits it (STAR, RCV-IRV, top-two, Condorcet methods), because "who advances" is not additive. Distinct from summability (next entry): STAR's tallies still add across precincts — what can't be added is each district's declared winner. → exercise Two districts, one mayor (live BV trio BV2188–90); catalog the multiple-districts (reinforcement) paradox
• Summability / precinct-summable — results can be computed by adding independent precinct totals (STAR can; RCV-IRV cannot). → page STAR Is Summable — Add Up Precinct Totals; demo 04b_c4_b3_display-options-all
• Central tabulation / central count — what a non-summable count forces: the ballots (or their cast-vote records, CVRs — one electronic record per ballot listing everything the voter marked) must be gathered in one place before the count can run. A single point of failure (one facility, one software configuration) and a heavier, slower audit than adding published precinct tables. Structural for RCV-IRV/STV; a mere logistics choice for summable methods. → concept page Central tabulation — when every ballot must travel
• Preference matrix (pairwise matrix) — the summable head-to-head table the runoff and audits use: for every pair of candidates, how many ballots are For – Equal Support – Against. One artifact, several names: preference matrix = pairwise (comparison) matrix = head-to-head table; the engine prints it as the "Runoff (Preference) Matrix". Pairwise counting is the process that fills it — each ballot is a tiny matrix of pair verdicts, and the election's matrix is the ballots' sum (which is exactly why it's precinct-summable). → concept page Pairwise counting — every ballot is a tiny matrix; demo 04b_c4_b3_display-options-all
• Strategyproofness — no voter can ever gain by voting insincerely; impossible for any method (Gibbard). → The Gibbard–Satterthwaite theorem
• Gibbard / Gibbard–Satterthwaite theorems — proofs that every reasonable voting method is manipulable. → page The Gibbard–Satterthwaite theorem
• Strategy resistance — how rarely and riskily strategy pays; STAR is resistant, not proof. → Strategic Voting Across the Equal Vote Methods; measured as PVSI
• Strategic / tactical / insincere voting — casting a ballot that misstates your true preferences to try for a better result. Every method is manipulable (Gibbard); what matters is whether it's actionable and whether it pays. → page Strategic Voting Across the Equal Vote Methods
• Compromising (strong insincerity) — scoring/ranking a "lesser evil" above your true favorite; the same thing as favorite betrayal, and the defining flaw of choose-one. → strategic voting
• Burial (weak insincerity) — keeping your favorite on top but placing a rival below candidates you like even less, to knock the rival out. The named strategic risk for Ranked Robin; notorious in Borda; rarely pays in STAR; and largely closed to IRV, which satisfies later-no-harm. → hub Burial · taxonomy strategic voting
• Bullet voting / tactical minimization (truncation) — supporting only your favorite and zeroing (or omitting) everyone else. The central Approval tension; STAR's runoff discourages it. → strategic voting
• Tactical maximization — the opposite of bullet voting: inflating support for a front-runner you don't love, to hedge. The other side of the Approval threshold; STAR's runoff neutralizes it. → strategic voting
• Candidate viability — whether a candidate is seen as able to win; under choose-one it pressures voters toward the "electable" lesser evil, and it's the lever establishment/media use to steer votes. → strategic voting
• Voter Satisfaction Efficiency (VSE) — a simulation metric for how well a method's outcomes reflect voter preferences, and how much strategy shifts that; the basis for the strategic "backfire ratio" figures (STAR ≈ 1:1, IRV ≈ 3:1, Plurality ≈ 17:1). Peer-reviewed source, with the ratios' provenance and the lean disclosed: Wolk, Quinn & Ogren (2023). → strategic voting
• Pivotal Voter Strategic Incentive (PVSI) — VSE's companion metric: how much a pivotal voter gains on average by voting strategically rather than honestly. ~0% means strategy rarely pays; negative means it backfires more often than it works (STAR ≈ 2%, Approval ≈ 10%, Plurality ≈ 14%). → PVSI
• Spatial model — the picture of voters and candidates as points in an issue space (1-D = the left–right spectrum), where closer = preferred (utility = −distance); the realistic electorate model behind most simulations. → The spatial model
• MaxVoting — a 2024 advocacy rebrand (Tedman Getschman / Common Sense for Uniting America) of cardinal (rated) voting — "each candidate independently evaluated by all voters." STAR, Approval and Score are all MaxVoting methods; it is not a new method. The name bundles the family's real strength (independent per-candidate evaluation → no vote-splitting) with the strong claim that it "ends political division" — kernel and overreach separated in → Does a better ballot end polarization?
• Median voter theorem — in a 1-D spatial model, the candidate nearest the median voter beats every other head-to-head, so a Condorcet winner (the center) always exists (Duncan Black, 1948). → The spatial model
• Equal Vote / Test of Balance — any support a ballot expresses can be exactly cancelled by an opposite ballot; STAR's precise sense of equal weight. → The Equally Weighted Vote
• One-person-one-vote — equal voting weight. (Caution: the constitutional OPOV doctrine governs district population, not ballot expressiveness.) → One person, one vote
• Utilitarian vs majoritarian — maximizing total support vs guaranteeing a majority; STAR blends both. → What makes a good winner?

Other methods (for contrast)

• Approval voting — score each candidate 0 or 1 (approve / not); most approvals wins. → page Approval voting; demo approval_101_c3_b5 (0/1 marks are also legal on a STAR ballot — star_ala_approval)
• Score voting (pure) — score 0–5; highest total/average wins, with no runoff (more manipulable than STAR). → Range / Score voting
• Combined Approval Voting (CAV) — Approval with a third option: vote For (+1), abstain (0) or Against (−1); highest net score (approvals minus disapprovals) wins. Proposed by Dan Felsenthal in 1989 and reinvented often enough to answer to six other names — Dis&approval voting, Balanced Approval Voting (BAV), Evaluative Voting (EV-3), net approval voting, AWAO, TWV1. Mathematically it is three-level score voting, so it inherits score's criteria exactly; under strategy it collapses back into plain Approval, since a voter maximising influence never uses the middle option. Its one distinctive property is that a blank counts as the MIDDLE grade, not the lowest — the opposite of every other score ballot in this library. → engine + the reversal that turns on it 06_Other/Combined_Approval/
• 3-2-1 voting — rate each candidate Good / OK / Bad, then narrow in three steps: 3 semifinalists (most Good) → 2 finalists (fewest Bad) → 1 winner (pairwise runoff). Jameson Quinn / CES; a reference method, not EVC-endorsed — a center-squeeze-free, summable cousin of STAR with a coarser 3-level ballot and explicit dark-horse/clone guards. → concept & STAR comparison 3-2-1 voting; engine + Tennessee demo 06_Other/three_two_one/
• RCV (Ranked-Choice Voting) — a ranked ballot type (rank candidates 1st, 2nd, 3rd). A family, not one method; in the US it's commonly (loosely) used to mean IRV specifically. → Tips — Terminology: RCV vs IRV vs RCV-IRV (and friends); episode "Is It RCV or IRV? Why Do You Keep Saying RCV-IRV?"
• IRV (Instant-Runoff Voting) — one tabulation of a ranked ballot: eliminate the lowest, transfer, repeat until a majority. The single-winner method usually meant by "RCV."
• RCV-IRV — disambiguating label for "the RCV that is IRV"; preferred in this repo for STAR-vs-method comparisons so it's clear we mean the eliminate-and-transfer method, not the ballot family. → Tips — Terminology: RCV vs IRV vs RCV-IRV (and friends); episodes "Is It RCV or IRV? Why Do You Keep Saying RCV-IRV?", "Exhausted Ballots" — What FairVote's Word Actually Hides
• Ranked Robin (RCV-RR / "Consensus") — a Condorcet tabulation of the same ranked ballot (most head-to-head wins, Copeland-style). Has no center squeeze; do not lump it with IRV. Meet it under other names: the algorithm is Copeland's method, also called the Llull method for the man who described it in 1299; a rival campaign brands it Consensus Choice and another Instant Round-Robin Voting (IRRV). → which word means what: the naming decoder
• STV (Single Transferable Vote) — the proportional, multi-winner tabulation of ranked ballots (the proportional cousin of IRV, not IRV itself). → method door 06_Other/STV; demo 03a_stv_3seats; comparison page Proportional Representation: STV vs STAR-PR; Curriculum 301.2
• Condorcet method — any ranked method that always elects the candidate who beats every other head-to-head (the Condorcet winner) when one exists. A family: Ranked Robin, Ranked Pairs, Schulze, Minimax, Copeland. The family answers to several names — round-robin voting (Wikipedia's umbrella), paired comparison, tournament voting — all describing the same everyone-plays-everyone format. Say one of these, not "Ranked Robin," when you mean the whole family. → family tree in Tips — Terminology: RCV vs IRV vs RCV-IRV (and friends)
• Ranked Pairs (Tideman) — a Condorcet method: lock in the strongest pairwise victories first, skipping any that would create a cycle. → Cycle resolution — why Minimax, Ranked Pairs, and Schulze exist
• Schulze (beatpath) — a Condorcet method that decides via the strongest "beatpaths" between candidates. → Cycle resolution
• Minimax (Simpson–Kramer) — a Condorcet method electing the candidate whose worst pairwise loss is the smallest. → Cycle resolution; runnable Minimax elects the absolute loser
• Borda — a positional ranked method (points by rank position). A ranked method but not Condorcet-compliant. → Borda
• Bucklin (Grand Junction) — a ranked, median-style method (add lower ranks until someone has a majority). Ranked but not Condorcet. (Spelled Bucklin, not "Buckling".) → the ranked-ballot method zoo (family 3, graduated majority)
• Reversal symmetry — a criterion: if every voter reverses their ballot (everyone now expresses the opposite preference, as if picking the worst candidate), the original winner should never win again. RCV-IRV and plurality fail it (a method's "best" can equal its "worst"); additive methods (Range/Score, Borda, Approval) and Ranked Pairs / Schulze satisfy it. A symptom of IRV's eliminate-on-first-choices logic. → runnable demo reversal symmetry (STAR & Ranked Robin avoid the winner=loser on the example).
• Turkey-raising (turkey raise) — a strategy of raising a weak third choice above your genuine second choice, hoping to knock out a rival so your favorite wins (a.k.a. pushover). STAR resists it structurally: if you fear your second choice is stronger than your favorite, then your favorite is effectively playing for the second runoff seat — and boosting a candidate you like even less is more likely to bump your favorite out of the runoff than to help. → strategic voting · related pathology Dark Horse
• Hare — historically the ranked-transfer idea; single-winner = IRV, multi-winner = STV (Hare quota). → the ranked-ballot method zoo; method doors RCV-IRV · STV
• ballot vs tabulation — the ballot is what the voter marks (ranked, or scored); the tabulation is how it's counted (IRV / Ranked Robin / STV for ranked; STAR / Approval / Score for scored). "RCV" names a ballot; "IRV" names a tabulation. → Tips — Terminology: RCV vs IRV vs RCV-IRV (and friends); episode "Is It RCV or IRV? Why Do You Keep Saying RCV-IRV?"
• Bloc STAR — multi-winner STAR that runs the whole single-winner count (score, then automatic runoff) once per seat, removing each winner before the next (at-large / majoritarian — not proportional). Not "the top N by score": every seat ends in a runoff, so the highest-scoring candidate can win no seat at all. → demo 01_c4_b2_bloc-star-2-seats; majoritarian-vs-proportional contrast in Proportional Representation: STV vs STAR-PR; STAR Voting — Curriculum (Voting 101 / 201 / 301) (201.5)
• Proportional STAR — multi-winner methods (Reweighted Range Voting, Allocated Score, Sequentially Spent Score) that give proportional representation. → demo 03b_star_pr_3seats; page Proportional Representation: STV vs STAR-PR (STV vs STAR-PR); STAR Voting — Curriculum (Voting 101 / 201 / 301) (301.1)
• District magnitude (M) — how many seats are elected from one district. The single biggest dial in any proportional system, because it sets the share of the vote a group needs to win a seat — roughly the Droop quota, 1/(M+1):

Seats per district (M)	Threshold for one seat
1 (single-member)	over 50% — no proportionality at all
3	~25%
5	~17%
10	~9%

This is why single-member districts aren't made unfair by gerrymandering — they're winner-take-all by construction. A party holding a third of a state's votes but spread evenly across it wins nothing: Massachusetts Republicans are roughly a third of the electorate and hold zero US House seats, with no gerrymander required. Raising M is what lets a minority win seats without drawing district lines around demographics. The trade-off: bigger M means more proportional results but a weaker local-representative link and longer ballots — which is the gap MMP (below) is designed to split. - MMP (Mixed-Member Proportional) — a hybrid: you elect local single-member districts and add compensatory "list" seats chosen so each party's total seat share matches its vote share (Germany, New Zealand, Scotland). Keeps a local representative while making the legislature proportional — the most widely adopted alternative to STV. → Two-Party Dominance - Effective Number of Parties (ENP) — the standard way to count a party system when parties differ wildly in size: ENP = 1 / Σ(sᵢ²), where sᵢ is each party's share (Laakso–Taagepera). Four equal parties → ENP 4; one dominant party with three tiny ones → ENP barely above 1. Roughly 2 in the US, >6 in Israel. It turns "does this reform break two-party dominance?" into a measurable question. → Two-Party Dominance - Electoral / party threshold — a minimum vote share (commonly 3–5%) a party must clear to win any seats. Intended to keep fringe parties out of a fragmented legislature, but a blunt instrument: votes for parties below the line are discarded entirely, so a bloc with well under half the vote can end up with a governing majority. Contrast individual/local thresholds, where a below-threshold candidate's votes transfer to a similar one instead of vanishing. → what "proportional" actually means - Free riding (in proportional methods) — a PR-specific strategy: because electing a candidate "uses up" the ballots that supported them, a voter can gain by withholding support from someone who is winning anyway, so their ballot survives to decide a later seat. The proportional analogue of strategic voting, and an incentive in nearly every PR method, STAR-PR included. Two named forms: Hylland free riding (bury a sure winner) and Woodall free riding (back someone you expect to be eliminated — needs vote transfer, so it has no scored analogue). In this library's worked case a bloc flips a seat by scoring a landslide winner 4 instead of 5, which is cheaper than the "modest incentive" framing suggests — though it achieves nothing if you misjudge the spend order, backfires if pushed too far, and cancels out once both sides try it. → Free riding in Proportional STAR - Apportionment — the older, party-list-shaped version of the same problem: given each group's claim, how many whole seats does each get? Its two-century literature is where quotas, rounding rules and the PR paradoxes were worked out, and it is the direct ancestor of STAR-PR's reweighting step. Canonical reference: Pukelsheim. The caveat that matters: apportionment takes party vote totals as input, while STAR-PR takes a ballot matrix and works sequentially — so the vocabulary transfers, the theorems do not automatically. - Quota method vs divisor method — the fundamental split. A quota method works out what one seat costs and hands it out (divide and rank) — Allocated Score is one. A divisor method repeatedly scales the numbers and rounds (divide and round) — RRV is one. This is exactly why they behave differently, and why RRV fails the Hare Quota Criterion. - Largest remainder / greatest remainders (residual fit) — after each group takes its whole quotas, seats are left over; largest-remainder hands them to whoever has the biggest fraction left. The classical relative of STAR-PR's fractional surplus handling. Also called the Hamilton method. → Pukelsheim - Seat bias — the systematic tendency of a rounding rule to over- or under-reward big groups, averaged over many elections. Pukelsheim gives it as a formula with three factors — a method factor, a party factor and a threshold factor — and two of its results are worth stating precisely, because the usual shorthand gets them slightly wrong: - Hare-quota with greatest remainders is unbiased — it is the unique member of its family with zero seat bias — and Droop favors stronger groups. So the accurate contrast is not "Hare helps small factions" but "Hare is even-handed, and Droop tilts toward the large." (Likewise, among divisor methods, standard rounding — Webster/Sainte-Laguë — is the unique unbiased one.) - The stronger third, the weaker two-thirds. Under a biased method the sign flips at roughly the top 37% of groups by size: the strongest third gain seats on average, the weaker two-thirds lose them. - Caveat on transfer: these are results about apportionment from party vote totals, proved asymptotically under a uniform model. STAR-PR's Allocated Score is a different, sequential method — the quota-choice intuition carries over, the unbiasedness theorem does not automatically. Nobody has checked it here. - Seat excess — one group's seats minus its ideal share, in a single election. Because the excesses always sum to zero, somebody is over-represented and somebody under-represented in every real apportionment: it is arithmetically unavoidable, not a sign of a broken method. → Pukelsheim - Success value of a vote — how much representation one vote actually buys, and therefore the precise thing "equal voice" means. Equalising success values across voters is what a proportional method is for, and it is the standard by which German constitutional challenges to apportionment have been argued. → Pukelsheim (§2.7–2.9 is the rigorous statement) - Ideal share of seats — the fractional, un-rounded number of seats a group "should" have. Never achievable exactly (seats are whole), so it is the benchmark against which disproportionality is measured — see what "proportional" actually means. - Threshold of exclusion / threshold of representation — a useful pair. The exclusion threshold is the share above which you are guaranteed a seat no matter how others vote; the representation threshold is the share at which you might win one under favourable conditions. Loose talk about "the threshold" usually conflates them, and they can be far apart. → what "proportional" actually means - Alabama paradox — adding a seat to the body reduces some group's seat count. Named for the 1880 US census, where Alabama got 8 seats in a 299-seat House and 7 in a 300-seat one. Whether Allocated Score can exhibit it is an open, testable question for this library — nobody here has checked. - Population paradox — a group that gains support relative to another loses a seat to it (a failure of vote-ratio monotonicity). Sibling of the no-show paradox and of the participation failures already documented for Bloc STAR. - The same method, two names — a recurring trap in the PR literature. Jefferson = D'Hondt (divisor, downward rounding, favors large groups). Webster = Sainte-Laguë (divisor, standard rounding, near-unbiased). Hamilton = largest remainder (quota). American and European sources use different names for identical arithmetic. The trap is not hypothetical: Hagenbach-Bischoff proposed a divisor method, and political-science textbooks filed it for a century as a quota method — he had even objected in print to it being named after him at all. If a source's method name and its description disagree, trust the description. → Pukelsheim (chapter 16 is a biographical digest of whose name is on what) - Vote management — the organized, party-level version of free riding: a party instructs blocs of its supporters to divide their votes across its candidates so its vote share converts into the maximum number of seats. Long practised under STV (Malta, Ireland) and Japan's old SNTV. A reason to prefer PR methods where the gain from managing votes is small. - AVEC (Average Voter Effective Choice) — an attempted multi-winner analogue of VSE: AVE × AVC, where AVE is how much of the electorate's voting power actually elected someone (wasted votes drag it down) and AVC is how much genuine choice voters had. Its author, Jameson Quinn, abandoned it unfinished — so quote it as a sketch, not a score. Worth knowing mainly because it marks the gap: proportional methods have no settled accuracy metric. → which proportional method is best? - Sortition — filling a body by random selection from the population (ancient Athens; modern citizens' assemblies) rather than by election. The limiting case of proportionality: a large random sample reproduces every trait of the electorate in proportion, without any ballot at all. Useful as the benchmark PR methods are approximating — and as a reminder that "representative" and "elected" are separate ideas.

Approval committees (ABC rules & Thiele methods)

Multi-winner approval theory (Lackner & Skowron). Not STAR, but the cleanest place to see proportionality — and the family RRV descends from. Pages: ABC rules 101 · 301 spectrum · Thiele methods.

• ABC rule — an Approval-Based Committee rule: takes an approval profile + committee size k, outputs one or more size-k winning committees. Resolute = always one committee; irresolute = may return several tied committees (broken by a pre-published order, like STAR's lot). → ABC rules 101
• AV (Multi-Winner Approval Voting) — seat the k most-approved candidates; maximises total approvals (utilitarian). The LH engine's Approval_Multi_Winner. → ABC rules 101
• Approval Chamberlin–Courant (CC) — maximise the number of voters with ≥ 1 approved winner (egalitarian coverage); the "opposite" of AV (Thiele/Chamberlin–Courant, 1895/1983). → the 301 spectrum
• Thiele method (w-Thiele) — a family scoring a committee by Σ_i w(|W∩A(i)|) for a non-decreasing w with w(0)=0; AV is w(x)=x, CC is w(x)=min(1,x), PAV is the harmonic w. The single "diminishing-returns" dial from utilitarian to egalitarian. → Thiele methods
• PAV (Proportional Approval Voting) — the w-Thiele rule with the harmonic w(x)=1+½+…+1/x; the diminishing weights make it proportional (balances big and small groups). seq-PAV / rev-seq-PAV = its greedy forward / backward algorithms. → Thiele methods
• SAV (Satisfaction Approval Voting) — Brams & Kilgour (2010): a voter's satisfaction is the fraction of their approved candidates elected, and SAV maximises the sum — equivalently, each voter has one vote split evenly among their marks (1/|A(i)| each), top k win. Not a Thiele method: it divides by how many you approved, where Thiele divides by how many of yours won. Semi-proportional — d'Hondt over party lists, coordination-dependent over candidates. aka equal and even cumulative voting (Peoria, Illinois, since 1991). → SAV
• Welfare vector / welfarist rule — a committee's per-voter satisfaction (|A(1)∩W|,…); a rule is welfarist if it maximises a function of that vector (all Thiele methods are). → Thiele methods
• Monroe's rule / Phragmén — proportional rules that are not Thiele: Monroe assigns each winner a disjoint voter quota; Phragmén balances "load." → the 301 spectrum
• RRV = score-PAV — Reweighted Range Voting (a Proportional STAR method) is the score-ballot generalisation of sequential PAV; on 0/1 ballots it reduces to seq-PAV. Allocated Score / SSS instead follow the quota/STV lineage, not Thiele. See Thiele methods → "Does this apply to STAR-PR?".

The wider field (computational social choice)

Where STAR and these method comparisons sit academically. The frontier is surveyed in the Dagstuhl computational-social-choice seminar series (2007, 2010, 2012, 2015, and 2017 — "Voting: Beyond Simple Majorities and Single-Winner Elections").

• Computational social choice (comsoc) — the interdisciplinary field (social choice theory + computer science + economics) studying how to aggregate agents' preferences into a joint decision, with particular attention to computation: how hard a winner is to compute, to manipulate, or to audit. STAR, the Condorcet family, and the ABC/Thiele rules above all sit here; the active frontier is multi-winner elections, non-standard ballots, and settings like the two below. → the 2017 Dagstuhl seminar 17261.
• Aggregation (vote aggregation) — the umbrella verb for turning many individual ballots into one collective result. It earns a glossary slot not because it's hard but because it names four different things in the literature, and papers switch between them without warning. (1) Tabulation — the mechanical count an engine performs. (2) The aggregation problem — a profile in, a collective ranking (SWF) or a winner (SCF) out; this is the object Arrow and Gibbard–Satterthwaite quantify over, and the type you pick decides which impossibility applies. (3) Precinct aggregation — adding subtotals upward without the original ballots, which is summability and is a property some methods lack. (4) Hillinger's "cardinal aggregation of judgments" (2004) — the thesis that aggregation presupposes measurement, so the voting paradoxes are artifacts of aggregating what was never measured; not judgement aggregation in the technical sense, despite the word. The bit worth carrying away: calling the operation aggregation already assumes the inputs are commensurable enough to combine — which is precisely what Sen's comparability axis and the interpersonal-comparison objection dispute. Arrow aggregates bare orderings specifically to sidestep that assumption. → cardinal utility (measurability vs. comparability); what is a voting method?
• Distortion — the worst-case ratio between the social welfare (total voter utility) of the best possible candidate and of the one a rule actually elects, maximised over every electorate and every utility profile consistent with the ballots the rule saw. Distortion 1 = always optimal; "unbounded" = arbitrarily bad. The model decides the verdict, so never quote a number without naming it: under unit-sum utilities no deterministic ranked rule beats Θ(m²), while under metric (spatial) preferences the best ranked rules hit exactly 3, and any Condorcet winner is within 3. Defined by Procaccia & Rosenschein (2006) for software agents, which is why it assumes utilities exist and are known — the cardinal utility question it does not answer. Worst-case cousin of VSE, which measures the average case. No unconditional distortion number exists for STAR (the framework analyses rules reading only rankings) — don't quote one. → distortion; runnable same ranks, different utilities, the valuable Condorcet loser
• Unit-sum normalization — the standard restriction that makes distortion finite: every voter's utilities sum to the same total. On a 0–5 ballot it reads as everyone gets the same amount of ink. Not a technicality — Proposition 3 of Procaccia & Rosenschein proves it equivalent to leaving utilities unconstrained but weighting each voter by their own total, so refusing to normalize is formally identical to giving louder voters more votes. Drop it and distortion is unbounded at 3 voters and 2 candidates. The equally weighted vote and one person, one vote argue this from principle; this is the theorem. → distortion
• Misrepresentation — distortion's tamer cousin, from Monroe's 1995 proportional-representation work: assume a voter's unhappiness with a candidate is just that candidate's rank position minus 1 (top = 0, last = m−1). Restricting utilities that way lifts the impossibilities — every method gets a finite bound (Plurality and top-two runoff both m−1, Copeland/Ranked Robin ≤ m−1, STV/RCV-IRV ≤ 1.5(m−1), Veto unbounded). Borda scores a perfect 1 — because the measure is the Borda count, which makes it a textbook case of a criterion built to fit the method rather than an endorsement. Also the single-winner face of the Monroe / Chamberlin–Courant objectives in the ABC rules above. → misrepresentation
• May's theorem — with exactly two alternatives, simple majority rule is the unique rule that is decisive, anonymous, neutral, and positively responsive (May, 1952). The positive result the impossibility theorems are measured against — and the fairest frame for Choose-One: at two candidates FPTP is majority rule, so it is provably optimal; every spoiler and vote-splitting pathology comes from running a two-candidate rule on three or more. Relax "only two" and you get Arrow. → May's theorem
• Anonymity — permuting which voter cast which ballot never changes the result: the rule sees the tally, not the names. One person, one vote, stated as an axiom. Failing it gives weighted voting, shareholder votes, or a dictatorship. → May's theorem; compare the Equally Weighted Vote
• Neutrality — swapping the names of two alternatives swaps the result; no option is the default. A supermajority threshold deliberately violates neutrality — a ⅔ bar to amend privileges the status quo by design, which is the point of it, not a flaw. Naming the axiom lets you price the trade exactly. → May's theorem; the agenda-voting failure
• Positive responsiveness — if the group is tied and one voter switches toward X, X wins outright. Strictly stronger than monotonicity, which only asks that added support never hurts. One of May's four conditions. → May's theorem
• Informational basis (Fishburn C1 / C2 / C3) — which statistic a voting rule actually reads. C1 needs only the tournament (who beat whom, and which pairs tied — direction, no sizes): Copeland, Smith set, Top Cycle. C2 needs the weighted tournament (the same graph with margins on it): Minimax, Ranked Pairs, Schulze, Kemeny — and Borda. C3 needs more than the pairwise matrix holds: Dodgson, Young, plurality, RCV-IRV. Three cautions. (1) The tiers are not a summability, difficulty, or quality ladder — plurality is C3 and the cheapest summable method there is, Kemeny is C2 and NP-hard. (2) Never say plurality "needs more information" than Borda — the two statistics are incomparable, not nested; the precise claim is that plurality's winner is not a function of the pairwise matrix. (3) STAR / Score / Approval have no class at all (see below). Fishburn 1977 framed this for Condorcet SCFs; extending it to Borda/plurality/IRV is later convention. → what a method reads; runnable same matrix, different plurality
• Tournament / weighted tournament — the pairwise results as a directed graph. The tournament records only the direction of each head-to-head; the weighted tournament puts the margin on each edge. A tournament solution is a rule reading only the first — that names the C1 tier specifically, not the Condorcet family as a whole. Ranked Robin is one (it is the Copeland set); the literature holds a dozen more (top cycle, uncovered set, Banks, bipartisan, Slater, Markov), and they disagree in a cycle. → tournament solutions; pairwise counting; what a method reads; runnable five answers, one election
• Uncovered set / Landau set / Fishburn set / covered candidate — three names for one object (graph theory says Landau set, after the pecking-order work the king comes from; Fishburn set follows Wikipedia — and note that everywhere else in this repo "Fishburn" means the C1/C2/C3 informational basis above, a different concept from the same 1977 paper). A covers B when A beats B head-to-head and also beats everyone B beats: B is strictly redundant on the pairwise evidence. The uncovered set is everyone nobody covers — equivalently, everyone who reaches every rival in at most two steps ("I beat you, or I beat someone who beat you"; graph theory calls these the tournament's kings). It is the weakest structural filter in the tournament-solutions family and the coarsest Pareto-optimal one — a tournament solution is Pareto-optimal iff it refines the uncovered set. Two cautions. (1) Covered ≠ Pareto-dominated (much stronger: every voter must prefer the other); a covered candidate can be someone's favourite. (2) The term is unambiguous only with no pairwise ties — four published variants (Gillies, Fishburn, Bordes, McKelvey) disagree once a tie appears. Uncovered ⊆ Smith. Ranked Robin never elects a covered candidate (Copeland ⊆ uncovered); STAR and RCV-IRV can. → the uncovered set; runnable STAR elects a covered candidate
• Condorcet extension — a rule that elects the Condorcet winner whenever one exists (aka the Condorcet winner criterion, Condorcet compliance / consistency). Ranked Robin, Ranked Pairs, Schulze, Minimax, Baldwin and Nanson are extensions; RCV-IRV, single-winner STV and the two-round runoff are not — all three decide eliminations on first preferences, so they can drop a candidate who beats every rival. Smallest proof: 3 candidates, 5 voters. → what a method reads; center squeeze
• Social welfare function (SWF) — a rule that maps a profile of individual rankings to a whole social ranking (f : L(A)ⁿ → R(A): strict orders in, a weak order out). This — not "a rule that picks a winner" — is the object Arrow's theorem quantifies over, which is why the type matters: pairwise majority rule is both Paretian and IIA, and escapes Arrow only because its output can cycle, so it isn't an SWF at all. → social welfare function
• Social choice function (SCF) — the winner-picking sibling: a profile in, a candidate out. STAR, Approval, RCV-IRV and Plurality are SCFs; Gibbard–Satterthwaite is the impossibility theorem aimed at this type, as Arrow's is at the SWF. Precise usage traces to Fishburn (1977). → social welfare function
• Pareto criterion (unanimity) — if every voter prefers A to B, then B must not win (for an SWF: B must not rank above A). Named for Vilfredo Pareto; a candidate is Pareto optimal when no rival is unanimously preferred over them. Two things it is not: it does not say a Pareto-optimal candidate must win (plurality is Paretian and still elects poorly), and it is not a bar that rules out bad rules — a dictatorship is Paretian, which is precisely why Arrow's conclusion bites. STAR passes; Approval fails, because an approval ballot never records a strict preference within the approved set. → worked: Felsenthal Ex.6; the agenda-voting failure; concept social welfare function
• Unrestricted domain (universal domain, UD) — Arrow's first condition: the rule must return an answer for every logically possible profile, refusing no input. It is a condition on the RULE, not a claim about voters — a point routinely muddled, because the profiles it quantifies over are conventionally taken to be strict, complete, transitive rankings, so the strictness rides in as part of the setup. Saari's Definition 1 states it that way explicitly and calls a voter without such a ranking irrational — which is where the cardinal camp's objection lands: indifference is ordinary, not irrational, and if a random pair is strictly ordered with probability 0.8 then a strict order over 6 candidates has probability 0.8¹⁵ ≈ 0.035. Restricting the domain is the standard escape from the impossibility, and it is never free — it buys the result by assuming what voters may think. Two restrictions worth knowing, both live in this repo: single-peakedness (opinions on one axis) guarantees a Condorcet winner; dichotomous preferences (an Approval ballot) make Approval, Borda and every Condorcet method agree. → Arrow's theorem and STAR; social welfare function; the empirical objection in full: cardinal utility; the SVN indeterminacy argument built on it: is Approval's outcome arbitrary?
• Compound scoring rule — a scoring rule (below) cascade: ties under a first score vector w₁ are broken by score differences under a second w₂ (e.g. plurality score to separate tied Borda winners), a third if any survive, and so on for any finite number of vectors. It matters because of an exact characterization — Smith (1973) / Young (1975): the anonymous, neutral, and reinforcing SCFs are precisely the compound scoring rules. Add continuity (the Archimedean property: enough copies of an electorate with a unique winner eventually carry the merged election) and the class narrows to the simple, single-vector scoring rules. The bite: since STAR fails reinforcement, STAR is provably not a compound scoring rule — no cascade of score vectors reproduces it, and the runoff is the step where it leaves the class. → the reinforcement paradox, worked
• Homogeneity — a rule's winner is unchanged when every voter is replaced by k identical copies (f(ks) = f(s)); the weakest member of the reinforcement / consistency family. It is the axiom quietly underwriting this repo's own house convention that weighted Count: blocs may be scaled ×N without changing the result — see choosing voter counts. Not automatic: a rule with a fixed voter threshold ("elect X if at least 100 people approve") is not homogeneous.
• Lifting simply — the precise form of "raise a candidate on your ballot" used in monotonicity statements (Fishburn, 1982): x moves from below one or more candidates to above them while the relative order of every pair not involving x stays unchanged. The italicised clause is load-bearing — without it a "lift" could smuggle in other reordering, so a flipped winner would prove nothing. → monotonicity
• Peleg monotonicity — the irresolute strengthening of monotonicity (above): after any simple lift of a winning x, x remains a winner AND no new winners are added (Peleg, 1981; argued for by Sanver & Zwicker, 2012). It exists because the ordinary resolute definition can be satisfied vacuously — modify any SCF whatsoever to add one tied alternative to every outcome, and "the winner must not change" can no longer bite. A standing caution: a criterion claim is only as strong as which version of the criterion is meant. Copeland/Ranked Robin, Simpson/minimax, the proper scoring rules, sequential majority comparison and Top Cycle all satisfy Peleg's version. → monotonicity
• Condorcet domain / Condorcet extension — the Condorcet domain is the set of profiles for which a Condorcet winner exists; Pairwise Majority Rule (PMR) elects that winner and is simply undefined elsewhere. An SCF is a Condorcet extension (Condorcet consistent) if it agrees with PMR on that domain — electing the Condorcet winner alone whenever one exists — and does whatever it likes on cycles. The fine print people skip: the label constrains a method only on the easy profiles and says nothing about cycles. Ranked Robin/Copeland, Minimax, Ranked Pairs, Schulze, Baldwin and Nanson qualify; STAR does not. → Campbell–Kelly theorem
• Campbell–Kelly theorem — "May's theorem for three or more alternatives" (2003): restricted to the Condorcet domain, PMR is resolute, anonymous, neutral and strategyproof, and for odd n is the unique such rule. The strongest positive result the Condorcet family has — and its price is the restricted domain, so it is silent on cycles and cannot rank one Condorcet method above another. It doesn't contradict Gibbard–Satterthwaite: G–S's bite comes from the full domain, not from having 3+ candidates. → Campbell–Kelly theorem
• Dichotomous profile / dichotomous preferences — the restricted domain in which every ballot is a weak ranking with exactly two indifference classes: a set of candidates the voter likes, a set they don't, and no expressed preference within either group. That is exactly what an Approval ballot is, which makes this the natural domain for approval theory — and three things that disagree everywhere else collapse into one there. Approval = Borda (applying the averaging convention for scoring weights under indifference); every profile has a Condorcet winner, since defining "x beats y" as more voters strictly prefer x to y reduces on these ballots to "more voters approve x than y," which is transitive and cycle-free; therefore Approval agrees with every Condorcet extension. One can fairly say approval voting reconciles Borda and Condorcet on this domain — and the reason is the cycle–cocycle split (next entry): the cyclic component, which is the only place Borda and Condorcet can disagree, is always zero on dichotomous ballots. The domain restriction is the whole content. Real approval ballots are compressed from richer opinions, and the Condorcet winner of what the voters thought can differ from the Condorcet winner of what they marked. → Approval in the theory literature; runnable: when compression moves the Condorcet winner
• Cycle–cocycle decomposition — every margin graph splits, uniquely and orthogonally, into a cocycle part (a pure quality signal — one number per candidate explains it completely, and it is exactly what the symmetric Borda count reads, since a Borda score is the graph's net outflow and circulations have none) plus a cycle part (pure rock-paper-scissors circulation: invisible to Borda, yet able to point a head-to-head sign against the quality order wherever it is locally stronger). Built by Zwicker (1991) to explain the Borda–Condorcet split; it is why Copeland can tie three candidates that Borda separates cleanly. → concept page the cycle–cocycle decomposition; worked: Copeland vs Borda — margins matter
• Scoring rule / score vector — a rule defined by a vector w = (w₁, …, w_m): each voter gives w₁ points to their first choice, w₂ to their second, and so on; highest total wins (proper when w₁ ≥ … ≥ w_m and w₁ > w_m). The unification worth knowing: Plurality (1,0,…,0), anti-plurality (1,…,1,0), k-approval, and Borda (m−1,…,0) are one method on different settings — Choose-One is simply the most extreme proper vector there is. The Formula One World Championship (25,18,15,12,10,8,6,4,2,1,0,…) is a positional voting rule too, with races as voters. → the ranked-ballot method zoo
• Parallel-universe tiebreaking — an RCV-IRV tiebreak that, when candidates tie for fewest first choices, explores every possible elimination sequence, computes each one's winner, and declares a tie among all winners found (Conitzer et al., 2009). The most principled answer to IRV's elimination ties — it refuses to let an arbitrary choice fork the count — at a combinatorial cost that makes it computationally hard in general. Contrast drop-them-all (Taylor & Pacelli, 2006), which eliminates every tied candidate at once and can leave nobody with majority support. → Tie-breaking: STAR vs RCV-IRV
• Nonimposition — a rule is imposed if some candidate is simply unelectable: no profile whatsoever makes them the sole winner. Nonimposition forbids that, and is a deliberately weak form of neutrality (above) — it only requires that everyone could win, not that the rule treat them alike. Pareto implies nonimposition (a unanimously top-ranked candidate must win, so nobody is unelectable), which is one more reason Pareto reads as a floor rather than a real constraint. → Ties Are Forced
• Resolute / irresolute (SCF) — a social choice function is resolute if it always returns exactly one winner, irresolute if it may return a tied set. The word matters because resoluteness is provably not free: no anonymous, neutral, Pareto rule can be resolute whenever the electorate size n has a divisor r with 1 < r ≤ m candidates — so for every even electorate, a forced tie exists (Moulin, 1983). Every tie-break in this repo is a choice about which axiom to spend. → Ties Are Forced; compare ABC rule above (the same word, used for committees)
• Reverse Borda — elect whoever has the lowest Borda count. It is perfectly anonymous and perfectly neutral, and obviously insane — which is exactly its use: it's the rule that shows why the Pareto criterion (above) earns its keep, since anonymity and neutrality alone don't exclude it. → Ties Are Forced
• Ordinal utility — a utility scale unique up to any increasing transformation: only the order survives rescaling. What a ranked ballot records, and the only input Arrow's theorem quantifies over. → cardinal utility
• Cardinal utility — a utility scale unique up to a positive affine transformation (u → au + b, a > 0), so that the order and the ordering of the differences survive rescaling. That second clause is the whole content: it is what lets a scale say "I prefer A to B more than I prefer B to C." It does not license ratio claims ("twice as good") — those die when you slide the origin. What a score ballot reaches for. → cardinal utility; runnable: the same election, rescaled
• Measurability vs. comparability — Sen's two independent axes (Collective Choice and Social Welfare, 1970), and the distinction that makes the standard objection to score voting precise. Measurability is how much structure exists within one person's utilities (ordinal / cardinal / ratio); comparability is how much of it reads across people (none / unit / level / full). Summing scores requires cardinal measurability and unit comparability — cardinality alone never licensed addition. So "your 5 and my 5 aren't the same thing" is a request for the second axis, not a quibble. (Rawlsian maximin has the opposite bill: it needs level comparability and no cardinality at all.) → cardinal utility
• von Neumann–Morgenstern (vNM) utility — the utility function representing preferences over lotteries (1944); genuinely cardinal, and the standard citation for "utility is cardinal." The trap: its cardinality is calibrated by risk attitude — the probability at which you'd swap a sure thing for a gamble — not by felt intensity of preference, and it says nothing across people. A ballot mark is not a vNM utility, so an argument that leans on vNM to justify adding up 0–5 marks has borrowed the word and left the theorem behind. → cardinal utility
• Harsanyi's aggregation theorem — vNM rationality + the veil of ignorance (judging a social arrangement as though you were equally likely to be any member of society, inheriting their circumstances and tastes) ⟹ the utilitarian social welfare function: maximize the sum of individual utilities (Harsanyi 1955, 1977; building on Fleming 1952). The cardinal camp's strongest formal card — and note its price: the utilities in it are vNM utilities, and the veil assumes a resolution of comparability rather than supplying one. → cardinal utility
• Evaluative voting (EV) / utilitarian voting — Hillinger's rule (2004): score every candidate on a uniform, unrestricted scale; the largest sum wins. EV-3 is (−1, 0, +1) — his recommendation for general elections — and EV-5 is (−2 … +2) for expert committees. Mechanically Score voting with a negative pole; the −1 lets a voter vote against, which he argues is worth real turnout. Approval is EV-2. STAR is not EV: its runoff re-imposes a majoritarian check on the sum, which is exactly the correction Hillinger says is unneeded. → cardinal utility; runnable: Hillinger's own example
• Context-dependent vs. independent scale — Hillinger's second axis, alongside ordinal/cardinal. A scale is context dependent when its values depend on which other objects are being measured. A ranking is: the distance between two candidates is measured in intervening candidates, so it shifts when a third party enters or leaves though nobody's opinion changed. On an independent scale a candidate's value depends on that candidate alone, so IIA holds automatically. The cleanest available answer to "why does adding a candidate change the result between two others?" → cardinal utility
• Trichotomous / multichotomous preferences — Brams & Fishburn's K, the number of indifference classes a voter actually has: K = 2 dichotomous (an Approval ballot), K = 3 trichotomous, K ≥ 4 multichotomous. It matters because theory usually assumes strict complete rankings, and that assumption decays fast: if a random pair is strictly ordered with probability 0.8, the chance of a strict order over 3 candidates is 0.8³ ≈ 0.51, and over 6 it is 0.8¹⁵ ≈ 0.035. On a rated ballot a voter may report a strict order but is not forced to. → cardinal utility; weak ranks
• Voting pathology — Hillinger's preferred term for the "paradoxes of voting": they are defects of ballots that restrict what a voter may say, not logical curiosities of collective choice. Useful framing even if you don't buy his whole argument, since it puts the ballot format rather than the counting rule at the centre. → cardinal utility; paradoxes, worked
• Judgement aggregation — a cousin of voting where agents vote yes/no on several logically linked propositions (not on candidates), and the collective verdict is required to stay logically consistent. The question is when that's even possible. → doctrinal paradox, next. Watch the collision: Hillinger's "voting as the aggregation of judgments" (2004) is a different, looser use — he means evaluations on a measured scale, not yes/no verdicts on logically linked propositions, and none of the doctrinal-paradox machinery applies to it. → cardinal utility
• Bayesian incentive compatibility (BIC) — honesty is a best response when everyone else is honest, in expectation over a prior everyone shares: truth-telling is a Bayes–Nash equilibrium rather than a dominant strategy. Strictly weaker than strategy-proofness, and the weakening is the point — G–S no longer applies, so incentive-compatible rules worth having become possible. What it costs: a published poll destroys the shared symmetric prior it is stated over, which is where most real strategic voting comes from. → ordinal vs. cardinal as mechanism design
• (A,B)-scoring rule — Myerson's (2002) three-candidate family: each voter hands in a permutation of (1, A, 0) or (1, B, 0), with 0 ≤ A ≤ B ≤ 1 — one dial, what your second choice is worth. Its corners are the familiar rules: (0,0) Plurality, (½,½) Borda, (1,1) negative voting, and (0,1) Approval — which is the one corner a ranking cannot fill in, because there the voter picks. → ordinal vs. cardinal as mechanism design; runnable: one dial, three winners
• Negative voting (anti-plurality) — the (1,1) corner of the family above: when your second choice scores exactly as much as your first, the only thing your ballot still says is who you left out. Effectively one vote against somebody; the winner is whoever is ranked last least often. → ordinal vs. cardinal as mechanism design
• First-best vs. second-best rule — the welfare-maximizing rule assuming honesty (first-best) versus the best rule that also survives the incentive constraint (second-best). The gap between them is the price of strategy; the gap between second-best and the best ordinal rule is the price of the ballot format. Kim (2017) reports the second gap as much the larger — the ballot format costs more than strategy does. → ordinal vs. cardinal as mechanism design
• Neutral environment — alternatives are symmetric ex ante: before any ballot is cast, no candidate is likelier than another to be a given voter's favorite. A modelling assumption, not a description of an election — frontrunners, incumbents and polls all violate it — and it is load-bearing wherever it appears. → ordinal vs. cardinal as mechanism design
• Doctrinal paradox (discursive dilemma) — the judgement-aggregation analogue of a Condorcet cycle: taking a proposition-by-proposition majority can yield a collectively inconsistent verdict even when every individual voter is perfectly consistent. Textbook case: a court where a majority affirms premise P, a majority affirms premise Q, yet a majority rejects the conclusion (P∧Q) those premises logically force. Same lesson as the ranked cycle — aggregation can manufacture an incoherence that none of the voters hold.

Civic / adoption

• Equal Vote Coalition — the organization that developed and advocates STAR Voting.
• BetterVoting.com — site to try a STAR ballot and run your own elections (help & FAQ: docs.bettervoting.com). The visual result it shows is one of two reports of an election in this repo — the other is the LH engine's text report; how they relate is BetterVoting and the LH engine.
• Credentialing — confirming, before a ballot is issued, that a voter is who they say they are, is eligible, and votes only once. The data points are ordinary — name, date of birth, address, email, a signature, or a password — and the method scales with the stakes: photo ID in person; signature matching or a mailed address-confirmation code by post; a chain-of-registration link for remote voting; a check against the public voter-registration roll. Three things worth keeping straight:
• It's what produces the quorum denominator. eligible_voters is an external number in this engine precisely because it comes from the roll, not from the ballots — no credentialing, no honest turnout figure. → Quorum
• It is not about vote weight. Both senses of "one person, one vote" argue over whether ballots weigh the same; credentialing settles how many there are. Each quietly assumes the other is handled.
• The credential must separate from the ballot. Credentialing links a person to the act of voting, and the design rule is that the link stops there: carry it through to the ballot and you have undone the secret ballot and handed a coercer exactly the proof receipt-freeness forbids (both below). The "who has voted" list credentialing produces is also half of the delta-analysis leak — the other half is a live tally.
• Our own demo polls have none of it. An open BetterVoting API poll keys a ballot to a temp_id cookie the caller sets freely, so "one voter" is an honour system — fine for a teaching demo, not for an election. → BV API notes → the procedure itself, with the in-person / by-mail / remote variants: BetterVoting — paper ballots & credentialing (Equal-Vote-adjacent, but this is its own factual procedure doc)
• Ballot marking device (BMD) — a machine the voter uses to mark choices on screen, which then prints a paper ballot for scanning. The paper is the legal record, so the security argument rests on voters actually checking the printout — and research consistently finds most don't, or don't catch deliberately introduced errors. → voter verification
• Summary ballot — a BMD printout listing only the voter's selections (contest → choice) rather than reproducing the full ballot face. Compact and OCR-friendly, but it's what the voter must read to verify, so its legibility is a real design variable — and a score ballot puts far more on it than choose-one does. → voter verification
• Voter verifiability — whether a voter can confirm their ballot records what they intended, before casting. Distinct from auditability (whether observers can confirm the count — see summability): the first protects the individual ballot, the second protects the tally. A method can be strong on one and weak on the other. → STAR's honest limits
• Secret ballot (Australian ballot) — voting in private on a uniform, officially printed ballot, so nobody can tell how you voted. Spread through the 1800s (Australia 1856; most US states by 1892) for one specific reason: when ballots were spoken aloud or printed by parties, employers, landlords and political machines could verify compliance and pay or punish accordingly. Ballot secrecy isn't decorum — it's the mechanism that makes vote-buying and coercion unenforceable. → counting under encryption
• Delta analysis (live-tally leak) — de-anonymising a ballot by watching a running tally change. If one ballot lands in a quiet window, the movement in the totals is that ballot. Pair a live tally with a list of who has voted — which admins normally have, to send reminders — and the ballot gets a name attached. No screen ever displays "this voter chose X"; it falls out of the arithmetic, so it can't be fixed by hiding a field. Score ballots leak far more per delta than choose-one: a plurality delta reveals one bit (which candidate), while a 0–5 delta reveals the voter's rating of every candidate — their whole ballot. If ballot secrecy matters, keep the tally hidden until the election closes. → preliminary results
• Receipt-freeness — the property that a voter cannot prove to anyone else how they voted, even if they want to. This is why verifiable voting is hard: hand a voter a receipt showing their choices and you have rebuilt the vote-buying market the secret ballot abolished. End-to-end verifiable systems thread the needle by letting you confirm your ballot was counted without revealing what it said. Coercion resistance is the stronger form — safe even if the coercer is standing over you. The direct tension with voter verifiability above is the central design problem of every cryptographic voting scheme. → counting under encryption

Worth knowing when you run an election online: most web voting platforms store the voter-to-ballot link and hide it by access control rather than discarding it — so secrecy is a policy promise, not a structural one, and features like an emailed "view your ballot" receipt hand the voter exactly the proof that receipt-freeness forbids. That's a reasonable trade for a club or board vote, where it buys real usability; it is a genuine risk wherever someone has power over the voter (an employer, a union, an HOA). Ask any platform the direct question — is the link discarded, or merely hidden? — and prefer the ones that answer it in public. BetterVoting, to its credit, documents this openly. - Risk-limiting audit (RLA) — a hand count of a random sample of the paper ballots, sized so that if the reported outcome is wrong the audit escalates to a full recount with at least a pre-set probability. The name is exact: it limits the risk of certifying a wrong outcome, and does not try to find every mis-read ballot. Sample size tracks the margin — a decisive result needs surprisingly few ballots, a close one needs many, and as the margin goes to zero the sample goes to everything. Two prerequisites carry the whole method: the paper must be the record (the audit compares hand-read ballots against what the machines reported), and a ballot manifest must say where every ballot is — which is what makes chain of custody below load-bearing rather than clerical. Per-method state of play: plurality and majority contests are routine; RCV-IRV needs specialized assertion machinery (RAIRE, Blom, Stuckey & Teague) and complete central CVRs; and STAR is in scope by name — the social choice functions Stark's assertion-based SHANGRLA framework covers are enumerated in its own abstract as majority, super-majority, plurality, multi-winner plurality, IRV, Borda, approval, and STAR-Voting. So "can you rigorously audit a STAR election?" has a published answer rather than a promise. See central tabulation and summability above for why a summable method makes the cheap version — recompute the precinct table, add it up — available at all. - Optical mark recognition (OMR) — reading hand-marked paper ballots with a scanner and software instead of by eye. What it doesn't need is the teaching point: OMR runs on ordinary office scanners, so a jurisdiction can machine-count hand-marked paper without a vendor-certified voting system, and the paper stays the record for an RLA. The costs are small-city sized and public: for Eugene, OR (pop. ~75k) Gravic quoted $21,530 for Remark OMR, of which $19,030 is fixed — $4,030 for four licences plus a $15,000 custom utility to turn scanned marks into STAR and choose-one results — the balance being optional ballot design the city could instead do itself at no cost. Remark has already tabulated STAR ballots in a full-scale Democratic Party of Oregon pilot. One label to correct: BetterVoting's page calls Remark "open sourced software"; it isn't — it's a commercial Gravic product, priced per licence in that very quote. The claim that survives is the one that matters: no proprietary hardware, so commodity scanners suffice. Filed 2026-08-08 as #1496. → BetterVoting — paper ballots; our own return path is still a human transcribing marks, by design: Run a paper-ballot STAR demo - Chain of custody — the documented, unbroken record of who held the ballots and when: sealed containers, signed transfer logs, two-person handling, a reconciled count at every hand-off. It is what makes the paper trustworthy enough for an RLA to mean anything — auditing ballots that could have been swapped audits nothing. Two notes for this library: a summable method lets each precinct publish its own subtotal, so the ballots needn't travel to one facility — a shorter custody chain, not merely a faster count, which is the half of the central tabulation cost (above) that isn't about speed; and BetterVoting's integrity guidance covers the human half rather than the paperwork — at least two people to scrutinize, observe and document every step, a hand count staffed with a caller, a tallier and two observers, and a representative from each candidate in the room, on the principle that no election should rest on trust alone. - LH engine (starvote) — Larry Hastings' STAR tabulator (this repo's fork), which prints the full text audit report and the generated _tabulated.txt copies; handles the score methods (STAR, Bloc / Proportional STAR, Approval). Ranked ballots go to a separate vendored RCV-IRV engine (pyrankvote). Upstream: GitHub · PyPI. See BetterVoting and the LH engine.

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See also: 00_START_HERE.md (teaching sequence) · Why_STAR_Voting.md (presentation + debate prep) · CURRICULUM.md (lesson outline).