method_comparisons — same ballots, different methods¶
The library's crown jewels: teaching sets where the contrast between methods is the lesson. Each set keeps its matched files together — splitting them into per-method folders would destroy the pedagogy.
| Set | The lesson |
|---|---|
| The Black Curtain — one electorate, four "identical" landslides | four elections, identical first-choice "landslides" — Approval, Score, STAR, and RCV-IRV reveal (or hide) four very different electorates |
| Center squeeze — RCV-IRV eliminates the consensus, STAR elects it | the same 1-D electorate: RCV-IRV eliminates the consensus center; STAR elects it |
| The crowded field — one electorate, three ballot sizes | 65 voters who never change their minds, and a field that grows 3 → 5 → 7. Diego beats every rival head-to-head at all three rungs; at three candidates all six methods elect him, at seven four different people win. Rung 2 is vote-splitting (his first choices collapse 34 → 9 with nobody persuaded); rung 3 is the 0–5 ballot running out of rungs — he reaches STAR's runoff and still loses, because 25 of 65 voters can no longer tell him from his neighbour. Every ballot derived from the candidates' positions, nothing settled by a tie-break |
| Hillinger's evaluative voting — the paper, made runnable | his "mirror pathology" of IRV, run: 30 voters, three methods, three different winners — plus what "cardinal" guarantees under rescaling |
| One dial, three winners — Kim's (A,B)-scoring family | Myerson's family indexed by what your second choice is worth: one 36-voter electorate with fixed rankings elects Cocoa at A=0 (plurality), Almond at A=½ (Borda — which Kim proves is the best an ordinal ballot can do), Berry at A=1 (negative voting). Then the two Approval files hand the dial to the voters: identical rankings, different second-choice intensities, different winners — the half a ranking cannot record |
| Preference vs. Support, as a live election | BV2225/2226 live: a matched pair with byte-identical rankings — only the wings' score for the centrist changes (1→4). RCV-IRV and Ranked Robin return the same winners in both (they read only order); STAR is the lone method that moves — because support is the one thing that changed, and only a score ballot carries it |
| "Should I rank my favorite second?" — the plain RCV-IRV betrayal incentive | the simplest runnable form of favorite betrayal: 12 Left voters vote honestly (Left>Center>Right) and RCV-IRV elects their worst (Right); 2 of them ranking Center first flips it to Center; STAR & Ranked Robin elect Center from the honest ballots — no betrayal needed |
| The Dark Horse — Borda elects a nobody with zero support | Quinn's strategic-pathology: under Borda, factions bury rivals behind the harmless D, and if all do, D wins with zero honest support (a prisoner's dilemma). STAR & Ranked Robin can't be dark-horsed — a score lets you oppose without propping anyone up |
| The Chicken / Burr dilemma — allies forced to play chicken | under Approval, two allies who must beat a third tie 60–60 and face a slippery slope of bullet-voting that can elect the majority-opposed candidate; STAR's runoff makes it non-slippery — support both allies honestly, and the honest winner prevails |
| FairVote's official position on STAR, claim-checked | BV2229–2232 live: FairVote's 2018 white paper against STAR, checked evenhandedly — concede the real criterion failures (LNH, majority, mutual-majority) + reframe; run its French-2017 and Washington-2010 burial examples (honest STAR elects the centrist both times; coordinated burial can squeeze it — but IRV squeezes centers sincerely); flag the overclaims (RCV-elects-Condorcet "in practice" was already false in Burlington/Alaska) |
| FairVote's Condorcet article, counted | the claim-check demos: FairVote's own 40/15/40 hypothetical (majorities elect the moderate; IRV squeezes them out) and a shifted electorate where a pole candidate IS the Condorcet winner |
| The Equal Vote single-winner scorecard, checked for fairness | our own side's Plurality/RCV-IRV/STAR scorecard, reproduced as a table and assessed row by row — directionally sound, but the absolute "NO"s for STAR overclaim, and the numeric rows lean on a STAR-affiliated paper (cite the ordering, not the decimals) |
| Even Condorcet methods can be buried — Alaska 2022 | rb-j's burial attack on the real Alaska numbers, verified: 20 Peltola voters rank the Condorcet winner Begich last, manufacturing a cycle. MinMax/Schulze/Ranked Pairs shrug it off (Begich still wins); Condorcet-Hare/TTR falls for it (Peltola). The even-handed point: no method is strategy-proof — Condorcet included — and the completion method is the whole ballgame |
| Does STAR collapse to IRV under strategic "5-1-0" voting? | rb-j's r/EndFPTP challenge, counted: coordinated 5-1-0 min-max voting with a thin moderate base does squeeze the center like IRV (conceded) — but the "1s" carry real weight, so with a real moderate base 5-1-0 STAR still elects the Condorcet winner where IRV doesn't. STAR-degraded-by-strategy ≠ IRV |
| Proportional on both sides — what the ballot alone changes | one electorate on two papers, both counted proportionally: the 0–5 ballot seats Ben, every proportional approval rule seats Ella. The ballot alone moves a seat, because approval cannot see a floor |
| STV vs STAR-PR — ranks and transfers vs scores and reweighting | one 100-voter, 3-seat electorate counted five ways: STV and all three STAR-PR methods elect the identical slate (2 progressive + 1 business), and only majoritarian Bloc STAR differs — sweeping all three for the 58% majority. The head-to-head behind curriculum rungs 301.1 and 301.2, plus the honest coda: no settled metric ranks proportional methods against each other (Quinn shelved AVEC unfinished), so the defensible comparisons are mechanical — summability, expressiveness, auditability — never a satisfaction score |
| Edelman's "Myth of the Condorcet Winner," counted | the steelman anti-Condorcet argument (BV2173 live): the 81-voter cancellation profile — majoritarian counts (RR, IRV, STAR runoff) elect Ada, positional counts (Borda, score sum, Choose-One) elect Ben — plus the all-tied "Condorcet component" alone |
| Brams' grading paradox, counted | the steelman Approval-over-STAR argument (Brams & Potthoff 2015), three cases: the slide example (grade leader Adams vs Condorcet winner Baker — STAR's runoff catches it), Example 6 (Score, median, and head-to-head crown THREE different winners; STAR sides with head-to-head), and the two-candidate strong paradox; plus the "Approval prevents this" theorem shown to hinge on where each voter draws the 0/1 line |
| Approval and the majority criterion — Hamlin & Hua's own example | the Approval camp's academic case (Hamlin & Hua 2023, Constitutional Political Economy — the companion article to the STAR paper in the same issue), §4 claim-checked on its own worked example: 60% rank A first, B is approved on every ballot and wins. Five readings of one electorate — A is also the Condorcet winner; a runoff can't rescue it (60 of 100 voters express no preference); and the paper's own "the utility gap would be tiny" defence, written as a 0–5 ballot, is right (380 v 370) and still elects A. Compression doesn't just lose the 2% gap, it reports a 40-point landslide the other way |
| The majority illusion, counted — CES's own example, run | the Center for Election Science prints a profile to argue the Condorcet winner isn't always best (Alice beats everyone head-to-head; Brian averages 4.2 to her 2.6). Two things the article doesn't say: Alice holds an outright 51.2% absolute majority, so the example indicts the majority criterion, not Condorcet — and STAR elects her, 21–20 in the runoff, while Score and Approval elect Brian. The profile sits exactly on the Relaxed-Majority-Criterion line; change one score (Colin 0 → 3) and Alice loses, with STAR the lone method that drops her. Section-by-section claim-check |
| "Single-elimination RCV," claim-checked | a conservative think-tank paper (Cardinal Institute, WV) proposes streamlining RCV to "rank two, then jump straight to the top two" — which is the Supplementary Vote, used for the Mayor of London until the Elections Act 2022 repealed it. Run on the paper's own five-way example, the streamlining worsens the exact flaw the paper concedes: its winner is always a top-two first-choice finisher, so a compromise candidate who'd win the full count is ineligible by construction (Cora wins full RCV-IRV from third; the paper's model can't elect her). Also: the 2-mark ballot causes exhaustion rather than curing it (16% vs 0% on identical ballots), and "essentially the same in all forms of RCV" is false — Ranked Robin discards nothing. Concedes what the paper gets right, including the summability argument it under-sells |
| rangevoting.org's anti-IRV examples, counted | the claim-check that cuts against our own side: Warren Smith's score-voting page calls IRV an "idiot voting system," so the polemic is unusable — but its two constructed profiles reproduce exactly. Ossipoff's 303 is sharper than its usual filing: the Condorcet winner C holds the largest first-choice bloc (100 of 303), beats every rival ~2:1, and is cut in round 3 by one vote — so the "nobody wanted them first" defence is unavailable. Brams's 21-ballot profile is hand-checkable in a minute (G beats B 14–7 and goes out second). Ranked Robin elects the Condorcet winner in both on the identical ballots — nothing asked of the voter. Includes the refusal: Smith's "IRV ignores ~100% of the information, Approval ignores none" fails on its own terms, since the same accounting certifies plurality as maximally efficient |
| Participation / no-show — one electorate, told twice | BV2174/75 live: 8 voters decide whether to show up; Choose-One and STAR reward their sincere ballots, RCV-IRV hands them their LAST choice instead of their second — the no-show paradox across three races per election |
| The Post-it RCV example — Equal Vote's whiteboard demo, live | BV2176/77/78 live: the video's 20 voters — RCV-IRV elects Purple as counted on the whiteboard, but Blue wins the 10–9 head-to-head STAR actually holds; all SEVEN BV methods on the same ballots elect four different candidates; a two-ballot flip makes the video's round-2 hypothetical real; plus the fair-and-balanced claim-check lesson (invented scores, threshold traps, the RR ladder divergence live) |
| Monotonicity — when more support makes a candidate lose | before/after pairs where MORE support makes a candidate LOSE under IRV — and doesn't under STAR |
| Cycle resolution, counted — where the Condorcet family stops agreeing | the two profiles behind the cycle-resolution page, runnable: one where Copeland ties three trails and all four refined rules rescue Alder, and one where Schulze elects Ana while Ranked Pairs elects Bruno on identical ballots (Split Cycle returns both). "Condorcet method" is a family, and in a cycle the family splits |
| Tournament solutions, counted — five defensible winners from three ballots | the C1 sibling of the cycle-resolution exhibit: Brandt–Brill–Harrenstein's own Figures 3.1 and 3.3 (Handbook of Computational Social Choice, ch. 3) turned back into ballots. On three rotated ballots the top cycle returns everyone, the uncovered/Banks/bipartisan sets return {A,B,D}, Copeland returns {A,B} and Slater/Markov return {A} — five published answers, one election. Ranked Robin is Copeland, so it lands on the tie and breaks it by margin, electing B where Slater and Markov elect A: the moment RR reaches for margins it has left C1. The five-candidate companion shows Copeland electing D alone where composition-consistency demands all five — the theory name for RR's teaming weakness |
| The minimal tilted cycle — five voters, and already the methods disagree | the smallest lopsided majority cycle that can exist (4–1 / 3–2 / 3–2), with the minimality proved by hand and by brute force: 3 voters force a symmetric cycle, 4 voters admit none at all, 5 voters leave exactly one tilted shape. On it, Copeland/Ranked Robin still ties all three while the whole maximin family drops Ben — the smallest possible proof that Ranked Robin is not in that family |
| Manipulability — the textbook example is an attack on our method | Zwicker's P₃ and Definition 2.3, run: a single voter reverses their ballot and overturns the Copeland winner. Since Ranked Robin is Copeland, the canonical textbook illustration of strategic manipulation is a manipulation of a method this library advocates — so the page leads with that, adds a milder three-swap compromise that works just as well (52 of 119 ballots do), and then shows STAR falling to burial by two voters on the same ballots. Each method fails to the strategy it is known to be exposed to. Plurality survives one liar and folds to two; Borda is manipulable but provably not by reversal; IRV's baseline is a coin flip and is reported as indeterminate |
| Margins matter — one electorate, four different answers | Zwicker's P₂ (Handbook of Computational Social Choice, ch. 2), shrunk from 304 ballots to 12 with the symmetric Borda scores preserved exactly (0 / +2 / −2). Copeland throws the margins away and ties all three; Borda is the same tournament weighted by those margins and picks Berry; Plurality picks Almond, RCV-IRV eliminates the Borda winner first and picks Cocoa. Also shows that the LH engine's Ranked Robin "Margin" tiebreak column is the symmetric Borda score — and discloses that STAR's answer here is not robust to the rank→score spacing |
| Reinforcement paradox — both halves pick Ada, the whole picks Cara | Brandt–Dong–Peters' Theorem 2 profile as two towns: Ada wins South outright and ties North, but the merged electorate elects Cara. Additive rules (Score, Approval, Plurality) keep the consistency promise by construction; STAR and Ranked Robin break it — and at ≥ 8 voters no Condorcet method can avoid it |
| The valuable Condorcet loser — what a majority runoff costs, priced by theorem | runnable companion to Ebadian–Latifian–Shah (AAMAS 2023): in the unit-sum model, adding a majority runoff makes approval voting's distortion worse (Θ(m) → Θ(m²)), because a runoff structurally blocks the valuable Condorcet loser. Their pivotal profile on nine ballots: Amy holds nearly double anyone's score total (20 vs 11) and loses every head-to-head 4:5 — Score elects her, STAR's runoff rejects her (welfare ratio 1.8). The mirror image of the metric model, where the same runoff is the ≤ 3× insurance — the model decides the verdict |
| Same ranks, different utilities — the founding impossibility, on three ballots | Procaccia & Rosenschein's Proposition 1 (CIA 2006), the result that named distortion: no rule reading only rankings is ever perfect, proved at 3 voters and 2 candidates. Two files with identical rankings (A>B, B>A, A>B) and opposite welfare-optimal winners — every voter spending exactly 5 points, so the paper's unit-sum model is literally "same amount of ink." Score voting gets both right; every ranked method must answer twice the same and be wrong once; STAR prints the difference in its scoring round (B 9, A 6) and its runoff overrules it, because at two candidates STAR is majority rule. Collides productively with May's theorem |
| The weak Condorcet loser — the candidate who beats nobody | five voters where both STAR finalists beat nobody, so STAR must elect one: Ada is the Condorcet winner but is eliminated on score, and the Ben–Cora runoff ties 2–2, handing it to the score tiebreaker. The precise fine print on a guarantee STAR is usually credited with — it can never elect a strict Condorcet loser (a strict loser always loses the runoff), but a tie is not a loss. Ranked Robin passes cleanly (Beats: — is the marker); Approval elects the same candidate and can't even represent the problem |
| Split Cycle vs. Schulze — a spoiler nobody voted for | Holliday & Pacuit's claim (arXiv:2004.02350), run: Cascade beats Bryce 40–0 — not one voter prefers Bryce — yet Schulze elects Cascade without her and Everglade with her. Split Cycle keeps Cascade both ways. Limits stated: it needs a knotted 5-candidate cycle, and Split Cycle's escape is returning two winners |
| Reversal symmetry — a method's "best" = its "worst" | a 24-voter cycle where RCV-IRV elects A whether voters pick the best candidate or reverse every ballot to pick the worst; STAR & Ranked Robin avoid the winner=loser. A criterion IRV/plurality fail; Range-advocacy source, lean disclosed |
| Vote-Splitting / Spoiler Examples | the spoiler progression: how choose-one splits, and what each reform does about it |
| Summability demo — one example, three methods | two districts + the combined count: STAR subtotals add up, IRV's don't |
| Paradoxes & whoopses — when methods disagree 🎭 | the classics — Tennessee, Condorcet cycles, Ossipoff's centrist, Brams' many-pathologies election |
| BV_Library — real BetterVoting elections, imported and verified | real BetterVoting elections across methods (STAR, Approval, Ranked Robin, plurality), imported and verified |
| Loose comparison files — STAR-vs-IRV count simplicity | loose comparison files (e.g. STAR-vs-IRV count simplicity) |
| The divergence ledger — every STAR election re-counted | the GENERATED ledger: every curated STAR election re-counted under RCV-IRV / Ranked Robin / Approval, grouped by why they disagree (refreshed by pre-commit) |
Measured studies (simulation-backed, not case sets)¶
These pages answer a "how often?" question with a seeded, runnable simulation rather than a curated election — the numbers live with their model and caveats, and disagreement is checkable:
| Study | The question |
|---|---|
| Why more candidates make every method miss | why Condorcet efficiency falls with field size, for every method, in every electorate model. Three measured causes — the Condorcet winner's first-choice share halves, their narrowest margin thins to a third, and the fraction of a 0–5 ballot that goes tied doubles — plus which mechanism hits which method, and the crowded field as the worked election |
| How often do STAR and Approval disagree? | there is no single rate — it depends on the electorate model and on where each voter draws their approval cutoff |
| Does the qualifying round throw away the consensus winner? | in a two-stage reform (open primary → top N → good general), a Plurality primary drops the consensus winner 17.3% of the time at top-4; Approval drops it 0.4%. The method matters far more than the number of slots |
The by-method view of every file in the repo is auto-generated at the by-method index.