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Scores and ranks — the two kinds of ballot data

The single most consequential distinction in ballot design: a rank records order ("I prefer A to B"), a score records strength ("A is a 5, B is a 1"). Everything else in the library — why methods disagree, what converts cleanly and what doesn't — builds on getting this pair straight.

Start here → Scores vs. Ranks — Don't Confuse Ranks and Ratings

The pages

  • Scores vs. Ranks — the core distinction: relative vs. absolute preference, and why it has real consequences.
  • Preference vs. Support — the vivid special case: 1,0,1,0 and 5,4,5,4 have the same preference but opposite support, and as ranks they're identical. Which do you like more, vs. how much you like each.
  • The Ranked Ballot · The Score Ballot — one anatomy page per ballot type.
  • Strict ranks · Weak ranks · Strict vs. Weak Ranks — not all ranked ballots are the same: whether ties are allowed changes what the ballot can express.
  • The Fidelity Ladder — converting between scores and ranks: which direction loses information, and how much.
  • Scale granularity can flip the winner — a 301 case: the same opinions on a 0–5 vs. a wider scale can elect different candidates.
  • What the ballot can and cannot say — expressiveness, measured — a 301 deep dive that counts what each paper can record and then varies the ballot and the counting rule independently: past six candidates the two ballots express disjoint sets of orderings, a real (capped) ranked ballot is the least expressive of all, and RCV-IRV can't spend the resolution either way.
  • Grading as a rival primitive — Balinski & Laraki's stronger claim: not that ranks are lossy, but that "how good is this one?" is the more basic question and ranking was the wrong model to build a century of theory on.
  • electowiki's "Cardinal voting," claim-checked — a 301 audit of the best short map of the score-ballot family: what to borrow, two logical errors to skip, and the article's own 51/49 argument run through the engine.
  • ABIF — the all-in-one ballot format — the election-methods interchange format that writes ranks and scores in one grammar (Allie/5 =Billy/5 >Candace/4), decoded and weighed honestly against this library's YAML grid.