01_STAR/03_Criteria — what STAR guarantees, and where it doesn't¶
The formal side of STAR, always as runnable elections rather than assertions: each set below isolates one criterion or one tie behavior, small enough to check by hand. The prose companions live in 01_Learn/properties_and_limits/ — this folder is where those claims get numbers.
Levels follow the curriculum: 🟢 101 · 🟡 201 · 🔴 301.
Criteria¶
| Set | Level | What it shows |
|---|---|---|
| The Majority Criterion | 🔴 301 | Two 5-voter elections isolating STAR's Majority-Criterion behavior — and the Relaxed Majority Criterion ("needs two rivals, not one"). |
| Favorite betrayal | 🔴 301 | STAR is not formally FBC-compliant, and the leak lives in the runoff: the score you give your favorite can keep your compromise out of the top two. Rare, constructed, and conceded honestly. |
| IIA & the cycle spoiler | 🔴 301 | Independence of Irrelevant Alternatives, shown mechanically: in a genuine Condorcet cycle a candidate who cannot win still changes who does — with perfectly sincere ballots. |
| Tactical maximization | 🟡 201 | The hedge that looks generous: four voters raise a rival to 5 without lowering anyone, register Equal Support in the runoff, and lose the election they'd otherwise have won. |
| Equal and opposite | 🟡 201 | The Equal Vote Coalition's Test of Balance: two voters with exact-opposite ballots cancel completely, so the winner never moves. What an equally weighted vote means. |
| None of the Above | 🔴 301 | A protest electorate where NOTA tops the scores and wins the runoff — STAR counts a formal rejection like any other candidate. |
Ties & tie-breaking¶
STAR resolves ties with a deterministic cascade (pairwise → five-star → lot). These two sets walk it from the happy path to the case where it runs out.
| Set | Level | What it shows |
|---|---|---|
| The tie-break ladder | 🟡 201 | The happy path: elections that tie but never reach the lot, because the deterministic rungs settle it. The live companion to the tie-breaking doc. |
| The dead rung | 🔴 301 | When no tied candidate holds a 5, the five-star rung reads 0–0, the cascade has nothing left, and the lot decides. |
The exhaustive sweep behind these two — eight ballots engineered to tie at every locus, including the fully-flat degenerate shapes — is kept off the path in 09_Parked.
Related: the honest-limits prose → STAR's honest limits · practice these on paper → 05_Practice · the cross-method criterion gallery → Voting 401.