collective transitivity fails (social choice)
Theorem.collective transitivity fails (social choice) — 6 of 216 three-voter profiles cycle A>B>C>A under majority rule (Condorcet).
Proof.of all 216 three-voter profiles over three options, 6 are majority-rule cycles (A>B>C>A) though every individual ranking is transitive — individual rationality does not lift to the group (Condorcet/Arrow cited).
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/9/1/index.ts#discoveredTheoremsWaveNineteen
1 · Classification
finite-complete — computed witness within a cited frame (the unbounded form leans on the cited literature)
2 · Provenance
Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.
Acknowledgment
"collective transitivity fails (social choice)" is a re-derivation, acknowledged to documented mathematics — the original proof is the prior art this re-derivation acknowledges; not new to humanity — the contribution is the reproducible computation discoveredTheoremsWaveNineteen.
- Prior art
- documented mathematics — the original proof is the prior art this re-derivation acknowledges
- Novelty
- not new to humanity — a re-derivation (humanityNovel = false)
- Contribution
- a reproducible computation (discoveredTheoremsWaveNineteen @ src/9/1) that re-derives the result at zero tokens — the contribution is the verifiable recomputation, NOT the theorem
3 · Reproducibility
Recompute from source: npm run theorems:verify recomputes discoveredTheoremsWaveNineteen (src/9/1/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.