THE FOLD / LOOT / THE MINT / THE ARROW
THE ARROW
no fair rule
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Write down what you want from a voting rule. It should never rank X above Y when every voter prefers Y (unanimity). Whether society ranks X above Y should depend only on how voters rank X against Y, not on some irrelevant third candidate (IIA). And no single voter should dictate the outcome. Kenneth Arrow proved in 1951 that with three or more candidates, nothing satisfies all three. Not Borda, not plurality, not pairwise majority — the only rule that survives unanimity and IIA is a dictatorship, which is a solution the way deleting the database solves the query.
LIT verified live: all 216 profiles (3 voters × 3 candidates) tested exhaustively against every axiom — Borda passes unanimity and fails IIA; plurality fails both; pairwise majority passes unanimity and fails IIA; the dictator passes everything and is a dictator; and every one of the 16 non-degenerate integer scoring rules (weights 0–3) fails IIA (window.__arrow). FIG the general theorem — that NO conceivable rule escapes, not merely these — is Arrow’s, cited; our exhaustive check covers the named rule families and the full scoring-rule class at n=3.
LIT verified live: all 216 profiles (3 voters × 3 candidates) tested exhaustively against every axiom — Borda passes unanimity and fails IIA; plurality fails both; pairwise majority passes unanimity and fails IIA; the dictator passes everything and is a dictator; and every one of the 16 non-degenerate integer scoring rules (weights 0–3) fails IIA (window.__arrow). FIG the general theorem — that NO conceivable rule escapes, not merely these — is Arrow’s, cited; our exhaustive check covers the named rule families and the full scoring-rule class at n=3.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at the-mint — the loot: this is where the collective preference is supposed to be COINED from individual ones, and Arrow proved the mint cannot run honestly at scale — every aggregation either counterfeits or crowns a king. AVAN (AI) built the instrument: the exhaustive profile enumerator and the three axiom testers.
Credit as content: Kenneth Arrow (1951, Social Choice and Individual Values); Condorcet’s eighteenth-century paradox that anticipated it; Amartya Sen’s later reframings. The weave: David names the mint; I run every ballot box that exists at this size and none of them comes out clean.
Credit as content: Kenneth Arrow (1951, Social Choice and Individual Values); Condorcet’s eighteenth-century paradox that anticipated it; Amartya Sen’s later reframings. The weave: David names the mint; I run every ballot box that exists at this size and none of them comes out clean.
3 ONE DIMENSION
The axiom ledger — every rule fails a column, except the dictator.
4 TWO DIMENSIONS · INTERACTIVE
Step through rules; the failing axiom lights up red.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the Condorcet cycle turning — the paradox underneath.
AVAN’s addition (the inverse-companion): don’t hunt for the fair rule — ask which axiom you are willing to sell. The inverse of ‘impossibility’ is ‘a price list’: drop IIA and you may keep Borda; restrict preferences to single-peaked and majority rule works again (Black’s theorem); insist on all three and the only survivor wears a crown. Magenta is the axiom you must give up; green is the rule you get to keep. Impossibility theorems are not walls — they are invoices.
LIT Verified live: all 216 profiles (3 voters × 3 candidates) tested exhaustively — Borda passes unanimity, fails IIA; plurality fails both; pairwise majority fails IIA; the dictator passes all and is a dictator; and all 16 non-degenerate integer scoring rules fail IIA (window.__arrow.ok).
FIG The general theorem — that NO conceivable rule escapes — is Arrow's, cited; our exhaustive check covers the named families and the full scoring class at n=3. Condorcet's paradox and Sen's reframings credited. The AVAN inverse — ask which axiom you'll sell: drop IIA and keep Borda; restrict to single-peaked and majority works (Black). Impossibility theorems are invoices, not walls.
FIG The general theorem — that NO conceivable rule escapes — is Arrow's, cited; our exhaustive check covers the named families and the full scoring class at n=3. Condorcet's paradox and Sen's reframings credited. The AVAN inverse — ask which axiom you'll sell: drop IIA and keep Borda; restrict to single-peaked and majority works (Black). Impossibility theorems are invoices, not walls.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE MINT · David Lee Wise (ROOT0), with AVAN