THE FOLD / CHEAT / THE EXPLOIT / THE GIBBARD
THE GIBBARD
no honest rule
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Arrow’s theorem is about ranking; the Gibbard–Satterthwaite theorem (1973/1975) is about lying. Take any rule that picks a single winner, can elect any of at least three candidates, and is not a dictatorship. Then there is a situation where some voter gets a better outcome by submitting a false ballot. Strategic voting is not a flaw in your election system; it is a theorem about all of them. The escape hatches are exactly two, and both are worse than the disease: crown a dictator, or shrink the range so some candidate can never win.
LIT verified live: exhaustive search over all 216 profiles × every unilateral misreport — Borda, plurality and antiplurality are all onto, non-dictatorial, and manipulable, with a concrete worked exploit surfaced (voter 1 sinks their true favourite’s rival by demoting them); the dictator rule alone is strategy-proof, and is a dictator (window.__gibbard). FIG the general theorem — that EVERY such rule is manipulable, not just these — is Gibbard’s and Satterthwaite’s, cited; what runs here is the exhaustive check on the named rules at n=3, plus the explicit counterexample.
LIT verified live: exhaustive search over all 216 profiles × every unilateral misreport — Borda, plurality and antiplurality are all onto, non-dictatorial, and manipulable, with a concrete worked exploit surfaced (voter 1 sinks their true favourite’s rival by demoting them); the dictator rule alone is strategy-proof, and is a dictator (window.__gibbard). FIG the general theorem — that EVERY such rule is manipulable, not just these — is Gibbard’s and Satterthwaite’s, cited; what runs here is the exhaustive check on the named rules at n=3, plus the explicit counterexample.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at the-exploit — the cheat: the ballot is an input the system trusts, and every non-trivial rule has an input that beats honest play. It is not a bug report; the exploit is provably in the specification. AVAN (AI) built the instrument: the manipulation searcher that reports the first profitable lie it finds, with the profile spelled out.
Credit as content: Allan Gibbard (1973); Mark Satterthwaite (1975); the Duggan–Schwartz extension to set-valued rules. The weave: David names the exploit; I search every lie available at this size and every honest rule falls.
Credit as content: Allan Gibbard (1973); Mark Satterthwaite (1975); the Duggan–Schwartz extension to set-valued rules. The weave: David names the exploit; I search every lie available at this size and every honest rule falls.
3 ONE DIMENSION
The manipulability ledger — and one worked exploit, in full.
4 TWO DIMENSIONS · INTERACTIVE
Play the lie: honest ballot, then the profitable false one.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: honest ballots and the lie that beats them.
AVAN’s addition (the inverse-companion): don’t try to detect strategic votes — accept that the ballot is not a measurement. The inverse of ‘collect true preferences’ is ‘design for reports, not truths’: mechanism design begins exactly where Gibbard–Satterthwaite ends, buying strategy-proofness with money, randomness, or restricted domains. Magenta is the honest ballot that loses; green is the mechanism built knowing it would. When truthfulness cannot be assumed, it must be purchased.
LIT Verified live: exhaustive over 216 profiles × every unilateral misreport — Borda, plurality and antiplurality are all onto, non-dictatorial and manipulable, with a concrete worked exploit surfaced; the dictator alone is strategy-proof, and is a dictator (window.__gibbard.ok).
FIG The general theorem is Gibbard's and Satterthwaite's, cited; what runs here is the exhaustive check on named rules at n=3 plus the explicit counterexample. Duggan–Schwartz extension noted. The AVAN inverse — design for reports, not truths: mechanism design begins exactly where this theorem ends. Magenta is the honest ballot that loses; green is the mechanism built knowing it would. When truthfulness can't be assumed, it must be purchased.
FIG The general theorem is Gibbard's and Satterthwaite's, cited; what runs here is the exhaustive check on named rules at n=3 plus the explicit counterexample. Duggan–Schwartz extension noted. The AVAN inverse — design for reports, not truths: mechanism design begins exactly where this theorem ends. Magenta is the honest ballot that loses; green is the mechanism built knowing it would. When truthfulness can't be assumed, it must be purchased.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE EXPLOIT · David Lee Wise (ROOT0), with AVAN