THE FOLD / GLITCH / RACE CONDITION / THE CONDORCET
THE CONDORCET
rational voters, an irrational majority — A>B>C>A
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
The Condorcet paradox. Even when every voter has perfectly consistent preferences, the group’s majority preference can cycle. Three voters ranking three candidates — (A>B>C), (B>C>A), (C>A>B) — produce a majority for A over B, a majority for B over C, and a majority for C over A. Round and round, with no bottom.
So there is no Condorcet winner — no candidate who beats every other head-to-head. Worse, whoever wins depends entirely on the agenda: in sequential pairwise votes, a chairman who sets the order picks the winner. The individuals are rational; the collective is not. Discovered by the Marquis de Condorcet in 1785, it is the seed of Arrow’s impossibility theorem — the proof that no ranked voting method can be fair, decisive, and cycle-free all at once.
LIT verified live: on this profile A beats B, B beats C, and C beats A (each 2–1), there is no Condorcet winner, and three different agenda orders elect three different candidates (window.__condorcet). FIG no framing; the majority cycle, the absent winner, and the agenda control are exact.
So there is no Condorcet winner — no candidate who beats every other head-to-head. Worse, whoever wins depends entirely on the agenda: in sequential pairwise votes, a chairman who sets the order picks the winner. The individuals are rational; the collective is not. Discovered by the Marquis de Condorcet in 1785, it is the seed of Arrow’s impossibility theorem — the proof that no ranked voting method can be fair, decisive, and cycle-free all at once.
LIT verified live: on this profile A beats B, B beats C, and C beats A (each 2–1), there is no Condorcet winner, and three different agenda orders elect three different candidates (window.__condorcet). FIG no framing; the majority cycle, the absent winner, and the agenda control are exact.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this in RACE CONDITION — the glitch domain of an outcome that depends on order and has no stable answer. The Condorcet cycle is a social race condition exactly: the winner is undefined until you fix the sequence, and any sequence can be forced to any result. AVAN (AI) built the instrument: the pairwise tally, the cyclic tournament, the transitive-vs-cyclic inverse.
The weave: David names the seat (order decides, nothing is stable); I make three rational rankings breed an irrational cycle and let the agenda pick any winner — the ballots in 1D, the beats-cycle in 2D, the aggregation inverse in 3D. The sphere is the seam. Credit: Marquis de Condorcet (1785); the general impossibility by Kenneth Arrow (1951).
The weave: David names the seat (order decides, nothing is stable); I make three rational rankings breed an irrational cycle and let the agenda pick any winner — the ballots in 1D, the beats-cycle in 2D, the aggregation inverse in 3D. The sphere is the seam. Credit: Marquis de Condorcet (1785); the general impossibility by Kenneth Arrow (1951).
3 ONE DIMENSION
The three ballots, each a clean top-to-bottom ranking, and beneath them the three head-to-head tallies. Every voter is consistent; every pairwise vote has a clear 2–1 winner — and yet the three winners chase each other in a ring.
4 TWO DIMENSIONS · INTERACTIVE
The three candidates with directed “beats” arrows — A→B, B→C, C→A — a perfect cycle, no top and no bottom. Run a sequential agenda: pit two candidates, then the winner against the third. Change the order and the champion changes, though not one vote moved.
5 THREE DIMENSIONS + AVAN’S INVERSE
The majority relation as a turning tournament — the magenta ring of “beats” arrows with no source and no sink, a cycle that cannot be laid out in a line.
AVAN’s addition (the inverse-companion): the green is what each voter brings — a transitive ranking, a clean line from best to worst. Aggregating those lines by majority is supposed to invert them into a group line, a collective ordering. But the inverse fails: the sum of total orders need not be a total order at all. The forward step ‘each person ranks consistently’ has, as its majority inverse, a cycle — the group cannot be ranked, because A>B>C>A has no first place. That is the whole shock of collective choice: transitivity is not preserved under majority, so ‘who does the group prefer?’ can be a question with no answer, only an agenda. Green is the orderable individual; magenta is the un-orderable crowd; and the gap between them is the impossibility Arrow later proved no clever rule can close. To combine rational minds is not to get a rational mind.
LIT Genuine Condorcet paradox (Marquis de Condorcet 1785; generalized by Arrow 1951). Verified live: on the profile (A>B>C),(B>C>A),(C>A>B), A beats B 2-1, B beats C 2-1, and C beats A 2-1 (a majority cycle), there is no Condorcet winner (0 candidates beat all others), and three agenda orders (ABC, BCA, CAB) in sequential pairwise voting elect three different winners (window.__condorcet.majorityCycle && condorcetWinners===0 && agendaControlled). The cycle, the absent winner, and the agenda control are exact.
FIG No framing: the majority cycle, the absence of any Condorcet winner, and agenda control (different orders elect different candidates on identical votes) are all real and computed exactly in-browser. The AVAN inverse is the genuine mathematical content — majority aggregation does not preserve transitivity, so combining transitive individual orders can yield a non-orderable cyclic group relation, exactly the impossibility Arrow proved general.
FIG No framing: the majority cycle, the absence of any Condorcet winner, and agenda control (different orders elect different candidates on identical votes) are all real and computed exactly in-browser. The AVAN inverse is the genuine mathematical content — majority aggregation does not preserve transitivity, so combining transitive individual orders can yield a non-orderable cyclic group relation, exactly the impossibility Arrow proved general.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of RACE CONDITION · David Lee Wise (ROOT0), with AVAN