The strongest case against the Condorcet winner — Edelman's "Myth of the Condorcet Winner," tabulated¶

Paul H. Edelman — Professor of Mathematics and Law at Vanderbilt — published "The Myth of the Condorcet Winner" (22 Supreme Court Economic Review 207, 2015; journal page) to refute "the consensus among legal scholars that, when choosing among multiple alternatives, the Condorcet winner, should it exist, is the preferred option." Where the FairVote article we claim-checked fails on contact with a countable election, this paper is the serious version of the anti-Condorcet argument — the math is right, the theorems are real, and engaging it honestly makes the whole debate sharper. So we tabulated it, live.

▶ Live on BetterVoting: vote · results ↗ (election gmfv4c, BV2173) — Edelman's 81-voter profile, four races on the same voters: STAR, Ranked Robin, RCV-IRV, Choose-One.

The cancellation argument¶

Edelman's centerpiece (his Section III) is this 81-voter profile — which, per his own footnote, was invented by Condorcet himself as an attack on Borda, and was later turned against the Condorcet criterion by Saari and by Balinski & Laraki:

Voters	Preference
30	Ada > Ben > Cara
1	Ada > Cara > Ben
29	Ben > Ada > Cara
10	Ben > Cara > Ada
10	Cara > Ada > Ben
1	Cara > Ben > Ada

Ada is the Condorcet winner: 41–40 over Ben, 60–21 over Cara. But Edelman points at two buried voter blocs — (10 Ben>Cara>Ada, 10 Cara>Ada>Ben, 10 Ada>Ben>Cara) and (1 Ada>Cara>Ben, 1 Cara>Ben>Ada, 1 Ben>Ada>Cara). Each is a perfectly symmetric cycle he calls a Condorcet component: within the bloc, every pairwise vote ties exactly, so — he argues — "the only reasonable conclusion is that all three alternatives are tied," and a bloc that collectively ties should cancel out. Remove those 33 voters and the remaining 48 say something unambiguous: 20 Ada>Ben>Cara vs 28 Ben>Ada>Cara — "it is rather clear that B should be the winner." Yet Ada, not Ben, is the Condorcet winner. Balinski & Laraki proved this isn't a fluke: no social choice function is Condorcet consistent and "cancels properly" — you must pick a side.

What the methods say — live¶

Every majoritarian count elects Ada; every positional/summation count elects Ben. That's not a coincidence — it's the two worldviews the theorem says can't coexist:

Elects Ada (majoritarian / pairwise)	Elects Ben (positional / cancellation-respecting)
Condorcet winner (41–40, 60–21)	Borda count (Ben 109, Ada 101, Cara 33)
Ranked Robin — record 2–0–0	Score sum (5/2/0 map): Ben 257, Ada 233, Cara 77
RCV-IRV — Cara out (31/39/11), then 41–40	Choose-One Plurality: Ben 39, Ada 31, Cara 11
STAR's automatic runoff — Ada 41–40	STAR's scoring round — Ben first, 257–233

STAR is the one method that shows both counts in one election — its scoring round is a proper-cancelling summation (a Condorcet component adds the same total to every candidate, so it cancels exactly, like Borda), and its runoff is the majoritarian step. The engine's [Runoff Reversal] block narrates the handoff:

[Divergence from STAR]
  STAR                   = Ada
  Choose-One (Plurality) = Ben   (differs from STAR)
  Approval               = Ben   (differs from STAR)

[Runoff Reversal]
 - Score Round Winner(s) = (Ben)
 - Runoff Round Winner   = (Ada)
  Candidate Ben earned the highest total score, but
  Candidate Ada won the automatic runoff — not a malfunction,
  STAR working as designed: the runoff elects the finalist preferred
  by the majority (of voters with a preference).

--- STAR Voting Method (single winner) ---

[STAR Voting]
 Tabulating 81 ballots.
Count × Ada,Ben,Cara
   30 ×   5,  2,   0
   29 ×   2,  5,   0
   10 ×   0,  5,   2
   10 ×   2,  0,   5
    1 ×   5,  0,   2
    1 ×   0,  2,   5

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Ben           -- 257 -- First place
   Ada           -- 233 -- Second place
   Cara          --  77
 Ben and Ada advance.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   Ada           -- 41 -- First place
   Ben           -- 40
   Equal Support --  0
 Ada wins.
   Runoff math:
     81  ballots cast
   −  0  Equal Support (no preference between the two finalists)
     ──
     81  voters with a preference  (majority = 41)
           Ada 41 (51%)  ·  Ben 40 (49%)

[STAR Voting: Winner — STAR Voting Method (single winner)]
 Ada

So "who should win Edelman's election?" is precisely the repo's majoritarian-vs-utilitarian split, with a 240-year pedigree: Condorcet built the example to embarrass Borda's count; Saari — Borda's great modern champion — reversed the polarity and used the same example to embarrass Condorcet's criterion. Neither side ever "won," because the two ideals genuinely disagree here, 41 voters to 40.

The component on its own — everything ties, and the engine says so¶

The 30-voter Condorcet component is worth tabulating alone: edelman_perfect_component_c3_b30. Every pairwise vote is 20–10 in a cycle, every score sum is 70, every candidate holds exactly ten 5s. The LH engine's tiebreak ladder exhausts — scores tie 70/70/70, pairwise ties 30/30/30, five-star counts tie 10/10/10 — and it prints its rare honest flag: "[Lot-decided tie — rare] … the result here was set by lot, not by the votes." Then the cycle itself decides the runoff (whichever pair the lot admits, one beats the other 20–10). Any method must do something arbitrary with this electorate; the teaching value is an engine that tells you it's being arbitrary. This one is LH-only deliberately — a BetterVoting version would resolve the ties at random, so its result couldn't be frozen.

The no-show argument (Section IV) — real, and it cuts every direction¶

Edelman's second line is theoretical: by a theorem of H. Peyton Young, "No social choice function that is Condorcet consistent is also join consistent" — if two electorates separately pick C, a Condorcet-consistent method can pick something else when they vote together. His worked example (sequential pairwise voting, the agenda A-vs-B then winner-vs-C): group X (3 A>B>C, 3 C>A>B, 5 B>C>A) chooses C; group Y (5 B>A>C, 1 A>C>B, 5 C>B>A) also chooses C; the combined 22 voters choose B — Ben beats A 15–7 and C 13–9, a genuine Condorcet winner that neither group wanted. A delegation could advance its interests by staying home — the no-show paradox, which Riker called a "very serious defect." Edelman's real-world illustration is Burlington 2009 — where, as he notes, the method in use was IRV, "which is not Condorcet consistent," and the Condorcet winner came in third.

Two honest notes, both already in this repo's canon:

This critique reaches STAR too. STAR's runoff step makes it fail the Participation criterion in rare constructed cases — the same family of pathology, documented openly in RCV-IRV vs STAR and STAR's honest limits. No method escapes Gibbard–Satterthwaite; the choice is which failures, how often, and how visibly.
It reaches IRV harder. IRV fails join consistency and Participation and the Condorcet criterion — Edelman's Burlington example is an IRV election. This paper lends no comfort to "RCV fixes everything" claims; Edelman himself advocates none of these methods (he ends by gesturing at behavioral economics, not a ballot reform).

Where this leaves us¶

Edelman's conclusion — "There are, alas, no self-evident correct alternatives even in the situations where a Condorcet winner exists" — is, verbatim, the thesis of this repo's What makes a "good" winner? The paper demolishes Condorcet-as-axiom; it does not crown a rival. Read it alongside the FairVote claim check as the pair of anti-Condorcet arguments: one that dissolves under tabulation, and one that survives it — and notice that the survivor's lesson is symmetrical. If the Condorcet winner isn't sacrosanct, then a method missing it occasionally (STAR, by design, in rare profiles) isn't automatically broken — and by the same token, electing it usually is a chosen ideal, not a proof of correctness. Name your ideal, show the ballots, count.

The demo elections¶

Page (start here)	What it shows	Live results	Source	Full report
BV2173 — Edelman's 81 voters	Condorcet winner Ada vs cancellation/Borda winner Ben; STAR shows both counts (Ben 257–233 in scores, Ada 41–40 in the runoff); RR and IRV → Ada, Plurality → Ben	results ↗	yaml	tabulated
The perfect component, alone	30 voters, everything ties (70/70/70 scores, 20–10 cyclic pairwise); the engine's tiebreak ladder exhausts and flags the lot-decided result — LH-only by design	— (not freezable on BV)	yaml	tabulated

file: edelman_condorcet_myth.md¶