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RCV-IRV Fails the Equal Vote (Equality) Criterion

One line: RCV-IRV does not deliver an equally weighted vote. Because it counts only one ranking at a time and eliminates candidates sequentially, two voters with exactly opposite preferences often cannot cancel each other out — so vote-splitting and the spoiler effect survive. STAR, Score, and Approval pass this test; RCV-IRV does not.

→ The property itself, and why STAR passes it: The Equally Weighted Vote. Related IRV-specific failures: center squeeze · exhausted ballots. Curriculum: 301.5.

The test it fails

The Equal Vote Criterion (the "Test of Balance") asks: for any ballot one voter casts, can another voter cast an equal-and-opposite ballot so the two together change nothing? If yes, no voter's ballot outweighs another's. The full concept — and the worked example where two opposite score ballots cancel — is on the STAR page, The Equally Weighted Vote. RCV-IRV fails it for two connected reasons: vote-splitting and ballot exhaustion.

Why RCV-IRV fails: one active ranking at a time

Under RCV-IRV your ballot only counts for one candidate at a time, and candidates are eliminated round by round. Whether your later preferences ever get counted depends on the order others are eliminated — which is outside your control. So two opposite voters don't reliably net to zero the way two opposite score ballots do.

A worked scenario

Three candidates, A, B, C. Two voters hold opposite views of the front-runners:

  • Voter X loves A, hates B.
  • Voter Y loves B, hates A.

Under a method that passes the Equal Vote (Score or STAR), X and Y cancel perfectly on A-vs-B and weigh C equally — balance holds. Under RCV-IRV they often can't:

  • X ranks A > C, Y ranks B > C.
  • A and B split the anti-C support. If both are eliminated before consolidating, both ballots transfer to C — and C wins.

X and Y did not have an equal-and-opposite effect. They inadvertently both helped C by splitting the opposition. Their votes were not equally weighted — the hallmark failure of the Equality Criterion.

The same failure, counted — balanced ballots flip the winner

Here it is with real numbers — the exact mirror of the STAR case where opposite ballots do cancel (equal & opposite). Three candidates on a line — Ada (left), Bruno (center), Cyrus (right) — and a small electorate where Bruno is the compromise:

4: Bruno > Ada  > Cyrus
3: Ada   > Bruno > Cyrus
2: Cyrus > Bruno > Ada

Before. Bruno is the Condorcet winner — he beats Ada 6–3 and Cyrus 7–2 — and RCV-IRV elects him too: Cyrus has the fewest first-choices (2) and is eliminated, his ballots flow to Bruno, Bruno wins 6–3. IRV and the head-to-head agree.

Now add three exact-opposite pairs — each Ada > Bruno > Cyrus matched by its perfect reverse Cyrus > Bruno > Ada. Under Score, STAR, or Ranked Robin these cancel: every pairwise margin just grows symmetrically and Bruno stays the Condorcet winner (now 9–6 and 10–5). The balanced ballots changed nothing about whom a majority prefers.

But watch RCV-IRV:

Round 1:  Ada 6   Cyrus 5   Bruno 4     ← Bruno now has the FEWEST first-choices
          → Bruno eliminated
Round 2:  Ada 10  Cyrus 5               → Ada wins

The six new ballots put their first-choices on the two extremes (Ada +3, Cyrus +3) and none on the center (Bruno +0) — because IRV only ever counts the top of each ballot. Perfectly balanced ballots, which cancel under every other method, squeezed the center candidate out and handed the win to an extreme. Equal and opposite in, a flipped winner out — the effect was not zero.

That is the Test of Balance failing in a single election, and the mechanism is exactly center squeeze: under sequential elimination it's first-choice counts that decide who survives, so opposite ballots don't cancel — they pile onto the ends and starve the middle. Run it: 06_Other/RCV_IRV/equal_vote_balance/ (base → Bruno, plus-balanced → Ada).

Is this a fair test, or an anti-IRV gotcha? Fair — and the fairness is in what passes: Ranked Robin is also a ranked method, and the opposite ballots cancel under it perfectly. So the lesson is not "ranks are worse than scores" — it's that summable and pairwise counts cancel opposites, while sequential elimination doesn't. A score ballot cancels in the sum; a ranked-Condorcet count cancels in the pairwise matrix; only IRV's round-by-round elimination breaks the symmetry. That's also why Ranked Robin is the natural olive branch to ranked-choice voters — the same ranked ballot, counted in a way that keeps every voter's weight equal. (And this is a constructed illustration; center squeeze is a genuine IRV property but concentrated in competitive 3-way races — the honest scope is spelled out just below.)

Vote-splitting and exhaustion, precisely

  • Vote-splitting. Elimination order means a faction that runs more candidates is statistically disadvantaged; opposite preferences don't cancel, they interact with who gets eliminated when. (This is the same root cause as center squeeze.)
  • Ballot exhaustion. In the deciding round, some voters' later choices are never counted because their ballot already exhausted — so those voters get no equal-and-opposite say at the moment it matters. See exhausted ballots.

The other side, fairly stated

FairVote argues RCV-IRV upholds "one person, one vote" better than Choose-One: voters can name a favorite without wasting the vote and still weigh in on the front-runners (their essay). The equal-vote reply: that defends RCV-IRV against Choose-One, not against the Test of Balance — RCV-IRV still discards some voters' later rankings in the deciding round, so the balance fails precisely in the competitive, 3+-candidate races where it matters.

Is this a fair criticism? (the honest version)

Mostly yes — when stated precisely, with two caveats worth stating out loud:

  • Fair: it is provably true that RCV-IRV fails the cancellation / Equal-Vote criterion that Score, STAR, and Approval pass, and this isn't abstract — it lines up with real, documented behavior (center squeeze and spoilers in competitive 3+-candidate races, and ballot exhaustion in the deciding round).
  • Caveat 1 — don't overstate it. "RCV-IRV gives some people an unequal vote" can mislead a lay listener into thinking some voters literally get more ballots. They don't. Every voter casts one ballot and every first choice is counted equally; the inequality is subtler — it's about whose later preferences get counted once elimination starts. RCV-IRV does satisfy "one person, one vote" in the ordinary legal sense (courts have upheld it), which is a different bar than the Test of Balance.
  • Caveat 2 — the criterion isn't neutral. The Equal-Vote / cancellation criterion is promoted mainly by cardinal-method advocates (the Equal Vote Coalition), and cardinal methods pass it essentially by construction; even its formalizer notes it may not fully capture the informal intent. So "RCV-IRV fails our criterion" carries some method-favoring flavor, and it's largely the spoiler/center-squeeze critique in equal-vote language rather than a wholly separate defect.

Bottom line: precise and fair as "RCV-IRV fails a specific, well-defined balance property that cardinal methods pass, with real spoiler/exhaustion consequences." It tips into unfair if sold as "IRV literally weights some votes more" or as a neutral, method-agnostic gold standard.

Keep the scope precise

This is an RCV-IRV failure, not a property of ranked ballots in general. With only two candidates every method passes. And Ranked Robin — also an RCV (ranked) method — reads every rank and compares pairwise, so it passes the Equal Vote. "RCV fails the equal vote" would be the imprecise overclaim; it's RCV-IRV's sequential-elimination count specifically that fails.

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