Tie-Breaking: STAR vs. RCV-IRV — Fewer Ties, or Easier Ties?¶

One line: RCV-IRV (Hare) has fewer places a tie can occur, but its strict ranks carry less information, so a genuine tie is harder to resolve deterministically — and more often falls to a lot or coin toss. STAR's richer score data gives it more deterministic tiebreakers before the lot. So the ranked method has the simpler-looking rule, but not the easier problem.

It's natural to assume that because RCV-IRV uses plain rankings, breaking a tie should be simpler than in a score method. The reverse is closer to the truth, for three reasons: where ties happen, what you have to break them with, and how much a tie changes the outcome.

→ Companion to STAR Tie-Breaking — The Full Chain and Strict vs. Weak Ranks. Part of the Ties & Tie-Breaking topic hub. Level 301.

1. Where a tie can occur¶

STAR — two rounds, so two loci. A tie can appear in the Scoring Round (two candidates with the same total score, tied for a finalist slot) or in the Automatic Runoff (the two finalists preferred by an equal number of voters). Each has its own tiebreak ladder.

RCV-IRV — rounds of elimination, so essentially one locus. The tie that matters is the elimination tie: two or more candidates tied for the fewest current top-choice votes — which one do you drop? (A final-round tie for the win reduces to the same coin-flip question.)

On this axis alone, RCV-IRV is simpler: one kind of tie, not two.

2. What you have to break the tie with — the part that flips the intuition¶

STAR has more to work with, because scores carry more than order. When STAR hits a tie it can consult, in order, real deterministic tests before any randomness:

pairwise — of the tied candidates, whom do more voters prefer head-to-head;
five-star — who has the most maximum-score votes;
only then the lot.

RCV-IRV has only the ranks. When two candidates are tied for last, nothing cardinal distinguishes them — there's no "strength of support" to look at. Real statutes therefore reach for ad-hoc rules: who had fewer votes in a prior round, forward/backward elimination, occasionally a Borda-style total — and, very commonly, drawing lots. (Equal ranks aren't available to help either: IRV uses strict ranks, so a voter can't even mark two candidates the same — see Strict vs. Weak Ranks.)

The headline: more information means more deterministic rungs, so the lot is reached less often. Strict ranks give fewer tools, so the coin comes out sooner. STAR's tiebreak rules look more elaborate precisely because it has more data to spend before giving up to chance — and that spending pays off.

3. The consequence of a tie is bigger in RCV-IRV¶

A STAR scoring-round tie usually just decides which of two finalists advances; the runoff still runs, and the winner is whichever finalist more voters prefer. The tie rarely decides the winner by itself.

An IRV elimination tie decides who gets removed — and removing a different candidate transfers different ballots, which can change every later round and flip the winner. This is the same order-sensitivity that produces IRV's non-monotonicity and center squeeze. So the one tie RCV-IRV has tends to matter more, and is harder to reason about, than either of STAR's.

4. The unavoidable floor¶

To be fair to both: a perfectly symmetric tie can't be broken from the ballots by any method. STAR reaches the lot; RCV-IRV coin-tosses the elimination; neither can do better, because the voters genuinely said nothing to separate the candidates. (See the real BetterVoting jfk7pd case and its three-candidate analog.) The difference between methods shows up in near-ties: STAR's extra signals can separate candidates who tie on one measure but differ on another; strict-rank RCV-IRV more often has nothing left but chance.

5. Reproducibility and consistency¶

Random tie-breaks are not a STAR-specific wart. RCV-IRV jurisdictions commonly break elimination ties by lot, so "same ballots, different winner on a re-count" happens there too. And there is no single canonical RCV-IRV tie-break rule — it varies by statute, so two jurisdictions can resolve the identical tie differently. STAR (as specified by the Equal Vote Coalition) publishes one deterministic cascade (pairwise → five-star → lot); the remaining reproducibility gap is only whether the lot order is drawn and published in advance (the point of the jfk7pd writeup).

And the academic literature is no tidier — the question is openly described as vexing and often simply ignored. Two named proposals, both with real costs, both worth knowing because they show the problem isn't a drafting oversight:

Drop them all (Taylor & Pacelli, 2006): eliminate every candidate sharing the lowest plurality score. Clean and deterministic — but if k ≥ 3 survivors are all tied it removes all of them at once, so no candidate ever reaches majority support. The rule only terminates if you abandon stop-when-someone-has-a-majority and declare everyone eliminated in the final round to be co-winners. This is the convention the reference implementations use — Pacuit's SEP entry states both Hare and Coombs this way, and pref_voting implements it — and the co-winners clause is not a patch but the point: on a symmetric profile an all-candidate tie is the only outcome an anonymous, neutral rule may return. Worked in full, with three runnable cases: Batch elimination — what happens when the batch is everyone.
Parallel universes (Conitzer et al., 2009): at each stage eliminate one of the tied candidates, but explore every possible elimination sequence, compute the winner of each, and declare a tie among all winners found. Arguably the most principled answer — it refuses to let an arbitrary choice decide — and it is the set-valued approach applied to IRV. The cost is combinatorial: the number of sequences explodes with the number of tied candidates, and this style of tiebreak is known to be computationally hard in general. Some real RCV statutes specify something of this shape.

Both reinforce section 3's point from the other direction. In STAR a tie is a question about who wins; in IRV it's a question about who is eliminated, which then changes every subsequent round — so an IRV tiebreak doesn't resolve one comparison, it forks the entire count. That's why the literature ends up enumerating universes.

6. In fairness to RCV-IRV¶

The single-rule simplicity is a real virtue: "eliminate the candidate with the fewest votes, break ties by lot" is easy to explain to voters and to legislate, whereas STAR's three-rung cascade is more to teach and to display. And exact ties are rare in both methods at any real scale. The claim here is not that RCV-IRV is "worse at ties" — it's the narrower, more interesting point: strict ranks do not make tie-breaking easier. They trade a simpler rule for less resolving power and a more consequential tie, and they lean on chance sooner.

And a ranked ballot has more left in it than "lot" suggests — implementations use it. The comparison above describes IRV as legislated, where a tie for last typically does go straight to a draw. It is not what a good implementation has to do. Our own vendored engine's ladder is most second choices → thirds → fourths → coin — the same shape as STAR's cascade, and for the same reason: keep reading the ballot while it still says something. So the honest version of the row below is that ranks carry fewer rungs than scores, not that they carry one; the gap is in resolving power, not in whether anybody bothered. Where the two ladders genuinely converge is at the bottom: STAR's dead rung and a ranked ladder exhausted at every rank are the same dead end, and both hand the result to something outside the ballots. What differs there is disclosure — see batch elimination, where our engine's dead ladder quietly lets the ballot file order decide.

Side by side¶

	STAR	RCV-IRV (Hare)
Places a tie can occur	2 (scoring round, runoff)	1 (elimination)
Information to break it	scores → pairwise, five-star, then lot	ranks only → prior rounds / lot by statute; later ranks, then chance, in implementations
Deterministic rungs before chance	several	few (statute) — more in practice, but capped by the number of ranks
How often chance decides	less often	sooner
Rule complexity	higher (an explicit cascade)	lower per step, but non-canonical
What the tie decides	usually which finalist advances	who is eliminated → cascades, can flip the winner
Canonical rule?	one published cascade	varies by jurisdiction