How the Count Works — STAR vs RCV-IRV, Step by Step¶

One line: the same ballots, counted two ways. STAR scores then holds one runoff — two steps. RCV-IRV runs rounds of eliminate-and-transfer — here three. In this example both elect Carmen, so the page isolates the process (how each count works and what it costs), not the winner.

→ Companion to Is RCV "Simple"? — Which Half? (the "which half is simple?" argument) and STAR Is Summable — Add Up Precinct Totals. When the two counts elect different people, see Center Squeeze. Level 201.

Worked on one shared file: count_simplicity_star_vs_irv.yaml — 45 voters, 5 candidates (Andre, Blake, Carmen, Dana, Evan).

The shared ballots¶

Every voter scores all five candidates 0–5. STAR reads the scores directly; RCV-IRV reads each ballot as a ranking (highest score = 1st choice, and so on).

Count × Andre Blake Carmen Dana Evan
  14  ×   4     3     5     2    1      # Carmen base   (C > A > B > D > E)
  10  ×   5     3     4     2    1      # Andre first   (A > C > B > D > E)
   9  ×   3     5     4     2    1      # Blake first   (B > C > A > D > E)
   7  ×   3     2     4     5    1      # Dana first    (D > C > A > B > E)
   5  ×   3     2     4     1    5      # Evan first    (E > C > A > B > D)

Carmen is almost everyone's strong second choice but few voters' first — the detail that makes the two counts behave so differently.

STAR — two steps¶

Step 1 — Scoring Round. Add each candidate's scores (a column sum). The two highest advance.

Carmen  -- 194  -- First place
Andre   -- 169  -- Second place
Blake   -- 141
Dana    -- 106
Evan    --  65
 Carmen and Andre advance.

Step 2 — Automatic Runoff. On every ballot, see which finalist it scored higher. That's one head-to-head tally.

Carmen        -- 35  -- First place
Andre         -- 10
Equal Support --  0
 Carmen wins.

Two passes over the ballots — a sum, then one pairwise comparison. Both are summable: each precinct can report its score totals and its Carmen-vs-Andre split, and you just add them up.

RCV-IRV — rounds of eliminate-and-transfer¶

Count only each ballot's top surviving choice. No majority? Drop the lowest, move its ballots to their next choice, and re-count. Repeat.

ROUND 1                     ROUND 2                     FINAL RESULT
Carmen   14  Hopeful        Carmen   19  Hopeful        Carmen   26  Elected
Andre    10  Hopeful        Andre    10  Hopeful        Andre    10  Rejected
Blake     9  Hopeful        Blake     9  Hopeful        Blake     9  Rejected
Dana      7  Hopeful        Dana      7  Rejected        Dana      0  Rejected
Evan      5  Rejected        Evan      0  Rejected        Evan      0  Rejected

Round 1: nobody has a majority (needs 23 of 45). Evan is lowest → eliminated. His 5 ballots' next choice is Carmen → Carmen 14 → 19.
Round 2: still no majority. Dana is now lowest → eliminated. Her 7 ballots' next choice is Carmen → Carmen 19 → 26.
Final: Carmen has 26 of 45 (>half) → elected.

Three rounds, and to follow it you have to track which ballots moved where each time. That bookkeeping is why an IRV count is not summable — a precinct can't report a partial result that adds up, because who gets eliminated depends on the whole electorate. Every ballot has to be in one place.

Exhausted (inactive) ballots. This example is tidy because every voter ranked all five candidates, so no ballot ever runs out of choices. In real RCV-IRV elections a ballot whose remaining ranks are all eliminated stops counting ("exhausted" / "inactive"), which is why an IRV winner's final-round majority is a majority of continuing ballots, not of everyone who voted. A faithful display should show the exhausted pile each round. STAR has no equivalent: every ballot's full score is read in the scoring round, and every ballot counts in the runoff. (See "Exhausted Ballots" — What FairVote's Word Actually Hides.)

Side by side¶

	STAR	RCV-IRV
Steps here	2 (score sum → one runoff)	3 rounds (eliminate + transfer ×2, then a majority)
Each step is…	a column sum; one head-to-head tally	re-tallying top choices among survivors, following every transfer
Reads…	the whole ballot at once (all scores)	only each ballot's top surviving mark
Summable / precinct-local?	Yes — add precinct totals	No — needs all ballots centrally, re-counted each round
Hand-auditable?	totals and one runoff split	re-run the whole transfer sequence
Winner (this example)	Carmen	Carmen

Same answer — but one count you can do with a calculator and a precinct sheet, the other needs the full ballot set and software to walk the rounds.

Is "shorter program = simpler"? (the Kolmogorov-complexity claim)¶

A common talking point tries to make that table objective: write a program to tabulate each method and STAR's will be shorter and faster — "Kolmogorov complexity," billed as the standard scientific measure of simplicity. There's a real kernel here: the minimal STAR count is two column sums and one head-to-head compare — no loop, no state — while the minimal RCV-IRV count needs an elimination loop that re-tallies after every transfer. STAR genuinely is the algorithmically simpler tabulation.

But "program length" is a slippery yardstick, and this repo is its own counterexample: the STAR engine here is ~3,300 lines while the vendored IRV counter is ~280 — because line-count measures the implementation (ours is a full reporting suite), not the algorithm. Kolmogorov complexity is also uncomputable in general and language-dependent in practice, so "the objective metric" oversells it. And taken literally it proves too much: the shortest tabulation program of all is plurality's (add the marks, done) — so "shortest program wins" would crown Choose-One, which no STAR advocate intends.

The rigorous, consequential version of "IRV is harder to count" isn't program length — it's summability: STAR's subtotals add up precinct-by-precinct and IRV's can't (the row above). That's a real auditing-and-transparency difference, not a rhetorical one. Keep the kernel; drop the "objective metric" dressing.

When the rounds change the winner¶

Here the methods agree, and Carmen even led the first round — but the first-round leader is not always the winner. In a center squeeze, the consensus candidate is almost everyone's second choice, so IRV eliminates her early (too few firsts) while STAR's scoring round keeps her in and she wins. Same ballots, different count, different winner — traced in Center Squeeze (demos center_squeeze_irv.yaml / center_squeeze_star.yaml). This is exactly why RCV-IRV results have to be read to the final round, never reported from first choices alone.

On displaying RCV-IRV results. The round-by-round table above follows the standard best practice (FairVote; Center for Civic Design): show every round with a written explanation, name the majority threshold, and treat the final round — not the first-choice lead — as the result. We deliberately show all the rounds rather than de-emphasizing the eliminations, because the whole point here is to see how the count works. See LINKS.md → "FairVote: displaying RCV results."

Run it yourself¶

python3 STARVote_LH_tabulation_engine/starvote_larry_hastings.py method_comparisons/_main/cases/count_simplicity_star_vs_irv.yaml
python3 06_Other/RCV_IRV/RCV_IRV_tabulation_engine/rcv_irv_tabulation.py    method_comparisons/_main/cases/count_simplicity_star_vs_irv.yaml

Cross-references¶

Is RCV "Simple"? — Which Half? — the simplicity argument this trace backs up.
STAR Is Summable — Add Up Precinct Totals — why STAR's count adds up locally and IRV's doesn't.
Center Squeeze — when the two counts elect different people.
What Is a Voting Method? — Ballot vs Count, Plurality vs Majority — ballot vs count, the 101 foundation.