Parallel universes — one count, two legal answers¶

Generated from put_two_universes_c3_b4.yaml — do not edit by hand. Regenerate: python STARVote_LH_tabulation_engine/tools_adam/scripts/build_yaml_pages.py.

Method: RCV-IRV (Instant Runoff) · 1 seat · Expected winner: Anna

Scenario¶

Four voters, three candidates, and an elimination tie in the very first round. Anna leads with 2 first choices; Blake and Cora have 1 each and are tied for last, so the rule must decide who goes — and that decision decides the election. Cut Blake, and his ballot (Blake>Anna>Cora) transfers to Anna: 3 of 4, elected outright. Cut Cora, and her ballot (Cora>Blake>Anna) transfers to Blake: Anna 2, Blake 2, no majority and nothing left to separate them — Blake shares the win. Both are legal executions of the same rules on the same ballots. This engine reports Anna, and it reports her cleanly: pyrankvote removes BOTH tied candidates in one step and elects Anna in a single round, with Blake and Cora listed side by side as Rejected. Nothing in the output says a tie was ever resolved. That batch step is justified by the observation that Blake and Cora hold only 2 votes between them, which cannot exceed Anna's 2 — but that reasoning quietly treats a 2-2 tie as a loss for Blake, which is exactly the question at issue. Parallel Universe Tiebreaking (PUT) refuses to assume it: it runs every legal elimination order and elects the union, reporting {Anna, Blake}. Cross-checked against pref_voting, an engine nobody here wrote: instant_runoff = {Anna}, instant_runoff_put = {Anna, Blake}, coombs_put = {Anna, Blake}. Worth noting what this case is NOT: the winner here does not turn on a coin flip. The engine seeds its RNG (random.seed(0)) because pyrankvote can break ties with random.choice, but this result is seed-independent — verified at seeds 0, 1, 2, 7, 42 and 99, all Anna. The single winner is perfectly reproducible and still incomplete, which is the whole lesson: reproducibility is not the same thing as correctness. Lesson: 07_Concepts/topics/ties/parallel_universe_tiebreaking.md

Ballots¶

Each row is one voter's ranking, most-preferred first (N: prefix = N identical ballots).

Anna>Blake>Cora
Anna>Blake>Cora
Blake>Anna>Cora
Cora>Blake>Anna

What the engine says¶

Round-by-round Sankey diagram: each candidate's votes as a band, and where the votes of an eliminated candidate transferred to.

Where the votes went. Band thickness is votes; a band leaving an eliminated candidate lands on whoever that ballot ranked next, or on inactive if it ranked nobody who was left.

The count, step by step — the rounds and how the winner is reached:

--- RCV / Instant-Runoff Voting (single winner) ---
  Parallel universes — one count, two legal answers
 Tabulating 4 ballots (ranked ballots).

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
Anna               2  Elected
Blake              1  Rejected
Cora               1  Rejected


Winner(s) — RCV / Instant-Runoff Voting (single winner)
  Anna

Full audit — preference matrix, Condorcet, and score distribution¶

--- Smith Set (the generalized Condorcet winner) ---
The smallest group whose every member beats every candidate outside it —
the honest answer to "who is even in contention?".
   Smith set (2 of 3): Anna, Blake
   Outside (1):        Cora
   More than one member ⇒ NO Condorcet winner: the top of the tournament is a
   dead heat (its members DRAW each other head-to-head), so the strongest
   "candidate" is a set, not a person. No member beats another, so there is no
   loop for Minimax / Ranked Pairs / Schulze to disagree about — which member
   wins is left to the tiebreak, not to a cycle rule. See
   05_Ranked_Robin/01_Learn/rr_tiebreak_lh_vs_bv.md.
   RCV-IRV winner Anna is INSIDE the Smith set. ✓
      Not guaranteed — RCV-IRV is not Smith-efficient — but it holds here.
   Fine print: this set contains a pairwise DRAW, and a draw is enough to keep a
   candidate in the Smith set but not in the tighter Schwartz set — so Schwartz
   may be smaller here.
   More: 07_Concepts/topics/smith_set.md

Everything in one file: the _tabulated mirror (regenerated on every run; every analysis forced on).

Run it yourself:

python STARVote_LH_tabulation_engine/starvote_larry_hastings.py 06_Other/RCV_IRV/cases/put_two_universes_c3_b4.yaml

Parallel universes — one count, two legal answers¶

Scenario¶

Ballots¶

What the engine says¶

Full audit — preference matrix, Condorcet, and score distribution¶

See also¶