Summability demo — RCV-IRV combined A+B (B eliminated; not summable)¶

Generated from irv_combined.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: A

Scenario¶

Districts A + B merged, counted by RCV-IRV. B won BOTH districts — but in the combined electorate B has the fewest first choices (8 vs 9 and 9), is eliminated first, and both B-bullet blocs exhaust. The race then ends in a GENUINE 9-9 tie between A and C; the engine's seeded coin flip elects A (see the note at expected_winners). No district subtotal can produce this result: IRV needs every ballot in one pile. Compare the star_* trio, where subtotals simply add.

Ballots¶

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

6:A
4:B
3:C>B>A
6:C
4:B
3:A>B>C

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) ---
  Summability demo — RCV-IRV combined A+B (B eliminated; not summable)
 Tabulating 26 ballots (ranked ballots).

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
A                  9  Hopeful
C                  9  Hopeful
B                  8  Rejected

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
A                  9  Elected
C                  9  Rejected
B                  0  Rejected
Blank Votes        8  Rejected


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

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 (1 of 3): B
   Outside (2):        A, C
   One member ⇒ B is the Condorcet winner, beating every rival head-to-head.
   RCV-IRV winner A is OUTSIDE the Smith set. ✗
      Every member of the set (B) beats A head-to-head, yet
      RCV-IRV elected A anyway. RCV-IRV is not Smith-efficient (nor
      Condorcet-efficient) — this is the shape a center squeeze leaves behind.
   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 method_comparisons/summability_demo/cases/irv_combined.yaml

Summability demo — RCV-IRV combined A+B (B eliminated; not summable)¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶