Summability demo — RCV-IRV district B (B wins)¶

Generated from irv_district_B.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: B

Scenario¶

District B of the RCV-IRV summability trio: B wins here too — both districts independently elect B. Yet the combined electorate does NOT elect B (see irv_combined.yaml: B is eliminated first there). District winners, and even full district round-by-round tallies, cannot be summed into the combined result — the non-summability this trio demonstrates.

Ballots¶

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

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 district B (B wins)
 Tabulating 13 ballots (ranked ballots).

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
C                  6  Hopeful
B                  4  Hopeful
A                  3  Rejected

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
B                  7  Elected
C                  6  Rejected
A                  0  Rejected


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

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):        C, A
   One member ⇒ B is the Condorcet winner, beating every rival head-to-head.
   RCV-IRV winner B is INSIDE the Smith set. ✓
      Not guaranteed — RCV-IRV is not Smith-efficient — but it holds 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 method_comparisons/summability_demo/cases/irv_district_B.yaml

Summability demo — RCV-IRV district B (B wins)¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶