Crowded field, rung 7 — 7 candidates, 65 voters, counted by RCV-IRV¶

Generated from crowded_field_c7_irv.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: Clara

Official tie-break (lot) order: Ana > Bruno > Clara > Diego > Elsa > Felix > Greta — consulted only if every deterministic tiebreaker stays tied (how the ladder works).

Scenario¶

RUNG 3 — seven candidates, and Diego is down to 9 first choices out of 65 while still beating all six rivals head-to-head.

He is eliminated; RCV-IRV elects Clara. Round 1 doubles as the Choose-One count, which elects Greta on 15 — the candidate standing furthest from the middle of the electorate, and one Diego beats 50–15 one-on-one.

Counted here on the ranked ballots, deliberately. At seven candidates the 0–5 ballot in crowded_field_c7_star.yaml carries ties on most rows, so reading IRV or Choose-One off it — as that file's divergence block is forced to — measures the score-to-rank tie-break rather than the method. These are the numbers to quote.

Same 65 voters and the same fixed candidate positions as crowded_field_c7_star.yaml, on a ranked ballot — the same ballots as crowded_field_c7_ranked_robin.yaml, counted by elimination instead of head-to-head.

Construction: build_ladder.py in this folder. 65 voters in seven blocs at 0, 4, 8, 12, 16, 20, 24 (sizes 6, 10, 13, 9, 12, 8, 7); candidates fixed at Ana 1 · Bruno 6 · Clara 9 · Diego 11 · Elsa 14 · Felix 16 · Greta 22; utility = minus distance; scores = each bloc's own min-max scaling onto 0–5. Nothing is tuned, and no count at any rung is settled by a tie-break.

Ballots¶

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

6:Ana>Bruno>Clara>Diego>Elsa>Felix>Greta    # bloc at 0
10:Bruno>Ana>Clara>Diego>Elsa>Felix>Greta    # bloc at 4
13:Clara>Bruno>Diego>Elsa>Ana>Felix>Greta    # bloc at 8
9:Diego>Elsa>Clara>Felix>Bruno>Greta>Ana    # bloc at 12
12:Felix>Elsa>Diego>Greta>Clara>Bruno>Ana    # bloc at 16
8:Greta>Felix>Elsa>Diego>Clara>Bruno>Ana    # bloc at 20
7:Greta>Felix>Elsa>Diego>Clara>Bruno>Ana    # bloc at 24

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) ---
  Crowded field, rung 7 — 7 candidates, 65 voters, counted by RCV-IRV
 Tabulating 65 ballots (ranked ballots).

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
Greta             15  Hopeful
Clara             13  Hopeful
Felix             12  Hopeful
Bruno             10  Hopeful
Diego              9  Hopeful
Ana                6  Rejected
Elsa               0  Rejected

ROUND 2
Candidate      Votes  Status
-----------  -------  --------
Bruno             16  Hopeful
Greta             15  Hopeful
Clara             13  Hopeful
Felix             12  Hopeful
Diego              9  Rejected
Ana                0  Rejected
Elsa               0  Rejected

ROUND 3
Candidate      Votes  Status
-----------  -------  --------
Clara             22  Hopeful
Bruno             16  Hopeful
Greta             15  Hopeful
Felix             12  Rejected
Diego              0  Rejected
Ana                0  Rejected
Elsa               0  Rejected

ROUND 4
Candidate      Votes  Status
-----------  -------  --------
Greta             27  Hopeful
Clara             22  Hopeful
Bruno             16  Rejected
Felix              0  Rejected
Diego              0  Rejected
Ana                0  Rejected
Elsa               0  Rejected

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
Clara             38  Elected
Greta             27  Rejected
Bruno              0  Rejected
Felix              0  Rejected
Diego              0  Rejected
Ana                0  Rejected
Elsa               0  Rejected


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

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 7): Diego
   Outside (6):        Ana, Bruno, Clara, Elsa, Felix, Greta
   One member ⇒ Diego is the Condorcet winner, beating every rival head-to-head.
   RCV-IRV winner Clara is OUTSIDE the Smith set. ✗
      Every member of the set (Diego) beats Clara head-to-head, yet
      RCV-IRV elected Clara 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/crowded_field/cases/crowded_field_c7_irv.yaml

Crowded field, rung 7 — 7 candidates, 65 voters, counted by RCV-IRV¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶