No Condorcet Winner — IRV (Hare): Dave wins by elimination¶

Generated from bv2138_cxrf8v_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: Dave

▶ Live on BetterVoting: vote · results ↗ (election cxrf8v · test BV2138).

Scenario¶

One of four races in the 'One Ranked Electorate, Many Tabulations' election (BV2138, bvid cxrf8v; BV-confirmed). 921 voters, five candidates, NO Condorcet winner (Smith set = Abby, Brad, Dave, Erin). Robert LeGrand's flagship 'the method decides' example: across ~15 methods the win splits five ways. IRV → Dave.

Ballots¶

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

98:Abby>Cora>Erin>Dave>Brad
64:Brad>Abby>Erin>Cora>Dave
12:Brad>Abby>Erin>Dave>Cora
98:Brad>Erin>Abby>Cora>Dave
13:Brad>Erin>Abby>Dave>Cora
125:Brad>Erin>Dave>Abby>Cora
124:Cora>Abby>Erin>Dave>Brad
76:Cora>Erin>Abby>Dave>Brad
21:Dave>Abby>Brad>Erin>Cora
30:Dave>Brad>Abby>Erin>Cora
98:Dave>Brad>Erin>Cora>Abby
139:Dave>Cora>Abby>Brad>Erin
23:Dave>Cora>Brad>Abby>Erin

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) ---
  No Condorcet Winner — IRV (Hare): Dave wins by elimination
 Tabulating 921 ballots (ranked ballots).

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
Brad             312  Hopeful
Dave             311  Hopeful
Cora             200  Rejected
Abby              98  Rejected
Erin               0  Rejected

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
Dave             609  Elected
Brad             312  Rejected
Cora               0  Rejected
Abby               0  Rejected
Erin               0  Rejected


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

--- Transfers and inactive ballots (what the round tables leave out) ---
The tables above give each candidate's round total but not where a
transferred vote came FROM, nor how many ballots stopped counting.
Both are recomputed from the ballots, using the eliminations the
count above actually made.

ROUND 1 — 921 of 921 ballots still active; majority = 461
   Erin eliminated with 0:
      → (held no ballots)
   Abby eliminated with 98:
      → Dave                     98
   Cora eliminated with 200:
      → Dave                    200

FINAL ROUND — 921 of 921 ballots still active; majority = 461
   Dave                    609  (66.1% of the still-active)  ← elected
   Brad                    312  (33.9% of the still-active)
   Never exhausted, never transferred:
      312 ballots held by Brad carried a lower ranking that was never read
      (the count stopped here, so those preferences did nothing).

Inactive ballots at the final round: 0 of 921 (0.0%).
   Dave's 609 is a majority of the 921 still active AND of all 921 cast (66.1%).

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 (4 of 5): Abby, Brad, Erin, Dave
   Outside (1):        Cora
   More than one member ⇒ NO Condorcet winner: the top of the tournament is a
   cycle, so the strongest "candidate" is a set, not a person. Which member of
   the set should win is exactly what Minimax / Ranked Pairs / Schulze disagree
   about — see 05_Ranked_Robin/01_Learn/cycle_resolution.md.
   Note: the Copeland leaders (Abby, Brad) are only part of the set — the
   win–loss table's top block understates how wide the contention is.
   RCV-IRV winner Dave 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/no_condorcet_bv2138/cases/bv2138_cxrf8v_irv.yaml

No Condorcet Winner — IRV (Hare): Dave wins by elimination¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶