Many IRV pathologies in one election — Brams' 21-voter sampler (BV2159)¶

Generated from bv2159_f4cjpy_brams_irv_pathologies.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

▶ Live on BetterVoting: vote · results ↗ (election f4cjpy · test BV2159).

Scenario¶

Steven Brams' example (Notices of the AMS, 1982; via rangevoting.org). IRV elects B, but G is the Condorcet winner (beats B 14-7, beats everyone). The same election shows a no-show paradox, a truncation incentive, favorite-betrayal, and non-monotonicity — several IRV pathologies at once. Sincere, academically sourced, ranked ballots. Approval/STAR/Condorcet/Ranked Robin would elect G. Level 301. Source: https://www.rangevoting.org/rangeVirv.html (section 12); Brams 1982. Live results: https://bettervoting.com/f4cjpy/results (all races LH<->BV confirmed). Lesson: bv2159_f4cjpy_brams_irv_pathologies.md Live on BetterVoting: https://bettervoting.com/f4cjpy/results (BV-confirmed; STAR is race 1).

Ballots¶

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

7:B>G>N>F
6:G>B>N>F
5:N>G>B>F
3:F>N>G>B

What the engine says¶

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

--- RCV / Instant-Runoff Voting (single winner) ---
 Tabulating 21 ballots (ranked ballots).

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
B                  7  Hopeful
G                  6  Hopeful
N                  5  Hopeful
F                  3  Rejected

ROUND 2
Candidate      Votes  Status
-----------  -------  --------
N                  8  Hopeful
B                  7  Hopeful
G                  6  Rejected
F                  0  Rejected

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
B                 13  Elected
N                  8  Rejected
G                  0  Rejected
F                  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 4): G
   Outside (3):        B, N, F
   One member ⇒ G is the Condorcet winner, beating every rival head-to-head.
   RCV-IRV winner B is OUTSIDE the Smith set. ✗
      Every member of the set (G) beats B head-to-head, yet
      RCV-IRV elected B 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/paradoxes_and_whoops/cases/bv2159_f4cjpy_brams_irv_pathologies.yaml

Many IRV pathologies in one election — Brams' 21-voter sampler (BV2159)¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶