Non-monotonicity (RCV-IRV) — part 1: baseline, X wins¶

Generated from monotonicity_irv_before.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: X

Scenario¶

Part 1 of the RCV-IRV monotonicity pair: 34 voters, X wins (Z is eliminated, Z's ballots transfer to X). This is the baseline for the paradox — in part 2 (monotonicity_irv_after.yaml) four voters RAISE X from second to first choice, change nothing else, and X LOSES. Keep both files side by side; the ballots differ only in those four voters.

Ballots¶

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

12:X>Y
12:Y>Z
10:Z>X

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) ---
  Non-monotonicity (RCV-IRV) — part 1: baseline, X wins
 Tabulating 34 ballots (ranked ballots).

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
Y                 12  Hopeful
X                 12  Hopeful
Z                 10  Rejected

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
X                 22  Elected
Y                 12  Rejected
Z                  0  Rejected


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

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 (3 of 3): X, Y, Z
   Outside (0):        —
   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.
   RCV-IRV winner X 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/monotonicity/cases/monotonicity_irv_before.yaml

Non-monotonicity (RCV-IRV) — part 1: baseline, X wins¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶