Non-monotonicity (RCV-IRV) — part 2: raising X makes X lose¶

Generated from monotonicity_irv_after.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: Z

Scenario¶

Part 2 of the RCV-IRV monotonicity pair: four Y>Z voters move X up to first (12:X>Y becomes 16:X>Y), a pure GAIN of support for X — and X now loses. The extra support changed the elimination order: Y goes out first, Y's ballots feed Z, and Z beats X 18-16. More support made the winner lose — IRV's non-monotonicity. STAR cannot do this (more points never hurt); see the monotonicity_star_* pair and the monotonicity topic hub.

Ballots¶

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

16:X>Y
8: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 2: raising X makes X lose
 Tabulating 34 ballots (ranked ballots).

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
X                 16  Hopeful
Z                 10  Hopeful
Y                  8  Rejected

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
Z                 18  Elected
X                 16  Rejected
Y                  0  Rejected


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

--- 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 — 34 of 34 ballots still active; majority = 18
   Y eliminated with 8:
      → Z                         8

FINAL ROUND — 34 of 34 ballots still active; majority = 18
   Z                        18  (52.9% of the still-active)  ← elected
   X                        16  (47.1% of the still-active)
   Never exhausted, never transferred:
      16 ballots held by X 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 34 (0.0%).
   Z's 18 is a majority of the 34 still active AND of all 34 cast (52.9%).

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 Z 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_after.yaml

Non-monotonicity (RCV-IRV) — part 2: raising X makes X lose¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶