Reversal symmetry — RCV-IRV, original: A wins (best)¶

Generated from reversal_irv_original.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: A

Scenario¶

A reversal-symmetry demonstration (from rangevoting.org / Warren Smith — a Range-advocacy source, so advocacy-leaning; disclosed). 24 voters, three candidates, a Condorcet CYCLE (A>B>C>A — no candidate beats all others). Counted by RCV-IRV, A wins: C has the fewest first-choices, is eliminated, and C's ballots flow to A (15-9). The companion reversal_irv_reversed reverses EVERY ballot — as if voters were choosing the WORST candidate — and A wins AGAIN. That winner=loser outcome is a failure of the reversal symmetry criterion, which RCV-IRV and plurality fail but additive methods (Range, Borda, Approval) and some Condorcet methods (Ranked Pairs, Schulze) satisfy. See ../README.md; STAR and Ranked Robin do NOT reproduce the winner=loser on this example.

Ballots¶

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

9:B>C>A
8:A>B>C
7:C>A>B

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) ---
  Reversal symmetry — RCV-IRV, original: A wins (best)
 Tabulating 24 ballots (ranked ballots).

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
B                  9  Hopeful
A                  8  Hopeful
C                  7  Rejected

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
A                 15  Elected
B                  9  Rejected
C                  0  Rejected


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

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): B, C, A
   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 A 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/reversal_symmetry/cases/reversal_irv_original.yaml

Reversal symmetry — RCV-IRV, original: A wins (best)¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶