Nurmi Ex.16 truncated — RCV-IRV: ranking ONLY their favorite serves 17 voters better¶

Generated from bv2163_74j6vv_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: B

▶ Live on BetterVoting: vote · results ↗ (election 74j6vv · test BV2163).

Scenario¶

Race 2 of 3 in the RCV-IRV truncation pair, part 2 of 2 (BV2163, bvid 74j6vv; BV-confirmed; the pair is BV2162/63). Source: Dan S. Felsenthal, "Review of Paradoxes Afflicting Various Voting Procedures Where One Out of m Candidates (m ≥ 2) Must Be Elected", University of Haifa / LSE, revised 26 May 2010; Appendix A6, Example 16, due to Nurmi (1999: 63). Identical to BV2162 except one datum, ceteris paribus: the 17 voters whose full ordering is D>C>B>A TRUNCATE and rank only D. D is eliminated first exactly as before — but the truncated ballots EXHAUST instead of transferring to C, so C (24) is eliminated instead of B, C's transfers flow to B, and B wins. The truncators prefer B to A (the sincere-IRV winner of BV2162), so ranking FEWER candidates got them a BETTER result: the Truncation paradox, live. It also accidentally repairs IRV's Condorcet failure — B, the Condorcet winner, now wins. Live results: https://bettervoting.com/74j6vv/results

Ballots¶

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

33:A>B>C>D
29:B>A>C>D
24:C>B>A>D
17:D

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) ---
  Nurmi Ex.16 truncated — RCV-IRV: ranking ONLY their favorite serves 17 voters better
 Tabulating 103 ballots (ranked ballots).

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
A                 33  Hopeful
B                 29  Hopeful
C                 24  Hopeful
D                 17  Rejected

ROUND 2
Candidate      Votes  Status
-----------  -------  --------
A                 33  Hopeful
B                 29  Hopeful
C                 24  Rejected
D                  0  Rejected
Blank Votes       17  Rejected

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
B                 53  Elected
A                 33  Rejected
C                  0  Rejected
D                  0  Rejected
Blank Votes       17  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): B
   Outside (3):        A, C, D
   One member ⇒ B is the Condorcet winner, beating every rival head-to-head.
   RCV-IRV winner B 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/felsenthal_paradoxes/cases/bv2163_74j6vv_irv.yaml

See also¶