Felsenthal Ex.4 after two no-shows — Runoff/IRV: the abstainers do better¶

Generated from bv2151_97hbpw_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: Beth

▶ Live on BetterVoting: vote · results ↗ (election 97hbpw · test BV2151).

Scenario¶

Race 1 of 3 in the No-Show-paradox pair, part 2 of 2 (BV2151, bvid 97hbpw; BV-confirmed; the pair is BV2150/51). 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 A2, Example 4 (the No-Show and Twin paradoxes). Ceteris paribus, TWO of the four Andy>Beth>Carl voters stay home: 9 voters — 2×(Andy>Beth>Carl), 3×(Beth>Carl>Andy), 1×(Carl>Andy>Beth), 3×(Carl>Beth>Andy). First choices are now Andy 2, Beth 3, Carl 4, so the runoff procedure (IRV; identical for three candidates) deletes ANDY — and Beth beats Carl 5–4. The two abstainers get Beth (their second choice) instead of Carl (their last, BV2150): staying home served them better than voting — the No-Show paradox. Read in reverse it is the weak TWIN paradox: add two voters identical to the Andy pair, and the twins' arrival elects their common worst choice. Live results: https://bettervoting.com/97hbpw/results

Ballots¶

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

2:Andy>Beth>Carl
3:Beth>Carl>Andy
1:Carl>Andy>Beth
3:Carl>Beth>Andy

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) ---
  Felsenthal Ex.4 after two no-shows — Runoff/IRV: the abstainers do better
 Tabulating 9 ballots (ranked ballots).

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
Carl               4  Hopeful
Beth               3  Hopeful
Andy               2  Rejected

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
Beth               5  Elected
Carl               4  Rejected
Andy               0  Rejected


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

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 3): Beth
   Outside (2):        Andy, Carl
   One member ⇒ Beth is the Condorcet winner, beating every rival head-to-head.
   RCV-IRV winner Beth 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/bv2151_97hbpw_irv.yaml

See also¶