Felsenthal Ex.4 full electorate — Runoff/IRV: their worst choice wins¶

Generated from bv2150_dxg8pb_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: Carl

▶ Live on BetterVoting: vote · results ↗ (election dxg8pb · test BV2150).

Scenario¶

Race 1 of 3 in the No-Show-paradox pair, part 1 of 2 (BV2150, bvid dxg8pb; 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). The full electorate: 11 voters — 4×(Andy>Beth>Carl), 3×(Beth>Carl>Andy), 1×(Carl>Andy>Beth), 3×(Carl>Beth>Andy). No first-round majority (Andy 4, Beth 3, Carl 4), so plurality-with-runoff (run as IRV; identical for three candidates) deletes BETH — and Carl beats Andy 7–4. Carl is the WORST outcome for the four Andy>Beth>Carl voters, and Beth is the Condorcet winner (beats Andy 6–5, Carl 7–4), so this race also exhibits the Condorcet winner paradox. Part 2 (BV2151): two of the Andy voters stay home and their side does BETTER — the No-Show paradox. Live results: https://bettervoting.com/dxg8pb/results

Ballots¶

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

4: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 full electorate — Runoff/IRV: their worst choice wins
 Tabulating 11 ballots (ranked ballots).

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

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
Carl               7  Elected
Andy               4  Rejected
Beth               0  Rejected


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

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 Carl is OUTSIDE the Smith set. ✗
      Every member of the set (Beth) beats Carl head-to-head, yet
      RCV-IRV elected Carl anyway. RCV-IRV is not Smith-efficient (nor
      Condorcet-efficient) — this is the shape a center squeeze leaves behind.
   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/bv2150_dxg8pb_irv.yaml

See also¶