BV2150 — Felsenthal Example 4 (1 of 2): everyone votes, and their worst choice wins¶

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

11 voters, three candidates. The four Andy>Beth>Carl voters all show up and vote sincerely — and get Carl, their last choice. Part 2 (BV2151) shows the sting: had two of them stayed home, their side would have gotten Beth. Three races on the same electorate: Runoff/IRV → Carl; Ranked Robin → Beth; STAR → Beth.

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 (Leverhulme Trust Voting Power in Practice workshop, Château du Baffy, Normandy). Appendix §A2, Example 4 — demonstrating the No-Show and (weak) Twin paradoxes.

The election¶

No. of voters    Preference ordering
      4          Andy > Beth > Carl
      3          Beth > Carl > Andy
      1          Carl > Andy > Beth
      3          Carl > Beth > Andy

First choices: Andy 4, Beth 3, Carl 4 — no majority, so plurality-with-runoff (= IRV for three candidates) deletes Beth, and Carl beats Andy 7–4. Meanwhile Beth is the Condorcet winner (beats Andy 6–5, Carl 7–4) — so the runoff race also exhibits the Condorcet winner paradox, electing Carl, whom Beth beats 7–4.

The paradoxes this pair demonstrates¶

The No-Show paradox (conditional): the four Andy>Beth>Carl voters would have done better if two of them hadn't voted — see BV2151, where the same procedure elects Beth. The Twin paradox (weak form) is the same pair read forward: start from the 9-voter electorate and add two "twins" identical to the Andy pair — their arrival elects Carl, the twins' common worst choice. Both live on one teaching page: no_show.md.

View 1 — BetterVoting¶

Live results: bettervoting.com/dxg8pb/results ↗. BV elects Carl (IRV), Beth (Ranked Robin), Beth (STAR) — matching LH on all three, no tiebreaks.

View 2 — LH engine¶

Runoff/IRV race (bv2150_dxg8pb_irv.yaml):

 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

Ranked Robin (bv2150_dxg8pb_ranked_robin.yaml) elects Beth — 2 pairwise wins (6–5, 7–4), the Condorcet winner. STAR (bv2150_dxg8pb_star.yaml) with the 5/3/1 map: Andy 29, Beth 37, Carl 33; Beth wins the automatic runoff 7–4. Full detail: IRV mirror · RR mirror · STAR mirror.

Agreement¶

Race	BetterVoting	LH engine	Agree?
Runoff (IRV)	Carl	Carl	✓
Ranked Robin	Beth	Beth	✓
STAR (ranks→scores)	Beth	Beth	✓

Frozen export: bv2150_dxg8pb_bv_export.json · Part 2: BV2151 — two supporters stay home.