BV2166 — Coombs' No-Show electorate (2 of 2): two voters stay home — and STAR flips too¶

▶ Live on BetterVoting: vote · results ↗ (election b7b8dv).

The same election as BV2165 with one change, ceteris paribus: the two Cass>Boone>Amy voters don't participate. Felsenthal's target is Coombs — which now elects Cass, the abstainers' top preference. The honest headline for this repo: STAR flips too, live and frozen. The two voters get their favorite by staying home under both counts.

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 §A7, Example 19 (continued — Felsenthal notes the same flip arises from truncation to Cass-only: the Truncation paradox). Full §A7 treatment: coombs.md.

The one changed datum¶

No. of voters    BV2165 (all vote)       BV2166 (two stay home)
      4          Amy  > Boone > Cass     Amy  > Boone > Cass
      4          Boone > Cass > Amy      Boone > Cass > Amy
      5          Cass > Amy  > Boone     Cass > Amy  > Boone
      2          Cass > Boone > Amy      —      (abstain)

Coombs, worked: on 13 ballots the last-place counts become Amy 4, Boone 5, Cass 4 — now Boone is deleted, and Cass wins. The abstainers' ordering was Cass>Boone>Amy: full turnout bought their second choice (BV2165), staying home buys their first — the No-Show paradox under Coombs.

The live STAR flip — shown honestly¶

With all 15 ballots STAR elects Boone (41/43/51; Boone beats Cass 8–7 in the runoff). On these 13: Amy 39, Boone 37, Cass 41 — the finalist pair changes to Cass/Amy and Cass wins the runoff 9–4. The absent pair's sincere ballots scored Boone a 3, which was exactly what had lifted Boone into (and through) the runoff; withholding them elects their favorite. That is a genuine STAR participation failure on this profile — the first live score-family entry in the no-show group. The mechanism is STAR's runoff stage (which costs it Moulin-style participation guarantees); a pure score count cannot be moved against an added sincere ballot. Choose-One elects Cass in both electorates, unmoved — the flip lives entirely in elimination/runoff machinery.

Agreement¶

Election	Race	BetterVoting	LH engine	Agree?
BV2165 all vote	STAR	Boone	Boone	✓
BV2166 two no-shows	STAR	Cass	Cass	✓
BV2165 / BV2166	Choose-One	Cass / Cass	Cass / Cass	✓
BV2165 / BV2166	Coombs (paper)	—	Boone / Cass	n/a

Files: star · plurality · frozen export · mirrors: star, plurality · Part 1: BV2165.