BV2165 — Coombs' No-Show electorate (1 of 2): everyone votes

▶ Live on BetterVoting: vote · results ↗ (election 9vxcj7).

15 voters, three candidates, everyone participates. Coombs (on paper) elects Boone; the live races split — STAR → Boone (runoff 8–7), Choose-One → Cass. Part 2 (BV2166) removes two voters and both Coombs and STAR flip to their favorite.

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 (Coombs' procedure), Example 19. Full §A7 treatment: coombs.md.

The election

No. of voters    Preference ordering
      4          Amy  > Boone > Cass
      4          Boone > Cass > Amy
      5          Cass > Amy  > Boone
      2          Cass > Boone > Amy

Coombs, worked: no first-choice majority (4/4/7); last-place counts are Amy 6 (4+2), Boone 5, Cass 4 — Amy is deleted, and Boone is then ranked first by 8 of 15 (his own 4 plus Amy's 4), an absolute majority — Boone wins. The pairwise preferences are a cycle (Amy>Boone 9–6, Boone>Cass 8–7, Cass>Amy 11–4), which is why there's no Ranked Robin race (random 3-way tie on BV) and no IRV race (random Amy/Boone elimination tie).

Agreement

Race	BetterVoting	LH engine	Agree?
STAR (5/3/1 map: 41/43/51 — Cass tops the scores; Boone wins the runoff 8–7)	Boone	Boone	✓
Choose-One (Plurality)	Cass (7 of 15)	Cass	✓
Coombs (paper only)	—	Boone (Amy deleted)	n/a

Files: star · plurality · frozen export · mirrors: star, plurality · Part 2: BV2166 — two voters stay home.