Felsenthal Ex.8 — Approval: the absolute loser wins on one strategic ballot¶

Generated from bv2154_wq6yv7_approval.yaml — do not edit by hand. Regenerate: python STARVote_LH_tabulation_engine/tools_adam/scripts/build_yaml_pages.py.

Method: Approval Voting · 1 seat · Expected winner: April

▶ Live on BetterVoting: vote · results ↗ (election wq6yv7 · test BV2154).

Scenario¶

Race 1 of 3 in the three-winners election (BV2154, bvid wq6yv7; BV-confirmed). 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 A3, Example 8. 15 voters, rankings 6×(April>Bruce>Clara), 4×(Bruce>Clara>April), 1×(Clara>April>Bruce), 4×(Clara>Bruce>April). The social ordering is Bruce>Clara>April: April is the Condorcet LOSER and the ABSOLUTE loser (an absolute majority — 8 of 15 — rank April dead last). But if the single Clara>April>Bruce voter approves the top two while everyone else bullet-votes, the approval totals are April 7, Bruce 4, Clara 5 — APPROVAL ELECTS APRIL: the Condorcet-loser and Absolute-loser paradoxes under Approval, triggered by one voter's cutoff choice. Live results: https://bettervoting.com/wq6yv7/results

Ballots¶

Row 1 = candidate names; each later row is one voter's approvals (1 = approve, 0/blank = not approved).

April,Bruce,Clara
1,0,0
1,0,0
1,0,0
1,0,0
1,0,0
1,0,0
0,1,0
0,1,0
0,1,0
0,1,0
1,0,1
0,0,1
0,0,1
0,0,1
0,0,1

What the engine says¶

Full report from the _tabulated mirror (regenerated on every run; every analysis forced on):

--- Approval Voting (single winner) ---
 Tabulating 15 ballots (any non-zero score = approval).

Ballots:
   columns = April, Bruce, Clara      (1 = approve; 0 = not approved)
     6 × 1,0,0
     4 × 0,1,0
     1 × 1,0,1
     4 × 0,0,1

   April -- 7 (47%) -- Elected
   Clara -- 5 (33%)
   Bruce -- 4 (27%)

[Approval Distribution] (how many candidates each ballot approved)
   16 approvals across 15 ballots — average 1.1 of 3 (range 1–2).
     approved 1: 14 ballots
     approved 2: 1 ballot

[Co-Approval Matrix]
 Of the voters who approved the ROW candidate, the % who ALSO approved the COLUMN candidate.
          | April  | Clara  | Bruce  |
   -----------------------------------
   April  |   --   |  14%   |   0%   |
   Clara  |  20%   |   --   |   0%   |
   Bruce  |   0%   |   0%   |   --   |

Winner — Approval Voting (single winner)
  April

Run it yourself:

python STARVote_LH_tabulation_engine/starvote_larry_hastings.py method_comparisons/felsenthal_paradoxes/cases/bv2154_wq6yv7_approval.yaml

See also¶