Felsenthal Ex.7 — Approval: a majority's first choice loses¶

Generated from bv2153_pcttmr_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: Bella

▶ Live on BetterVoting: vote · results ↗ (election pcttmr · test BV2153).

Scenario¶

Race 1 of 3 in the Absolute-Majority-paradox election (BV2153, bvid pcttmr; 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 7. 100 voters, rankings 51×(Amos>Bella>Chad), 48×(Bella>Chad>Amos), 1×(Chad>Bella>Amos). Amos is ranked FIRST by an absolute majority (51 of 100) and is the Condorcet winner. But when every voter approves their top TWO preferences, the approval totals are Amos 51, Bella 100, Chad 49 — APPROVAL ELECTS BELLA, approved by literally everyone, over a candidate an absolute majority ranked first. Felsenthal's Absolute Majority paradox. The companion ranked races (IRV, Ranked Robin) elect Amos. Live results: https://bettervoting.com/pcttmr/results

Ballots¶

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

Amos,Bella,Chad
51: 1,1,0
49: 0,1,1

What the engine says¶

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

--- Approval Voting (single winner) ---
 Tabulating 100 ballots (any non-zero score = approval).

Ballots:
   columns = Amos, Bella, Chad      (1 = approve; 0 = not approved)
    51 × 1,1,0
    49 × 0,1,1

   Bella -- 100 (100%) -- Elected
   Amos  -- 51 (51%)
   Chad  -- 49 (49%)

[Approval Distribution] (how many candidates each ballot approved)
   200 approvals across 100 ballots — average 2.0 of 3 (range 2–2).
     approved 2: 100 ballots

[Co-Approval Matrix]
 Of the voters who approved the ROW candidate, the % who ALSO approved the COLUMN candidate.
          | Bella  |  Amos  |  Chad  |
   -----------------------------------
   Bella  |   --   |  51%   |  49%   |
   Amos   |  100%  |   --   |   0%   |
   Chad   |  100%  |   0%   |   --   |

Winner — Approval Voting (single winner)
  Bella

Run it yourself:

python STARVote_LH_tabulation_engine/starvote_larry_hastings.py method_comparisons/felsenthal_paradoxes/cases/bv2153_pcttmr_approval.yaml

See also¶