Felsenthal Ex.7 — Ranked Robin: the Condorcet winner Amos¶
Generated from bv2153_pcttmr_ranked_robin.yaml — do not edit by hand. Regenerate: python STARVote_LH_tabulation_engine/tools_adam/scripts/build_yaml_pages.py.
Method: Ranked Robin (RCV-RR / Copeland) · 1 seat · Expected winner: Amos
▶ Live on BetterVoting: vote · results ↗ (election pcttmr · test BV2153).
Scenario¶
Race 3 of 3 in the Absolute-Majority-paradox election (BV2153, bvid pcttmr; BV-confirmed). Source: Dan S. Felsenthal (2010), Appendix A3, Example 7 — see bv2153_pcttmr_approval.yaml for the setup. The same 100 voters' full rankings counted by Ranked Robin (Copeland): Amos wins both head-to-heads (Bella 51–49, Chad 51–49) — the Condorcet winner, elected. A majority's first choice survives any pairwise count; it is the approval cutoff, not the ballots, that loses him. Live results: https://bettervoting.com/pcttmr/results
Ballots¶
Each row is one voter's ranking, most-preferred first (N: prefix = N identical ballots).
51:Amos>Bella>Chad
48:Bella>Chad>Amos
1:Chad>Bella>Amos
What the engine says¶
The count, step by step — the rounds and how the winner is reached:
--- Ranked Robin (RCV-RR / Copeland) Method (single winner) ---
Tabulating 100 ballots (ranked ballots).
Ballots:
51 × Amos > Bella > Chad
48 × Bella > Chad > Amos
1 × Chad > Bella > Amos
Round-Robin — every pair, head-to-head (For – Against):
Amos beats Bella 51 – 49
Amos beats Chad 51 – 49
Bella beats Chad 99 – 1
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Amos | Bella | Chad |
------------------------------------------------------
Amos > | --- |51 - 0 - 49 |51 - 0 - 49 |
Bella > | 49 - 0 - 51 | --- |99 - 0 - 1 |
Chad > | 49 - 0 - 51 | 1 - 0 - 99 | --- |
Win–loss record — Copeland score = wins + ½·ties (highest score wins; ties broken by total margin, then lot order):
# Candidate W–L–T Copeland Margin Beats
1 Amos 2–0–0 2 +4 Bella, Chad
2 Bella 1–1–0 1 +96 Chad
3 Chad 0–2–0 0 -100 —
Winner — Ranked Robin (RCV-RR): Amos
beats every opponent head-to-head — the Condorcet winner.
Full audit — preference matrix, Condorcet, and score distribution¶
--- Smith Set (the generalized Condorcet winner) ---
The smallest group whose every member beats every candidate outside it —
the honest answer to "who is even in contention?".
Smith set (1 of 3): Amos
Outside (2): Bella, Chad
One member ⇒ Amos is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Amos is INSIDE the Smith set. ✓
Guaranteed: Ranked Robin (Copeland) is Smith-efficient — every member of
the set outscores every outsider, so the top of the win–loss table is
always inside the set, however the tie among them is then broken.
More: 07_Concepts/topics/smith_set.md
Everything in one file: the _tabulated mirror (regenerated on every run; every analysis forced on).
Run it yourself:
python STARVote_LH_tabulation_engine/starvote_larry_hastings.py method_comparisons/felsenthal_paradoxes/cases/bv2153_pcttmr_ranked_robin.yaml
See also¶
More cases in this set: bv2144_mxfmhm_plurality · bv2144_mxfmhm_star · bv2145_6fj2kg_irv · bv2145_6fj2kg_ranked_robin · bv2145_6fj2kg_star · bv2146_krk2px_irv · bv2146_krk2px_ranked_robin · bv2146_krk2px_star · bv2147_9gdrqg_irv · bv2147_9gdrqg_star · bv2148_h87k6v_irv · bv2148_h87k6v_star · bv2149_byk9v2_irv · bv2149_byk9v2_star · bv2150_dxg8pb_irv · bv2150_dxg8pb_ranked_robin · bv2150_dxg8pb_star · bv2151_97hbpw_irv · bv2151_97hbpw_ranked_robin · bv2151_97hbpw_star · bv2152_r6ctvy_approval · bv2152_r6ctvy_ranked_robin · bv2153_pcttmr_approval · bv2153_pcttmr_irv · bv2154_wq6yv7_approval · bv2154_wq6yv7_irv · bv2154_wq6yv7_ranked_robin · bv2160_r6qc8h_plurality · bv2160_r6qc8h_star · bv2161_q3h4fk_plurality · bv2161_q3h4fk_star · bv2162_4htk44_irv · bv2162_4htk44_ranked_robin · bv2162_4htk44_star · bv2163_74j6vv_irv · bv2163_74j6vv_ranked_robin · bv2163_74j6vv_star · bv2164_xbqq8t_plurality · bv2164_xbqq8t_ranked_robin · bv2164_xbqq8t_star · bv2165_9vxcj7_plurality · bv2165_9vxcj7_star · bv2166_b7b8dv_plurality · bv2166_b7b8dv_star · bv2167_f3dxq9_plurality · bv2167_f3dxq9_star · coombs_ex18_monotonicity · coombs_ex20_amalgamated · coombs_ex20_district1 · coombs_ex20_district2 · coombs_ex21_twin_after · coombs_ex21_twin_before · coombs_ex22_scc · felsenthal_ex6_pareto_approval · felsenthal_ex6_ranked_robin · minimax_ex30_noshow_after · minimax_ex30_noshow_before · minimax_ex31_truncation · minimax_ex32_amalgamated · minimax_ex32_district2 · minimax_ex33_scc · succ_elim_ex10_amalgamated · succ_elim_ex10_district1 · succ_elim_ex10_district2 · succ_elim_ex11_twin_after · succ_elim_ex11_twin_before · succ_elim_ex12_sincere · succ_elim_ex12_truncated · succ_elim_ex9_noshow · succ_elim_ex9_pareto