Felsenthal Ex.7 — IRV: the majority favorite wins round one¶

Generated from bv2153_pcttmr_irv.yaml — do not edit by hand. Regenerate: python STARVote_LH_tabulation_engine/tools_adam/scripts/build_yaml_pages.py.

Method: RCV-IRV (Instant Runoff) · 1 seat · Expected winner: Amos

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

Scenario¶

Race 2 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 under instant runoff: Amos holds 51 first choices — an absolute majority — and wins in the first round. The contrast with the approval race (Bella, 100 approvals) is the whole point: a top-two approval cutoff erases the majority's first-vs-second distinction. 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:

--- RCV / Instant-Runoff Voting (single winner) ---
  Felsenthal Ex.7 — IRV: the majority favorite wins round one
 Tabulating 100 ballots (ranked ballots).

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
Amos              51  Elected
Bella             48  Rejected
Chad               1  Rejected


Winner(s) — RCV / Instant-Runoff Voting (single winner)
  Amos

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.
   RCV-IRV winner Amos is INSIDE the Smith set. ✓
      Not guaranteed — RCV-IRV is not Smith-efficient — but it holds here.
   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_irv.yaml

See also¶