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SOURCE FILE:     bv2153_pcttmr_irv.yaml
TABULATED FILE:  bv2153_pcttmr_irv_tabulated.txt
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election_title: "Felsenthal Ex.7 — IRV: the majority favorite wins round one"
scenario_description: |-
  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
bv_test_id: BV2153
bv_election_id: pcttmr
bv_results_url: https://bettervoting.com/pcttmr/results
paradoxes: [majority-failure]
voting_method: IRV
num_winners: 1
ballots: |-
  51:Amos>Bella>Chad
  48:Bella>Chad>Amos
  1:Chad>Bella>Amos
expected_winners:
  - Amos

# file: bv2153_pcttmr_irv.yaml

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TABULATION RESULTS
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--- 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

--- 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