election_title: "Successive elimination Ex.10 — amalgamated: every round ties, and the tie-break picks the winner"
scenario_description: |-
  The amalgamation half of Felsenthal's successive-elimination reinforcement example — and the case where this repo's count is more precise than the paraphrase it replaces. Source: Dan S. Felsenthal (2010), Appendix A4, Example 10.
  All four ballots: District I's three (A>B>C>D, B>D>C>A, D>C>A>B) plus District II's one (C>D>B>A). Each district elected C on its own under the agenda B vs D, winner vs A, winner vs C.
  Counted together, ALL THREE rounds are 2:2 ties. B vs D ties, the survivor vs A ties, the survivor vs C ties — so the elected candidate is decided entirely by the tie-break convention and not at all by the ballots. Breaking toward the earlier letter gives C, agreeing with both districts and producing NO paradox; breaking toward the candidate earlier on the agenda gives B, which neither district chose and which is the reinforcement failure. Felsenthal calls the break random and claims only that B CAN win, which is exactly right.
  Worth stating plainly because the earlier prose here said "B beats D in round 1": it does not, that round is a 2:2 tie like the other two. The failure is real but conditional, and the condition is the tie-break rule. A four-voter electorate is small enough that a tie is unremarkable; the lesson is that the procedure has no way to resolve one from the ballots.
  Labels are Felsenthal's own, capitalized, so the case can be read beside the paper's table.
  Tabulated as Ranked Robin, which elects C by a margin tiebreak inside a Copeland tie. Run the procedure both ways with tools_adam/pref_voting_tabulation_engine/successive_elimination_report.py --agenda B,D,A,C and --tiebreak agenda; the report re-runs the other convention itself and says when the winner moves.
paradoxes: [multiple-districts, condorcet-cycle]
voting_method: RankedRobin
num_winners: 1
ballots: |-
  1:A>B>C>D
  1:B>D>C>A
  1:D>C>A>B
  1:C>D>B>A
expected_winners:
  - C

# file: succ_elim_ex10_amalgamated.yaml