election_title: "Successive elimination Ex.11 — before: six voters, the agenda elects C"
scenario_description: |-
  The BEFORE half of Felsenthal's successive-elimination twin example. Source: Dan S. Felsenthal (2010), Appendix A4, Example 11, crediting H. Moulin, "Axioms of Cooperative Decision Making" (1988b: 54).
  Six voters, three candidates: 2×(A>B>C), 2×(B>C>A), 1×(C>A>B), 1×(C>B>A). Under the agenda A vs B, winner vs C: round 1 ties 3:3 and A survives on the earlier-letter convention; round 2 C beats A 4:2. C is elected.
  Now give the single C>B>A voter a TWIN — one more voter with the identical ranking. See succ_elim_ex11_twin_after.yaml: B becomes the Condorcet winner and the procedure elects B from any agenda. The original C>B>A voter ranked C first and B second, so the arrival of someone who votes exactly as they do cost them their first choice. That is the twin paradox, and it is stranger than the no-show paradox because the added ballot is a perfect copy of one already cast.
  Note the round-1 tie: with six voters A and B split 3:3, so C's victory here already leans on a convention. The paradox does not depend on it — B wins outright after the twin joins — but it is worth seeing that the "before" state was itself precarious.
  Labels are Felsenthal's own, capitalized, so the case can be read beside the paper's table.
  Successive elimination exists in neither the LH engine nor BetterVoting, so this file is tabulated as Ranked Robin, which elects B — already disagreeing with the agenda's C before any twin arrives. Run the procedure with tools_adam/pref_voting_tabulation_engine/successive_elimination_report.py --agenda A,B,C.
paradoxes: [twin, condorcet-cycle]
voting_method: RankedRobin
num_winners: 1
ballots: |-
  2:A>B>C
  2:B>C>A
  1:C>A>B
  1:C>B>A
expected_winners:
  - B

# file: succ_elim_ex11_twin_before.yaml