election_title: "Successive elimination Ex.9 — two D voters stay home and get a better result"
scenario_description: |-
  The no-show variant of Felsenthal's Example 9. Source: Dan S. Felsenthal (2010), Appendix A4, Example 9 — see succ_elim_ex9_pareto.yaml for the full 11-voter profile and the other three paradoxes it carries.
  The same electorate with two of the five D>A>B>C voters ABSENT: 9 voters. Their absence breaks the cycle, A becomes the Condorcet winner outright, and the procedure elects A from any agenda whatever — under D vs A, winner vs C, winner vs B the rounds run A beats D 5:4, A beats C 6:3, A beats B 9:0.
  With all 11 present the same agenda elects B. Both absent voters rank A second and B third, so staying home got them a strictly better outcome than voting did: the no-show paradox. Nothing about anyone's preferences changed — only the turnout.
  Note what makes this readable: once two D ballots are gone the profile has a Condorcet winner, and successive elimination is Condorcet-consistent, so the agenda stops mattering. All of Example 9's pathology lives in the cycle.
  Labels are Felsenthal's own, capitalized, so the case can be read beside the paper's table.
  Tabulated as Ranked Robin for the pairwise matrix the agenda consumes pair by pair; Ranked Robin also elects A, as any Condorcet method must here. Run the procedure with tools_adam/pref_voting_tabulation_engine/successive_elimination_report.py.
paradoxes: [no-show, condorcet-winner]
voting_method: RankedRobin
num_winners: 1
ballots: |-
  3:A>B>C>D
  2:C>A>B>D
  1:C>D>A>B
  3:D>A>B>C
expected_winners:
  - A

# file: succ_elim_ex9_noshow.yaml