election_title: "STAR elects a covered candidate — five ballots, four cities"
scenario_description: >-
  A candidate is COVERED when someone beats them AND beats everyone they beat:
  strictly redundant, on the pairwise evidence alone. The uncovered set — the
  candidates nobody covers — is the weakest structural filter in the
  tournament-solutions literature, usually leaving most of the field standing,
  and it is the coarsest filter that guarantees a Pareto-optimal choice. This
  election is five ballots where STAR's winner is outside it.
  Denver takes the STAR result: Austin leads the scoring round with 14 to
  Denver's 11, and Denver wins the automatic runoff 3-2. Now read the pairwise
  grid. Chicago beats Denver. And Austin — the only city Denver beats — is also
  beaten by Chicago. So Chicago does everything Denver does and more: Denver is
  COVERED by Chicago, the only covered city here, and the uncovered set is
  {Austin, Boston, Chicago}. Three of the four clear the bar; STAR elects the
  one that doesn't.
  Two honest halves to the lesson. Against STAR: no rule that reads only the
  win-loss graph would elect Denver, and "beaten by someone who also beats
  everyone you beat" is an objection a normal voter understands on hearing it.
  For STAR: covering is a purely ORDINAL verdict, and Denver is NOT
  Pareto-dominated — ballot 3 scores Denver 5 and Chicago 0, so no voter is
  overruled. Denver also outscores both Boston (9) and Chicago (10). STAR is
  deliberately reading the strength-of-preference information the tournament
  discards, and here the two kinds of evidence point different ways. Which one
  should govern is the actual disagreement between the score and pairwise camps;
  this election is small enough to hold both halves in view at once.
  Ranked Robin lands inside the uncovered set, as it always must: Boston and
  Chicago each go 2-1, so Copeland ties them — both uncovered — and the graph
  alone says only "one of these two." That Copeland tie is forced at this size:
  with exactly FOUR candidates a unique Copeland winner and a Condorcet winner
  are the same thing (verified exhaustively over all 64 four-candidate
  tournaments), so a cycle here guarantees a tie. Five candidates is the first
  size at which Copeland can be decisive inside a cycle (280 of the 1024
  five-candidate tournaments).
  The tie then breaks deterministically but differently per engine, which makes
  this a live example of the documented LH-vs-BetterVoting split: LH's rung is
  total margin, and Chicago (+1) beats Boston (-1), so the report below elects
  CHICAGO. BetterVoting's rung is the head-to-head between the tied pair, and
  Boston beats Chicago 3-2, so BV would elect BOSTON. No lot is involved on
  either side — the two published ladders simply disagree. Say which engine you
  are quoting.
  Every ballot uses four DISTINCT scores on purpose: score-to-rank conversion is
  then unambiguous, no Equal Support appears in any head-to-head, and none of
  the comparison methods below can be dismissed as a tie-breaking artifact.
  Search-built and verified twice: a search over random strict score ballots for
  a tie-free tournament whose STAR winner is covered, confirmed by the LH engine
  below and by pref_voting's four independent covering variants (Gillies,
  Fishburn, Bordes, McKelvey — all four agree here).
  LH-only as committed: the STAR result is engine-independent, but the Ranked
  Robin comparison line depends on which tiebreak ladder you run, so the full
  picture is quoted against the LH engine.
voting_method: STAR
num_winners: 1
ballots: |-
  Austin,Boston,Chicago,Denver
  0,4,2,1
  2,1,3,0
  4,1,0,5
  5,2,0,1
  3,1,5,4
expected_winners:
  - Denver

# file: star_elects_a_covered_candidate_c4_b5.yaml