election_title: "A full quota rates Dinah 5 and prefers her to everyone — and she wins no seat"
scenario_description: |-
  Nine voters, four candidates, three seats, counted by Allocated Score. Three of the nine — exactly one Hare quota — score Dinah a 5 and score every other candidate strictly lower. In the language of the proportional-representation literature those three are a SOLID COALITION for Dinah, and Proportionality for Solid Coalitions (PSC) says a solid coalition holding a full quota must win a seat. Allocated Score elects Arun, Bela and Curtis. Dinah gets nothing.
  The mechanism is visible in the round-by-round report and is the interesting part. Dinah's three supporters do not only support Dinah — two of them give Arun a 4. Arun wins the first seat on total score, and his quota is filled from the highest-scoring ballots available: one at score 5, then the score-4 group, which is where those two Dinah voters sit. Their ballots are spent, reweighted to a third of their value, and by round 2 the coalition no longer has a full quota of unspent support to elect anyone with. The seat was not lost to a rival faction; it was consumed paying for a candidate they merely liked.
  Why this file exists: the library's own page on [what "proportional" actually means] says that quota-owning schools — and it lists Allocated Score among them — "hand a cohesive quota-sized faction a seat by construction." That sentence is the design philosophy, sourced from electowiki's taxonomy, and it is a fair description of the intent. It is not a theorem, and this file is why the distinction matters. PSC is an ORDINAL axiom: it reads only the order on a ballot. Allocated Score is a CARDINAL method: it runs on the magnitudes. A ballot's ordinal projection is not what the method counts, so an ordinal guarantee does not follow from a cardinal design, however quota-shaped.
  Provenance, stated plainly because it changes how much the file is worth: this profile was FOUND BY RANDOM SEARCH over 0-5 ballots, not constructed to make a point, and it is one witness rather than a characterization. Violations turned up in roughly 1 in 100 random 9-voter, 4-candidate, 3-seat profiles under the weakest reading of the axiom (Hare quota, strict solid commitment); requiring every coalition member to score their candidate a full 5, as here, they turned up in roughly 1 in 1700. What the file establishes is the existence claim — Allocated Score does not satisfy PSC — and nothing about how often it matters in real elections, which is a separate and unanswered question.
  This is also NOT the free-riding result already documented in this folder's sibling page. Free riding is a strategy: withhold a star from a sure winner and get your ballot back. Every ballot here is sincere. The two share a mechanism — which score group a ballot is spent from — and make opposite points, one about manipulation and one about a guarantee that was never there.
  The related single-winner axiom, and the paper that motivated this check, are in method_comparisons/equal_rank_irv/README.md: respect for cohesive majorities is generalized PSC at one seat and one candidate, and STAR fails that too.
voting_method: allocated
num_winners: 3
ballots: |-
  Arun,Bela,Curtis,Dinah
  3,1,4,0
  3,4,0,5    # solid for Dinah — but a 4 for Arun, which is what spends this ballot
  0,4,4,0
  4,0,0,5    # solid for Dinah — and a 4 for Arun
  4,3,2,1
  5,3,5,0
  3,5,2,3
  2,1,2,1
  4,0,0,5    # solid for Dinah — and a 4 for Arun
expected_winners: [Arun, Bela, Curtis]

# file: solid_coalition_quota_gets_nothing.yaml