{"abstract":"An exact quotient omits the final quota increment.","category":"Voting rule computation","checks":6,"contract":"For nonnegative integer valid count and positive seats return floor(valid/(seats+1))+1, including when the quotient is integral.","contract_signature":"valid, seats","evaluation_group":"model-5ad69449e120c3d2","failed_approach":"Dividing by seats instead changes the allocation rule.","family":"z-voting_rules-droop-quota","id":"FA-12761","implementations":{"attempt":{"sha256":"a7dd2dfb4cc1ef36cdc79a010b621160aff904eefe6fea5286ee54aac93c907e","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(valid, seats):\n    return valid//seats+1\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('exact division', solve(6*N,2), 2*N+1)\ncheck('fractional division', solve(6*N+1,2), 2*N+1)\ncheck('zero ballots', solve(0,N), 1)\ncheck('one seat', solve(2*N,1), N+1)\ncheck('more seats than ballots', solve(1,N+2), 1)\ncheck('several seats', solve(20,3), 6)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"1e52accbef0981595cfec304a8e72bec67ce6d431715de9dedc78e9816a5330d","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(valid, seats):\n    return (valid+seats)//(seats+1)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('exact division', solve(6*N,2), 2*N+1)\ncheck('fractional division', solve(6*N+1,2), 2*N+1)\ncheck('zero ballots', solve(0,N), 1)\ncheck('one seat', solve(2*N,1), N+1)\ncheck('more seats than ballots', solve(1,N+2), 1)\ncheck('several seats', solve(20,3), 6)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"Abstract counting rules only; excludes jurisdictional law, ballot authentication and election operations. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"z-voting_rules-droop-quota","generated_at":"2026-09-29T14:38:59.926043+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"A deterministic toy ballot model makes the stated counting convention executable.","root_cause":"Ceiling division is substituted for floor plus one.","sha256":"647e1ef3f45a166d236215d242ea49081686323d609c1c46c1af7384858bc211","title":"An exact quotient omits the final quota increment · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":40.689,"exit_code":1,"observations":[{"actual":4,"check":"exact division","expected":3,"passed":false},{"actual":4,"check":"fractional division","expected":3,"passed":false},{"actual":1,"check":"zero ballots","expected":1,"passed":true},{"actual":3,"check":"one seat","expected":2,"passed":false},{"actual":1,"check":"more seats than ballots","expected":1,"passed":true},{"actual":7,"check":"several seats","expected":6,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"exact division\", \"actual\": 4, \"expected\": 3, \"passed\": false}, {\"check\": \"fractional division\", \"actual\": 4, \"expected\": 3, \"passed\": false}, {\"check\": \"zero ballots\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"one seat\", \"actual\": 3, \"expected\": 2, \"passed\": false}, {\"check\": \"more seats than ballots\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"several seats\", \"actual\": 7, \"expected\": 6, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":41.369,"exit_code":1,"observations":[{"actual":2,"check":"exact division","expected":3,"passed":false},{"actual":3,"check":"fractional division","expected":3,"passed":true},{"actual":0,"check":"zero ballots","expected":1,"passed":false},{"actual":1,"check":"one seat","expected":2,"passed":false},{"actual":1,"check":"more seats than ballots","expected":1,"passed":true},{"actual":5,"check":"several seats","expected":6,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"exact division\", \"actual\": 2, \"expected\": 3, \"passed\": false}, {\"check\": \"fractional division\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"zero ballots\", \"actual\": 0, \"expected\": 1, \"passed\": false}, {\"check\": \"one seat\", \"actual\": 1, \"expected\": 2, \"passed\": false}, {\"check\": \"more seats than ballots\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"several seats\", \"actual\": 5, \"expected\": 6, \"passed\": false}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}