{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:FZDYEQOCS7CFJBV6UWJZQTYMLZ","short_pith_number":"pith:FZDYEQOC","schema_version":"1.0","canonical_sha256":"2e478241c297c45486bea593984f0c5e6a0b875f3501434c89fa8e2b702d842b","source":{"kind":"arxiv","id":"1307.1252","version":1},"attestation_state":"computed","paper":{"title":"The Complexity of Fully Proportional Representation for Single-Crossing Electorates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.MA"],"primary_cat":"cs.GT","authors_text":"Edith Elkind, Lan Yu, Piotr Faliszewski, Piotr Skowron","submitted_at":"2013-07-04T09:33:24Z","abstract_excerpt":"We study the complexity of winner determination in single-crossing elections under two classic fully proportional representation rules---Chamberlin--Courant's rule and Monroe's rule. Winner determination for these rules is known to be NP-hard for unrestricted preferences. We show that for single-crossing preferences this problem admits a polynomial-time algorithm for Chamberlin--Courant's rule, but remains NP-hard for Monroe's rule. Our algorithm for Chamberlin--Courant's rule can be modified to work for elections with bounded single-crossing width. To circumvent the hardness result for Monroe"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1307.1252","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-07-04T09:33:24Z","cross_cats_sorted":["cs.MA"],"title_canon_sha256":"543145c8139ae59ba0b8054bb00b669f9af48b7a02303c1fd0cec833d9ceb2f7","abstract_canon_sha256":"1eab8d42cf3fec01f1875d4d7748c0a22729055fe54a66f907ff1cf3b3be0360"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:14.284897Z","signature_b64":"rriYdNVVTCP7xRAakf7AQLpdqEDWeasnnHd2LBuxl3lTvgD2aJwb3OTDa7GiK8nE1zbWIqGsPA+96aqrbHmxDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e478241c297c45486bea593984f0c5e6a0b875f3501434c89fa8e2b702d842b","last_reissued_at":"2026-05-18T03:19:14.284087Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:14.284087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Complexity of Fully Proportional Representation for Single-Crossing Electorates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.MA"],"primary_cat":"cs.GT","authors_text":"Edith Elkind, Lan Yu, Piotr Faliszewski, Piotr Skowron","submitted_at":"2013-07-04T09:33:24Z","abstract_excerpt":"We study the complexity of winner determination in single-crossing elections under two classic fully proportional representation rules---Chamberlin--Courant's rule and Monroe's rule. Winner determination for these rules is known to be NP-hard for unrestricted preferences. We show that for single-crossing preferences this problem admits a polynomial-time algorithm for Chamberlin--Courant's rule, but remains NP-hard for Monroe's rule. Our algorithm for Chamberlin--Courant's rule can be modified to work for elections with bounded single-crossing width. To circumvent the hardness result for Monroe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1252","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1307.1252","created_at":"2026-05-18T03:19:14.284226+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.1252v1","created_at":"2026-05-18T03:19:14.284226+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1252","created_at":"2026-05-18T03:19:14.284226+00:00"},{"alias_kind":"pith_short_12","alias_value":"FZDYEQOCS7CF","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"FZDYEQOCS7CFJBV6","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"FZDYEQOC","created_at":"2026-05-18T12:27:45.050594+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FZDYEQOCS7CFJBV6UWJZQTYMLZ","json":"https://pith.science/pith/FZDYEQOCS7CFJBV6UWJZQTYMLZ.json","graph_json":"https://pith.science/api/pith-number/FZDYEQOCS7CFJBV6UWJZQTYMLZ/graph.json","events_json":"https://pith.science/api/pith-number/FZDYEQOCS7CFJBV6UWJZQTYMLZ/events.json","paper":"https://pith.science/paper/FZDYEQOC"},"agent_actions":{"view_html":"https://pith.science/pith/FZDYEQOCS7CFJBV6UWJZQTYMLZ","download_json":"https://pith.science/pith/FZDYEQOCS7CFJBV6UWJZQTYMLZ.json","view_paper":"https://pith.science/paper/FZDYEQOC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.1252&json=true","fetch_graph":"https://pith.science/api/pith-number/FZDYEQOCS7CFJBV6UWJZQTYMLZ/graph.json","fetch_events":"https://pith.science/api/pith-number/FZDYEQOCS7CFJBV6UWJZQTYMLZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FZDYEQOCS7CFJBV6UWJZQTYMLZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FZDYEQOCS7CFJBV6UWJZQTYMLZ/action/storage_attestation","attest_author":"https://pith.science/pith/FZDYEQOCS7CFJBV6UWJZQTYMLZ/action/author_attestation","sign_citation":"https://pith.science/pith/FZDYEQOCS7CFJBV6UWJZQTYMLZ/action/citation_signature","submit_replication":"https://pith.science/pith/FZDYEQOCS7CFJBV6UWJZQTYMLZ/action/replication_record"}},"created_at":"2026-05-18T03:19:14.284226+00:00","updated_at":"2026-05-18T03:19:14.284226+00:00"}