{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:QBAKEPHLNP5JX5WDDW3WM7JTFR","short_pith_number":"pith:QBAKEPHL","schema_version":"1.0","canonical_sha256":"8040a23ceb6bfa9bf6c31db7667d332c572d16946041cd03c922d6bef0572f91","source":{"kind":"arxiv","id":"2401.12547","version":1},"attestation_state":"computed","paper":{"title":"Arrow's single peaked domains, richness, and domains for plurality and the Borda count","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"econ.TH","authors_text":"Bei Zhou, Klas Markstr\\\"om, S{\\o}ren Riis","submitted_at":"2024-01-23T08:09:07Z","abstract_excerpt":"In this paper we extend the study of Arrow's generalisation of Black's single-peaked domain and connect this to domains where voting rules satisfy different versions of independence of irrelevant alternatives.\n  First we report on a computational generation of all non-isomorphic Arrow's single-peaked domains on $n\\leq 9$ alternatives. Next, we introduce a quantitative measure of richness for domains, as the largest number $r$ such that every alternative is given every rank between 1 and $r$ by the orders in the domain. We investigate the richness of Arrow's single-peaked domains and prove that"},"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":"2401.12547","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"econ.TH","submitted_at":"2024-01-23T08:09:07Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"9e209e574e501ee34ba27f0cce59fffbd21cb3e1c48a6cba16e36e8429938023","abstract_canon_sha256":"3a85b0178b8e0ab68b7e4781f69d7a9d74d832c6b8741afabecbbf0ff0c60f50"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:36:32.324502Z","signature_b64":"ZnIUlj0tZicI+0ITZNJf/BXes/0F4x8/U9G4YLABcTQ/73ePyKjZ/pYRZBq5LF2VTv5o9UJFne8T9SKYufHLAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8040a23ceb6bfa9bf6c31db7667d332c572d16946041cd03c922d6bef0572f91","last_reissued_at":"2026-07-05T07:36:32.324068Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:36:32.324068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Arrow's single peaked domains, richness, and domains for plurality and the Borda count","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"econ.TH","authors_text":"Bei Zhou, Klas Markstr\\\"om, S{\\o}ren Riis","submitted_at":"2024-01-23T08:09:07Z","abstract_excerpt":"In this paper we extend the study of Arrow's generalisation of Black's single-peaked domain and connect this to domains where voting rules satisfy different versions of independence of irrelevant alternatives.\n  First we report on a computational generation of all non-isomorphic Arrow's single-peaked domains on $n\\leq 9$ alternatives. Next, we introduce a quantitative measure of richness for domains, as the largest number $r$ such that every alternative is given every rank between 1 and $r$ by the orders in the domain. We investigate the richness of Arrow's single-peaked domains and prove that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.12547","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.12547/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2401.12547","created_at":"2026-07-05T07:36:32.324129+00:00"},{"alias_kind":"arxiv_version","alias_value":"2401.12547v1","created_at":"2026-07-05T07:36:32.324129+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.12547","created_at":"2026-07-05T07:36:32.324129+00:00"},{"alias_kind":"pith_short_12","alias_value":"QBAKEPHLNP5J","created_at":"2026-07-05T07:36:32.324129+00:00"},{"alias_kind":"pith_short_16","alias_value":"QBAKEPHLNP5JX5WD","created_at":"2026-07-05T07:36:32.324129+00:00"},{"alias_kind":"pith_short_8","alias_value":"QBAKEPHL","created_at":"2026-07-05T07:36:32.324129+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.20629","citing_title":"An axiomatic framework from splitting and merging in MAT-labeled graphs, vines, and single-peaked domains","ref_index":19,"is_internal_anchor":false},{"citing_arxiv_id":"2605.20629","citing_title":"An axiomatic framework from splitting and merging in MAT-labeled graphs, vines, and single-peaked domains","ref_index":17,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QBAKEPHLNP5JX5WDDW3WM7JTFR","json":"https://pith.science/pith/QBAKEPHLNP5JX5WDDW3WM7JTFR.json","graph_json":"https://pith.science/api/pith-number/QBAKEPHLNP5JX5WDDW3WM7JTFR/graph.json","events_json":"https://pith.science/api/pith-number/QBAKEPHLNP5JX5WDDW3WM7JTFR/events.json","paper":"https://pith.science/paper/QBAKEPHL"},"agent_actions":{"view_html":"https://pith.science/pith/QBAKEPHLNP5JX5WDDW3WM7JTFR","download_json":"https://pith.science/pith/QBAKEPHLNP5JX5WDDW3WM7JTFR.json","view_paper":"https://pith.science/paper/QBAKEPHL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2401.12547&json=true","fetch_graph":"https://pith.science/api/pith-number/QBAKEPHLNP5JX5WDDW3WM7JTFR/graph.json","fetch_events":"https://pith.science/api/pith-number/QBAKEPHLNP5JX5WDDW3WM7JTFR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QBAKEPHLNP5JX5WDDW3WM7JTFR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QBAKEPHLNP5JX5WDDW3WM7JTFR/action/storage_attestation","attest_author":"https://pith.science/pith/QBAKEPHLNP5JX5WDDW3WM7JTFR/action/author_attestation","sign_citation":"https://pith.science/pith/QBAKEPHLNP5JX5WDDW3WM7JTFR/action/citation_signature","submit_replication":"https://pith.science/pith/QBAKEPHLNP5JX5WDDW3WM7JTFR/action/replication_record"}},"created_at":"2026-07-05T07:36:32.324129+00:00","updated_at":"2026-07-05T07:36:32.324129+00:00"}