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We introduce the generalized priority-aware Shapley value (GPASV), a random order value defined on arbitrary directed weighted priority graphs, in which pairwise edges penalize rather than forbid order violations. GPASV covers a range of classical models as boundary cases. We establish GPASV through an axiomatic characterization, develop the associated computational methods, and introduce a priority sweeping diagnostic extending PASV's. We apply GPASV to LLM ensemble valuation on the cyclic Chatbot Arena preference graph, illustrating that priority-aware valuation is not a one-button operation: different balances of pairwise graph priority ","title":"Generalized Priority-Aware Shapley Value","url":"https://arxiv.org/abs/2605.15018","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.15018v1 Announce Type: cross \nAbstract: Shapley value and its priority-aware extensions are widely used for valuation in machine learning, but existing methods require pairwise priority to be binary and acyclic, a restriction spectacularly violated in real-data examples such as aggregated human preferences and multi-criterion comparisons. We introduce the generalized priority-aware Shapley value (GPASV), a random order value defined on arbitrary directed weighted priority graphs, in which pairwise edges penalize rather than forbid order violations. GPASV covers a range of classical models as boundary cases. We establish GPASV through an axiomatic characterization, develop the associated computational methods, and introduce a priority sweeping diagnostic extending PASV's. We apply GPASV to LLM ensemble valuation on the cyclic Chatbot Arena preference graph, illustrating that priority-aware valuation is not a one-button operation: different balances of pairwise graph priority ","title":"Generalized Priority-Aware Shapley Value","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-15T04:43:17Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.15018"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:b9659be551a1972b78b4d7155c207481a9a115e5041644a4bae4a3a1157a959e42381cd2914e02fe07a2240092109c823c24cb4e6ffe887a49cc186b51dbe70d","signer":"crovia.substrate","subject":{"observed_at":"2026-05-15T04:43:17Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.15018"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"48fdd0757b4e1fe56825c9733d8359b0ee03ec70f52953c77cc2c75676e58e8e","leaf_index":134655,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"bf6fc53efcd25515eafd065b719e605d5dbb15d0710558ad80f33206c5dae00d","side":"left"},{"sibling":"06b03e1a44704cad64e5564d95e5dfabb70ffdcc49e5ac553920390f6b22c09d","side":"left"},{"sibling":"34d31675403829c5903de980cae814c808703be9807781b6976f3d83386f516b","side":"left"},{"sibling":"a8e97968fcdc7d0ceda119a5a0a1eb9c9a12e0898651c0d5a3339c64a1817c8a","side":"left"},{"sibling":"1891d8d4400aa8e78756821136250c8966757bc95d1db730521fdcdffe155ee8","side":"left"},{"sibling":"d8a5a20d2c9f87798d5d5a7ddb6384d4d9c06d4b4e588b536b63981364617af9","side":"left"},{"sibling":"46f96cb7883dcb2712dad253af0583c5b367609f9717fd33426973df576e51f6","side":"left"},{"sibling":"cbbed0225164fe227925f0fc2929e9ecbc520f5a86b19035c412206d51935e10","side":"left"},{"sibling":"4711a7f4329f1874c3aa1ae93c336e1d4fa402bdd4b3d766c2a95304ea226882","side":"left"},{"sibling":"8ce2a4687a8ceb409df2e1cb10e44a610b21dc294e518a8550b6d1122335ca2b","side":"right"},{"sibling":"36672459e5ed50c64ee1842b69cb6d2eb682c2a04844555be8d124257571994a","side":"left"},{"sibling":"727783827652adfa99c455bd80a01bfb33836228e51068b4f654ef3da468ca69","side":"left"},{"sibling":"623194cd30880ed223e306737fdb111aa0d781751bfc47553c404a6af6aad2c4","side":"right"},{"sibling":"fc8f53ed42756907fb79ee19a4ed09f72c560e5302b3d98198b96bf1da635a4a","side":"right"},{"sibling":"d6607539da7ba39ec68be2d12f27ed6768766c745e3120fd915f88c5e288e07c","side":"right"},{"sibling":"b63408a424d27cd6a75e0fb155e69a58a328f41e9cb9dba1eddef9a5289cc7fd","side":"right"},{"sibling":"356fb36a4e188f03d7a05c54cd8789bdd40eda454b9bc9560f667acc08e6c4e0","side":"right"},{"sibling":"d841ad93efda0869e5eb97678f348f03f5caab4353e05ff4bf18f47fb945b822","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":134886,"merkle_root":"c6c7ae28c065bced89e7f844216b073f1a7cc4b378db0d41a98bcd21b28066db","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260515T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-15T05:37:26Z","sig_algorithm":"ed25519","signature":"5a3978c26017daf4104adbb3e1c3099c5750157acbfc7242ece1815dc6740fe08a690291ce0afe42011e20cc565b5ebe64ec016bf658b5bab563a63337985c05","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_0a52765274720fe0039314c14101fe4a38a034e4ad3a753cee0c527ab2331a22"}}