Pith Number

pith:YHQP46OP

pith:2025:YHQP46OPXV2K4JIX52HU56SSVD

not attested not anchored not stored refs pending

Equal Treatment of Equals and Efficiency in Probabilistic Assignments

Yasunori Okumura

Equal treatment of equals can be achieved together with ordinal efficiency in probabilistic assignments of indivisible objects.

arxiv:2508.14522 v4 · 2025-08-20 · econ.TH

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\usepackage{pith}
\pithnumber{YHQP46OPXV2K4JIX52HU56SSVD}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

Since the ETE reassignment of a rank-minimizing assignment preserves rank-minimizing efficiency, there must exist an assignment satisfying both ETE and ordinal efficiency. Furthermore, we propose a computationally efficient method for constructing assignments that satisfy both ETE and ordinal efficiency under general upper bound constraints by combining the serial dictatorship rule with appropriately specified priority lists and the ETE reassignment procedure.

C2weakest assumption

The ETE reassignment of a rank-minimizing assignment preserves rank-minimizing efficiency (abstract, paragraph on preservation results). If this preservation fails under the extended ETE definition or general constraints, the existence claim for joint ETE and ordinal efficiency would not follow.

C3one line summary

Extends equal treatment of equals to general multi-unit probabilistic assignments, introduces ETE reassignment that preserves ex-post and rank-minimizing efficiency, and provides a method to achieve both ETE and ordinal efficiency using serial dictatorship.

Formal links

1 machine-checked theorem link

Cited by

1 paper in Pith

A Simple Method for School Choice Lotteries

Receipt and verification

First computed	2026-05-20T00:00:22.752748Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c1e0fe79cfbd74ae2517ee8f4efa52a8c2bb994530d1a2226fc5ffba2c9ffc87

Aliases

arxiv: 2508.14522 · arxiv_version: 2508.14522v4 · doi: 10.48550/arxiv.2508.14522 · pith_short_12: YHQP46OPXV2K · pith_short_16: YHQP46OPXV2K4JIX · pith_short_8: YHQP46OP

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YHQP46OPXV2K4JIX52HU56SSVD \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: c1e0fe79cfbd74ae2517ee8f4efa52a8c2bb994530d1a2226fc5ffba2c9ffc87

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "306d84bdb0cf7506362a51bdb2ede45a6ae2b33de24eac7982758d52107b3a11",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "econ.TH",
    "submitted_at": "2025-08-20T08:31:22Z",
    "title_canon_sha256": "ecb0824743f810fb6a07052a94bcd84c9d20429a22b60bbc1f93bed58a606725"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.14522",
    "kind": "arxiv",
    "version": 4
  }
}