Pith Number

pith:2MSZS5PR

pith:2026:2MSZS5PRAMEXOACADCOE2I3A7G

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The End Justifies the Mean: A Linear Ranking Rule for Proportional Sequential Decisions

Bailey Flanigan, Carmel Baharav, Maximilian T. Wittmann, Niclas Boehmer

The angular mean of voter vectors satisfies long-run individual proportionality for repeated linear rankings.

arxiv:2605.12717 v1 · 2026-05-12 · cs.GT · cs.AI

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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

Our main result is that, surprisingly, there is a simple rule that does satisfy long-run IP: the angular mean, the spherical analog of the arithmetic mean.

C2weakest assumption

That long-run average proportionality is acceptable even when per-batch outcomes can deviate substantially, and that voter preferences remain fixed across batches.

C3one line summary

The angular mean of voter scoring vectors satisfies long-run individual proportionality for sequential linear ranking decisions.

References

50 extracted · 50 resolved · 0 Pith anchors

[1] On the convergence of gradient descent for finding the Riemannian center of mass 2013

[2] The moral machine experiment 2018

[3] On the stability of moral preferences: A problem with computational elicitation methods 2024

[4] Optimal budget aggregation with single-peaked preferences 2024

[5] Justified representation for perpetual voting 2021

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-18T03:09:49.458299Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3259975f10309770040189c4d2360f990301ce34659fd7fb2556c9e10e25da3

Aliases

arxiv: 2605.12717 · arxiv_version: 2605.12717v1 · doi: 10.48550/arxiv.2605.12717 · pith_short_12: 2MSZS5PRAMEX · pith_short_16: 2MSZS5PRAMEXOACA · pith_short_8: 2MSZS5PR

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/2MSZS5PRAMEXOACADCOE2I3A7G \
  | 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: d3259975f10309770040189c4d2360f990301ce34659fd7fb2556c9e10e25da3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d75dc86c1844e7a8dd84391413281390a657c75edf6c0027e3995c1dc7b68d8d",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2026-05-12T20:26:37Z",
    "title_canon_sha256": "2033f25ac2c4fe99f6388d8642007658c5c673bb3d92d64cc7094117ca7b4ffc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12717",
    "kind": "arxiv",
    "version": 1
  }
}