Pith Number

pith:5M2RONR5

pith:2025:5M2RONR5EXJRB6BMUHNWBRYKGW

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Centralization and Stability in Formal Constitutions

Yotam Gafni

Only dictatorships are self-maintaining when social choice functions can vote to replace themselves.

arxiv:2512.22051 v2 · 2025-12-26 · econ.TH · cs.GT

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Claims

C1strongest claim

For the i.i.d. unbiased case with arbitrary tie-breaking and general Boolean functions, we prove an Arrow-Style Theorem for Dynamics: We show that only a dictatorship is self-maintaining, and any other SCF has a path of changes that arrives at a dictatorship.

C2weakest assumption

Agents vote according to their ex-ante belief over what decisions are considered, and whether they prefer them to be decided by the incumbent SCF or the suggested replacement.

C3one line summary

Only dictatorships are self-maintaining under i.i.d. unbiased beliefs with arbitrary tie-breaking, while rules with minimal winning coalitions of size at most 2 are stable under pessimistic beliefs and status-quo tie-breaking.

References

54 extracted · 54 resolved · 0 Pith anchors

[1] D. Acemoglu and J. A. Robinson. A theory of political transitions.American Economic Review, 91(4):938–963, 2001 2001

[2] K. J. Arrow. A difficulty in the concept of social welfare.Journal of political economy, 58(4): 328–346, 1950 1950

[4] J. Austgen, A. Fábrega, S. Allen, K. Babel, M. Kelkar, and A. Juels. Dao decentralization: Voting-bloc entropy, bribery, and dark daos, 2023. URLhttps://arxiv.org/abs/2311.03530 2023

[5] Y. Azrieli and S. Kim. On the self-(in)stability of weighted majority rules.Games and Economic Behavior, 100:376–389, 2016. ISSN 0899-8256. https://doi.org/https://doi.org/10.1016/j.geb.2016.10.010. U 2016 · doi:10.1016/j.geb.2016.10.010

[6] M. Bahrani, P. Garimidi, and T. Roughgarden. When Bidders Are DAOs. In J. Bonneau and S. M. Weinberg, editors,5th Conference on Advances in Financial Technologies (AFT 2023), volume 282 ofLeibniz Inte 2023 · doi:10.4230/lipics.aft.2023.21

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:00.364553Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eb3517363d25d310f82ca1db60c70a358918ed71f7d8d14d4446412441f4639c

Aliases

arxiv: 2512.22051 · arxiv_version: 2512.22051v2 · doi: 10.48550/arxiv.2512.22051 · pith_short_12: 5M2RONR5EXJR · pith_short_16: 5M2RONR5EXJRB6BM · pith_short_8: 5M2RONR5

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5M2RONR5EXJRB6BMUHNWBRYKGW \
  | 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: eb3517363d25d310f82ca1db60c70a358918ed71f7d8d14d4446412441f4639c

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "986b61cf744df2e59120df9bda40ae498b7793b64738339b5b960e983b66eb6b",
    "cross_cats_sorted": [
      "cs.GT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "econ.TH",
    "submitted_at": "2025-12-26T15:02:32Z",
    "title_canon_sha256": "f2e0d46b4041633b0ecd9bf6e1bf4c026c4c46a19e4f63da920a7c85b4a93a55"
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  "source": {
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    "kind": "arxiv",
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