Reference health
Optimal Apportionment
22/22 checkable references clean · checked 2026-08-07
Every reference with a DOI in the deposited reference list resolved to a known work in Crossref or DataCite at the dated check, and none carried a retraction, withdrawal, or removal notice.
13 without a DOI — not checked. A reference deposited without a DOI is never matched by title or guessed at; it stays outside the checked set, and this line discloses that.
The 22 checked references that resolve
resolves10.1007/s00355-007-0246-z
Welfarist evaluations of decision rules for boards of representatives
resolves10.1007/s00355-009-0399-z
Welfarist evaluations of decision rules under interstate utility dependencies
resolves10.1016/S0165-4896(98)00011-0
Minimizing the mean majority deficit: The second square-root rule
resolves10.1016/j.mathsocsci.2011.11.004
Voting power in the EU council of ministers and fair decision making in distributive politics
resolves10.1016/j.mathsocsci.2011.10.007
Computing the optimal weights in a utilitarian model of apportionment
resolves10.1016/j.mcm.2008.05.026
Several methods for degressively proportional allotments. A case study
resolves10.1007/s11238-012-9310-y
The doctrinal paradox, the discursive dilemma, and logical aggregation theory
resolves10.4000/msh.11904
Mesure des inégalités et dominance sociale : un chassé-croisé entre économistes et mathématiciens
The 13 references without a DOI — listed, not checked
no DOI — not checkedThe Works of Jeremy Bentham
no DOI — not checked2010. Institutional Design and Voting Power in the European Union
no DOI — not checkedEssai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix
no DOI — not checkedComm. Constitutional Affairs, European Parliament
no DOI — not checkedComm. Constitutional Affairs, European Parliament
no DOI — not checkedHandbook of Social Choice and Welfare
no DOI — not checkedManuscript
no DOI — not checkedOne Stake One Vote
no DOI — not checkedEuropean Parliament: The Cambridge Compromise.
no DOI — not checkedEconomic Analysis and Moral Philosophy
no DOI — not checkedFreedom in Economics: New Perspectives in Normative Analysis, edited by J.-F. Laslier, M. Fleurbaey, N. Gravel, and A. Trannoy, 17–44.
no DOI — not checkedMathematics and Democracy—Recent Advances in Voting Systems and Collective Choice
no DOI — not checkedInstitutional Design and Voting Power in the
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work were clean at the dated check: each resolved to a known work in a public registry, and none
carried a retraction notice at that time. It says nothing about the quality, findings,
or importance of the work itself, and nothing about references deposited without a DOI.
checked 2026-08-07 — re-checked daily as this page is visited; titles and statuses come from Crossref and DataCite and are not part of the signed record
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