Optimal Apportionment

@article{Koriyama2013OptimalA,
  title={Optimal Apportionment},
  author={Yukio Koriyama and Antonin Mac{\'e} and Rafael Treibich and Jean-François Laslier},
  journal={Journal of Political Economy},
  year={2013},
  volume={121},
  pages={584 - 608}
}
This paper provides a theoretical foundation that supports the degressive proportionality principle in apportionment problems, such as the allocation of seats in a federal parliament. The utility assigned by an individual to a constitutional rule is a function of the frequency with which each collective decision matches the individual’s own will. The core of the argument is that, if the function is concave, then classical utilitarianism at the social level recommends decision rules that exhibit… 
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References

SHOWING 1-10 OF 87 REFERENCES
The measurement of voting power
This book is the first of its kind: a monograph devoted to a systematic critical examination and exposition of the theory of a priori voting power. This important branch of social-choice theory
Majority Efficient Representation of the Citizens in a Federal Union
All the federal unions, like the United States of America or the European Union, face the issue of finding a “good” indirect voting mechanism. In particular, a crucial question is to know how many
Welfarist evaluations of decision rules for boards of representatives
We consider a decision board with representatives who vote on proposals on behalf of their constituencies. We look for decision rules that realize utilitarian and (welfarist) egalitarian ideals. We
On the Weights of Nations: Assigning Voting Weights in a Heterogeneous Union
We study indirect democracy in which countries, states, or districts each elect a representative who later votes at a union level on their behalf. We show that the voting rule that maximizes the
One stake one vote ∗
The weighted majority rule, which is widely applied — much more than the simple majority rule — has good properties when the weights reflect the stakes of the voters in the decision. These properties
Assessing success and decisiveness in voting situations
TLDR
This basic model for measuring ‘success’ or ‘decisiveness’ in voting situations provides a clear common conceptual basis for reinterpreting different power indices and some related game theoretic notions coherently from a unified point of view.
...
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