Proportionality and the Limits of Welfarism

@article{Peters2019ProportionalityAT,
  title={Proportionality and the Limits of Welfarism},
  author={Dominik Peters and Piotr Skowron},
  journal={Proceedings of the 21st ACM Conference on Economics and Computation},
  year={2019},
  url={https://api.semanticscholar.org/CorpusID:208291203}
}
An attractive committee rule is introduced which satisfies a property intermediate between the core and extended justified representation (EJR), and is computable in polynomial time, and it is shown that the new rule provides a logarithmic approximation to the core.
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Background Citations
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Methods Citations
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26 References

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This work investigates a number of election rules and investigates whether the committees that they return represent the voters proportionally, and measures the tradeoff between proportionality and utilitarian efficiency for a broad subclass of committee election rules.

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The development of social choice theory over the past three decades has brought many new insights into democratic theory. Surprisingly, the theory of representation has gone almost untouched by…

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It is shown that the sequential variant of Phragmén’s methods satisfies proportional justified representation, which is a rare property for committee monotonic methods.

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The main result is to show that stable lotteries always exist for these canonical voter preference models, and the procedure for computing an approximately stable lottery is the same for both models and therefore extends to the setting where some voters have the former preference structure and others have the latter.

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Proportional Justified Representation is proposed, which is more demanding than JR, but, unlike EJR, it is compatible with perfect representation, and a committee that provides PJR can be computed in polynomial time if the committee size divides the number of voters.

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This paper introduces the class of counting rules, provides an axiomatic characterization of this class and shows that counting rules are consistent, and axiomatically characterize three important consistent multi-winner rules: Proportional Approval Voting, Multi-Winner Approval voting and the Approval Chamberlin--Courant rule.

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EJR and PJR have the same worst-case complexity: the former is provided with two polynomial-time algorithms that output committees providing EJR, yet it is shown that it is coNP-complete to decide whether a given committee provides PJR.

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The computational complexity of computing a best response for both a single agent and a group of agents is examined, showing that it is NP-hard for an agent or agents to compute how to vote given a fixed set of approval ballots of the other agents.

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