Piotr Skowron : Proportionality and the Limits of Welfarism

22 novembre à 14h, en salle P505.

 

Proportionality and the Limits of Welfarism (with D. Peters)

Resumé: We study two influential voting rules proposed in the 1890s by Phragmen and Thiele,
which elect a committee or parliament of k candidates which proportionally represents
the voters. Voters provide their preferences by approving an arbitrary number of candidates. Previous work has proposed proportionality axioms satisfied by Thiele but not Phragmen. By proposing two new proportionality axioms (laminar proportionality and priceability) satisfied by Phragmen but not Thiele, we show that the two rules achieve two distinct forms of proportional representation. Phragmen's rule ensures that all voters have a similar amount of influence on the committee, and Thiele's rule ensures a fair utility distribution. Thiele's rule is a welfarist voting rule (one that maximizes a function of voter utilities). We show that no welfarist rule can satisfy our new axiom, and we prove that no such rule can satisfy the core. Conversely, some welfarist fairness properties cannot be guaranteed by Phragm\'en-type rules. This formalizes the difference between the two types of proportionality. We then introduce an attractive committee rule which satisfies a property intermediate between the core and extended justified representation (EJR). It satisfies laminar proportionality, priceability, and is computable in polynomial time. We show that PAV provides a multiplicative approximation to the core: there does not exist a deviation in which all coalition members increase their utility by a factor of more than 2. Our new rule provides a logarithmic approximation.