Session Title
Designing Allocation Mechanisms Under Informational Frictions
Topic
Auctions and Market Design Section
Co-Topic 1
Auctions and Market Design Section
Co-Topic 2
Auctions and Market Design Section

Approval-Based Apportionment: Like Portioning, Approximately like Committee Voting

9:30 AM - 9:45 AM
Program Number: 1
Hannane Yaghoubizade, Cornell University; Paul Goelz, Cornell University.
We study approval-based apportionment, a variant of committee elections in which candidates ("parties") can be selected several times.
We show that the proportionality axioms EJR, EJR+, and FJR coincide, and so do PJR, PJR+, and FPJR; that Lindahl priceability, an axiom implying core stability, is equivalent to a notion of approximate optimality with respect to the proportional approval voting (PAV) score; and that locally PAV-optimal committees are priceable.

Approval-based apportionment (where a candidate receives an integer number of seats) lies between committee elections (zero or one seat) and portioning (a fractional number of seats).
We formally connect portioning and apportionment by giving a construction that lifts axioms from apportionment to portioning and preserves implications between them.
Several of our new implications between apportionment axioms are natural from a portioning perspective, leading us to believe that apportionment sits closer to portioning than to committee elections.
None of them holds in committee elections, but several extend approximately, which makes apportionment a fruitful setting for conjecturing approximate relationships in approval-based committee elections.