20 October 2022, Computational Social Choice Seminar, Jan Maly

Abstract

The ability to measure the satisfaction of (groups of) voters is a crucial prerequisite for formulating proportionality axioms in approval-based participatory budgeting elections. Two common - but very different - ways to measure the satisfaction of a voter consider (i) the number of approved projects and (ii) the total cost of approved projects, respectively. In general, it is difficult to decide which measure of satisfaction best reflects the voters' true utilities. The goal of the presented work is, to define proportionality axioms with respect to large classes of approval-based satisfaction functions. I will establish logical implications among these axioms and related notions from the literature, and ask whether outcomes can be achieved that are proportional with respect to more than one satisfaction function. I will show that this is impossible for the two commonly used satisfaction functions when considering proportionality notions based on extended justified representation, but achievable for a notion based on proportional justified representation. For the latter result, I will introduce a strengthening of priceability and show that it is satisfied by several polynomial-time computable rules, including the Method of Equal Shares and Phragmén's sequential rule.

For more information on the Computational Social Choice Seminar, please consult https://staff.science.uva.nl/u.endriss/seminar/.