26 January 2023, Computational Social Choice Seminar, Julian Chingoma

Abstract

Proportionality is a fairness notion that has been extensively studied in the context of apportionment and multiwinner voting. Recent strides have also been made in adapting proportionality to the richer setting of Participatory Budgeting (PB) where citizens decide on the public projects, each having a cost, that are to be chosen with respect to some budget. In light of the work done in PB, we explore the possibilities of introducing proportionality to other, more complex, settings. In this work, we deal with two such settings, where for each, we aim to define a reasonable proportionality axiom and then investigate whether certain rules designed for the setting satisfy this axiom. The first setting is that of Judgment Aggregation (JA), a general framework fitted with logical constraints that make it a challenging task to develop natural proportionality notions for it. The second setting that we look at is a slight generalisation of approval-based multiwinner voting where instead of the committee seats being treated equally, each seat on the committee is now associated with some weight. This latter setting naturally models scenarios where specific seats, such as the seat held by the committee's chair, are of greater value, and thus have more weight, than ordinary committee seats.
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