Egalitarian judgment aggregation

Egalitarian considerations play a central role in many areas of social choice theory. Applications of egalitarian principles range from ensuring everyone gets an equal share of a cake when deciding how to divide it, to guaranteeing balance with respect to gender or ethnicity in committee elections. Yet, the egalitarian approach has received little attention in judgment aggregation—a powerful framework for aggregating logically interconnected issues. We make the first steps towards filling that gap. We introduce axioms capturing two classical interpretations of egalitarianism in judgment aggregation and situate these within the context of existing axioms in the pertinent framework of belief merging. We then explore the relationship between these axioms and several notions of strategyproofness from social choice theory at large. Finally, a novel egalitarian judgment aggregation rule stems from our analysis; we present complexity results concerning both outcome determination and strategic manipulation for that rule.publishedVersio

Egalitarian Judgment Aggregation

Egalitarian considerations play a central role in many areas of social choice theory. Applications of egalitarian principles range from ensuring everyone gets an equal share of a cake when deciding how to divide it, to guaranteeing balance with respect to gender or ethnicity in committee elections. Yet, the egalitarian approach has received little attention in judgment aggregation -- a powerful framework for aggregating logically interconnected issues. We make the first steps towards filling that gap. We introduce axioms capturing two classical interpretations of egalitarianism in judgment aggregation and situate these within the context of existing axioms in the pertinent framework of belief merging. We then explore the relationship between these axioms and several notions of strategyproofness from social choice theory at large. Finally, a novel egalitarian judgment aggregation rule stems from our analysis; we present complexity results concerning both outcome determination and strategic manipulation for that rule.Comment: Extended version of paper in proceedings of the 20th International Conference on Autonomous Agents and Multiagent Systems (AAMAS), 202

Multi-Issue Opinion Diffusion under Constraints

Most existing models of opinion diffusion on networks neglect the existence of logical constraints that might correlate individual opinions on multiple issues. In this paper we study the diffusion of constrained opinions on a social network as an iterated process of aggregating neighbouring opinions. Individual views are modelled as vectors of yes/no answers to a number of propositions subject to integrity constraints, and each individual updates her opinion by looking at the aggregated opinion of her influencers. To overcome the problem of updating towards inconsistent influencing opinions, we propose a model based on individual updates on subsets of the issues of limited size called propositionwise updates. By adapting notions from the theory of boolean functions, we identify classes of integrity constraints on which propositionwise updates decrease the influence gap between nodes of the network and their influencers caused by the presence of an integrity constraint. Furthermore, we provide a detailed study of the termination of the proposed diffusion processes