The Complexity Landscape of Outcome Determination in Judgment Aggregation

Abstract

We provide a comprehensive analysis of the computational complexity of the outcome determination problem for the most important aggregation rules proposed in the literature on logic-based judgment aggregation. Judgment aggregation is a powerful and flexible framework for studying problems of collective decision making that has attracted interest in a range of disciplines, including Legal Theory, Philosophy, Economics, Political Science, and Artificial Intelligence. The problem of computing the outcome for a given list of individual judgments to be aggregated into a single collective judgment is the most fundamental algorithmic challenge arising in this context. Our analysis applies to several different variants of the basic framework of judgment aggregation that have been discussed in the literature, as well as to a new framework that encompasses all existing such frameworks in terms of expressive power and representational succinctness.

Strategic manipulation in judgment aggregation under higher-level reasoning

“…The challenge posed by interactive reasoning is therefore apparent. It is known that computing the final outcome of an aggregation rule (taking certainty over the truthful judgments of the group for granted) is often intractable (Endriss et al, 2012(Endriss et al, , 2020-although this is not the case for the rules considered in this paper. Hence, one can imagine the difficulties that an individual would face for more complex rules when she has to compute, not only the outcomes compatible with her information, but also those that the rest of the group may consider possible according to the information each possesses, etc.…”

Designing Participatory Budgeting Mechanisms Grounded in Judgment Aggregation

“…In this section we present specific embeddings of enriched PB instances into JA. Given that the problem of computing outcomes for the JA rules defined in Section 2.2 is known to be highly intractable (Lang and Slavkovik, 2014;Endriss and De Haan, 2015), we need to ensure that PB instances are mapped into JA instances that permit efficient outcome determination. To this end, we first present a class of Boolean functions (to encode integrity constraints) for which the outcome determination can be solved efficiently.…”

Egalitarian Judgment Aggregation

“…For the latter, we are interested in exploring how computationally complex its use is in the worst-case scenario. This kind of question, first addressed by Endriss et al [28], is regularly asked in the literature of judgment aggregation [5,25,51]. As Endriss et al [26] wrote recently, the problem of determining the collective outcome of a given judgment aggregation rule is "the most fundamental algorithmic challenge in this context".…”