Complexity of Judgment Aggregation

We analyse the computational complexity of three problems in judgment aggregation: (1) computing a collective judgment from a profile of individual judgments (the winner determination problem); (2) deciding whether a given agent can influence the outcome of a judgment aggregation procedure in her favour by reporting insincere judgments (the strategic manipulation problem); and (3) deciding whether a given judgment aggregation scenario is guaranteed to result in a logically consistent outcome, independently from what the judgments supplied by the individuals are (the problem of the safety of the agenda). We provide results both for specific aggregation procedures (the quota rules, the premisebased procedure, and a distance-based procedure) and for classes of aggregation procedures characterised in terms of fundamental axioms

Aggregazione di giudizi

L’aggregazione di opinioni individuali per formare una decisione collettiva è l’oggetto di studio di Judgment Aggregation, una disciplina che coinvolge logica, economia, filosofia politica ed informatica. Il problema della presa di decisione collettiva a partire da posizioni individuali è comune nella vita di tutti i giorni e, sebbene la procedura da seguire sembri evidente, i risultati possono nascondere paradossi sorprendenti. La formalizzazione del problema dell’aggregazione di giudizi individuali ha permesso di portare un buon numero di risposte, di evidenziare legami con la teoria della scelta sociale e l’aggregazione di credenze, e di aprire la strada a nuove ricerche che permettono di applicare buona parte dei risultati ad altri paradigmi della decisione collettiva. Obiettivo di questo lavoro è di introdurre il problema dell’aggregazione di giudizi, motivare l’interesse per tali questioni, presentando i risultati principali ottenuti e indicando alcune delle piste di ricerca attuali.The aggregation of individual opinions to form a collective decision is the object of study of Judgment Aggregation, a discipline involving logic, economics, political philosophy and computer science. The problem of collective decision-making from individual positions arises in everyday life and, although the procedure to follow seems evident, the results can hide surprising paradoxes. The formalization of the problem of the aggregation of individual judgements has made it possible to bring a good number of answers, to highlight links with social choice theory and the aggregation of beliefs, and to pave the way to new research that allows to apply most of the results to other paradigms of collective decision-making. The aim of this work is to introduce the problem of judgement aggregation, to motivate interest in such issues, presenting the main results obtained so far and highlighting some of the current research tracks

Unifying preference and judgment aggregation

The paper proposes a unification of the two main frameworks commonly used for the analysis of collective decision-making: the framework of preference aggregation, developed from the seminal work of K. Arrow on social choice theory; and the more recent framework of judgment aggregation. Such unification provides several original insights on collective decision-making problems. The methods used are based on logic and, in particular, on formal semantics