Computational Intelligence, Volume , Number 000, 2015 A Hierarchical Approach for Judgment Aggregation with Abstentions GUIFEI J IANG AIRG, Western Sydney University, Australia IRIT, Universit´ e Toulouse Capitole, France DONGMO ZHANG AIRG, Western Sydney University, Australia LAURENT PERRUSSEL IRIT, Universit´ e Toulouse Capitole, France Judgment aggregation deals with the problem of how collective judgments on logically connected propositions can be formed based on individual judgments on the same propositions. The existing literature on judgment aggregation mainly focuses on the anonymity condition requiring that individual judgments be treated equally. However, in many real-world situations, a group making collective judgments may assign individual members or subgroups different priorities to determine the collective judgment. Based on this consideration, this paper relaxes the anonymity condition by giving a hierarchy over individuals so as to investigate how the judgment from each individual affects the group judgment in such a hierarchical environment. Moreover, we assume that an individual can abstain from voting on a proposition and the collective judgment on a proposition can be undetermined, which means that we do not require completeness at both individual and collective levels. In this new setting, we first identify an impossibility result and explore a set of plausible conditions in terms of abstentions. Secondly, we develop an aggregation rule based on the hierarchy of individuals and show that the aggregation rule satisfies those plausible conditions. The computational complexity of this rule is also investigated. Finally, we show that the proposed rule is (weakly) oligarchic over a subset of agenda. This is by no means a negative result. In fact, our result reveals that with abstentions, oligarchic aggregation is not necessary to be a single-level determination but can be a multiple-level collective decision-making, which partially explains its ubiquity in the real world. Key words: Judgement Aggregation, Lexicographic Aggregation Rule, Computational Social Choice. 1. INTRODUCTION Judgment aggregation is an interdisciplinary research topic in economics, philosophy, political science, law and recently in computer science (Dietrich and List, 2007a; Mongin, 1995; Pigozzi, 2006; Wilson, 1975; Konieczny and P´ erez, 2002; Brandt et al., 2013). It deals with the problem of how a set of group judgments on certain issues, represented by logical propositions, can be formed based on individuals’ judgments on the same issues. Although most of voting rules for social choice, such as majority rules, unanimity rules or Address correspondence to Dongmo Zhang, AIRG, Western Sydney University, Y.3.30, Penrith, NSW 2751, AU; to Guifei Jiang and Laurent Perrussel, Bureau ME305 - 2, rue du doyen Gabriel Marty, 31042 Toulouse Cedex, France. ✐ C 2015 The Authors. Journal Compilation ✐ C 2015 Wiley Periodicals, Inc.