A hierarchical approach for judgment aggregation with abstentions

Guifei Jiang, Dongmo Zhang, Laurent Perrussel

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

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 article 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.
Original languageEnglish
Pages (from-to)104-123
Number of pages19
JournalComputational Intelligence
Volume34
Issue number1
DOIs
Publication statusPublished - 2018

Keywords

  • artificial intelligence
  • group decision making
  • rational choice theory
  • social choice

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