Judgment Aggregation with Abstentions: A Hierarchical Approach

Judgment Aggregation with Abstentions under Voters’ Hierarchy

“…The next condition is the counterpart of Unanimity with Abstentions in [21] which is restricted to literals.…”

“…However, this by no means is a negative result. In fact, our previous work [21] demonstrates that with abstentions, oligarchic aggregation is no longer a single level determination but can also be a multiple-level democracy, which partially explains its pervasiveness in the real world.…”

“…However, such kind of expert rights has been rarely investigated in the current literature [22], let alone proposing a specific judgment aggregation rule to formally display how the hierarchical groups generate the group judgments. In [21] we deal with this issue by proposing a quasi-lexicographic judgment aggregation rule which works well over the limited agenda. It mainly focuses on the following two questions: How does the hierarchical group generate the group judgments?…”

“…We focus on judgment aggregation with abstentions under voter's hierarchy. Our contributions can be summarized in the following: First, we amend the"plausible" conditions in [21], which allows us to extend the set of propositions on which the quasi-lexicographic rule works well from a set of literals to logically interconnected formulas; Secondly, we propose a feasible literal-based aggregation rule for judgment aggregation with abstentions under voter's hierarchy, and show that it is neither dictatorial nor oligarchic over the whole set of agenda; Last but not least, to some extent, we circumvent the impossibility result in [23] by removing completeness from the requirements of both individual and collective levels.…”

“…In section 3, we list the conditions that sound natural in the context of abstentions and compare them with their counterparts in [19][20][21]. In Section 4, we propose a literal-based lexicographic judgment aggregation procedure and investigate its properties.…”