Judgment aggregation theory studies how to amalgamate individual opinions on a set of logically related issues into a set of collective opinions. Aggregation rules proposed in the literature are sparse. All proposed rules consider only two-valued judgments, thus imposing the strong requirement that an agent cannot abstain from giving judgments on any of the issues. All proposed rules are also insensitive to weights that can be assigned to different judgments. We construct a family of weight-sensitive rules for aggregating individual judgment sets with abstentions. We do so by generalizing known distance-based judgment aggregation rules. We study the relations between existing distance-based rules and the rules we propose and the computational complexity of the winner determination problem.
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