On Compatible Multi-issue Group Decisions

A crucial problem in the design of multi-issue group decisions is the definition of rules that select outputs that are consistent with existing correlations between multiple issues. A less known problem arises when the collective outcome is supported by none or by the fewest individuals, bringing into question the compatibility of a collective decision with respect to individual choices. The aim of this paper is to make a first step into providing a definition of compatible outcome for binary aggregation procedures. We provide several definitions of compatibility, both for complete binary ballots and for the more general case of allowing abstentions in the individual judgments. We define a number of rules that draw inspiration from the literature on argumentation theory, social choice theory and belief merging, and for each of these rules we investigate their behaviour with respect to compatibility and consistency, and we study their social choice theoretic properties.