Abstract
We explore how judgment aggregation and belief merging in the framework of fuzzy logic can help resolve the “Doctrinal Paradox.” We also illustrate the use of fuzzy aggregation functions in social choice theory.
Highlights
Social choice theory defines “preference aggregation” as forming collective preferences over a given set of alternatives
The doctrinal paradox can emerge when the members of a group have to make a judgment on several logically interconnected propositions, and the individually logically consistent judgments need to be combined into a collective decision
In some decision problems, propositions are “vague” and can have truth values between “true” and “false.” This might be so for “the economy is in a good shape,” as “in a good shape” is not precisely defined
Summary
Social choice theory defines “preference aggregation” as forming collective preferences over a given set of alternatives. The “Doctrinal Paradox” illustrates that proposition-wise majority rule leads to inconsistent collective decisions. This paradox has made the literature on “judgment aggregation” grow appreciably. Most of the discussions on this paradox have been in the domain of social choice theory, and a number of “(im)possibility theorems,” similar to those of Arrow [8] and Sen [9] have been proved These theorems show that there cannot exist any judgment aggregation procedure that simultaneously satisfies certain minimal consistency requirements (see Dietrich [10]). List and Pettit [6] have shown that the majority rule is but one member of a class of aggregation procedures that fails to ensure consistency in the set of collective judgments.
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