Một tính năng quan trọng của chương trình nghị sự trong bản gốc học thuyết nghịch lý là có một kết luận (ví dụ như trách nhiệm của bị đơn) có giá trị sự thật là duy nhất được xác định bởi các giá trị sự thật của một số cơ sở (ví dụ như hành động và nghĩa vụ). | 470 CHRISTIAN LIST AND CLEMENS PUPPE equivalently non-affineness and by applying the only if part of Theorem 7 showed that all regular and independent aggregation rules are dictatorial. The latter result is Arrow s theorem for strict Truth-Functional Agendas An important feature of the agenda in the original doctrinal paradox is that there is a conclusion . liability of the defendant whose truth-value is uniquely determined by the truth-values of several premises . action and obligation . An agenda is called truth-functional if it can be partitioned into a sub-agenda of premises and a sub-agenda of conclusions such that each conclusion is truth-functionally determined by the premises. Nehring and Puppe 2005a and Dokow and Holzman 2005 characterized classes of regular aggregation rules satisfying certain conditions on truth-functional agendas. The bottom line is that all regular independent and monotonic rules on such agendas are An oligarchic rule with default J0 c X specifies a nonempty set M c N the oligarchs such that for all p G X and all profiles J 1 . Jn in the universal domain p G Ji for all i G M or p G J0 and p G Ji for some i G M Clearly dictatorships are special cases with M singleton . Nehring and Puppe 2005a identified the truth-functional agendas admitting nondictatorial oligarchic rules ensuring collective rationality. For instance in the global warming example above with agenda X a a a b a b b b any oligarchic rule with default J0 a a b b is collectively rational. Agendas with Subjunctive Implications Dietrich 2006b argued that in many contexts the material interpretation of the implication operator is not natural. To illustrate consider again the global warming example above. Under a material interpretation of implication the set of propositions a a b b is inconsistent since negating the antecedent a makes the material implication a b true by definition. In everyday language however negating a .
