Judgments aggregation by a sequential majority procedure

We consider a standard model of judgment aggregation as presented, for example, in Dietrich (2015). For this model we introduce a sequential majority procedure (SMP) which uses the majority rule as much as possible. The ordering of the issues is assumed to be exogenous. The definition of SMP is given in Section 2. In Section 4 we construct an intuitive relevance relation for our model, closely related to conditional entailment, for our model. While in Dietrich (2015), the relevance relation is given exogenously as part of the model, we insist that the relevance relation be derived from the agenda. We prove that SMP has the property of independence of irrelevant issues (III) with respect to (the transitive closure of) our relevance relation. As III is weaker than the property of proposition-wise independence (PI) we do not run into impossibility results as does List (2004) who incorporates PI in some parts of his analysis. We proceed to characterize SMP by anonymity, restricted monotonicity, limited neutrality, restricted agenda property, and independence of past deliberations (see Section 3 for the precise details). SMP inherits the first three axioms from the Majority Rule. The axiom of restricted agenda property guarantees sequentiality. The most important axiom, independence of past deliberations (IPD), says that the choice at time (t+1) depends only on the choices in dates 1,…,t and the judgments at (t+1) (and not on the individual judgments in dates 1,…,t). Also, we use this occasion to point out that Roberts (1991) characterization of choice by plurality voting may be adapted to our model.