Complexity of Sequential Rules in Judgment Aggregation

The task in judgment aggregation is to find a collective judgment set based on the views of individual judges about a given set of propositional formulas. One way of guaranteeing consistent outcomes is the use of sequential rules. In each round, the decision on a single formula is made either because the outcome is entailed by the already obtained judgment set, or, if this is not the case, by some underlying rule, e.g. the majority rule. Such rules are especially useful for cases, where the agenda is not fixed in advance, and formulas are added one by one. This paper investigates the computational complexity of winner determination under a family of sequential rules, and the manipulative influence of the processing order on the final outcome.