 Another difference resides in the fact that judgment aggregation assumes that all members are rational, and so they all submit consistent judgment sets. In belief merging, this is not required. Agents can submit belief bases that are inconsistent with the IC (Grégoire 2004). If an individual submits a judgment that violates an integrity constraint, that judgment set will not figure among the candidates to represent the group position. However, his input will not be disregarded and will be taken into account in the merging process. The possibility to abstain from expressing an opinion on a certain item is also easily taken into account in a belief merging setting. If individuals need to have their say on p, q and r and one agent believes q and r to be true but does not have a clear opinion on p, this will be represented as \(\mymod(K_1)= \{(1, 1, 1),\) \((0, 1, 1)\}\) and the distances calculated accordingly. The completeness requirement on judgment sets has also been weakened in the judgment aggregation framework. List and Pettit (2002) first discussed the weakening of completeness in the context of supermajority and unanimity rules. Later, it was shown (Gärdenfors 2006; Dokow and Holzman 2010) that, when judgment sets are not assumed to be complete, any independent and unanimous aggregation function turns out to be weakly oligarchic, that is, a subset of the individuals will decide the collective outcome. Intuitively, this is a less negative result than dictatorship, though it reduces to dictatorship in the case in which only one individual belongs to that subset. Dietrich and List (2008a) independently obtained equivalent results on oligarchic rules to those in (Dokow and Holzman 2010).