Lifting integrity constraints in binary aggregation

We consider problems in which several individuals each need to make a yes/no choice regarding a number of issues and these choices then need to be aggregated into a collective choice. Depending on the application at hand, different combinations of yes/no may be considered rational. We describe rationality assumptions as integrity constraints using a simple propositional language and we explore the question of whether or not a given aggregation procedure will lift a given integrity constraint from the individual to the collective level, i.e., whether the collective choice will be rational whenever all individual choices are.